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diff --git a/test/geometry3k/test.jsonl b/test/geometry3k/test.jsonl
index a6a827e1c89a329ab1f4490383904fd02788db0d..14844d8281173c14986c4a026983cb2e850ee807 100644
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-{"prob_id": "prob_1", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3160.png", "question": "Line m is the perpendicular bisector of XZ, WZ = 14.9. Find WX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.900", "choices": [7.45, 14.9, 22.4, 25.3]}
-{"prob_id": "prob_17", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3834.png", "question": "If c = 5, find b. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.330", "choices": [1.7320508075688772, 2.598076211353316, 3.4641016151377544, 4.330127018922193]}
-{"prob_id": "prob_21", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1683.png", "question": "Find m \\angle 6. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [25.0, 28.0, 35.0, 55.0]}
-{"prob_id": "prob_27", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_423.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.000", "choices": [24.0, 33.941125496954285, 41.569219381653056, 48.0]}
-{"prob_id": "prob_31", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2339.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [35.0, 70.0, 75.0, 82.0]}
-{"prob_id": "prob_40", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1740.png", "question": "Quadrilateral DEFG is a rectangle. If m \\angle EFD = 2x-3 and m \\angle DFG = x+12, find m \\angle EFD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "51.000", "choices": [51.0, 55.0, 67.0, 102.0]}
-{"prob_id": "prob_51", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1340.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "113.000", "choices": [90.0, 113.0, 123.0, 157.0]}
-{"prob_id": "prob_74", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3559.png", "question": "\\triangle ABC \\sim \\triangle DEF. BG is a median of \\triangle ABC, and EH is a median of \\triangle DEF. Find EH if BC = 30, BG = 15, and EF = 15. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.500", "choices": [7.5, 15.0, 22.5, 30.0]}
-{"prob_id": "prob_87", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_883.png", "question": "If AB \\parallel DC, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [32.5, 65.0, 105.0, 115.0]}
-{"prob_id": "prob_89", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3755.png", "question": "If RL = 5, RT = 9, and WS = 6, find RW. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.500", "choices": [5.4, 6.0, 6.6, 7.5]}
-{"prob_id": "prob_90", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1226.png", "question": "Find XW. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [6.0, 12.0, 18.0, 24.0]}
-{"prob_id": "prob_94", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_121.png", "question": "If FGHJ is a kite, find m \\angle GFJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [72.0, 80.0, 128.0, 190.0]}
-{"prob_id": "prob_116", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3692.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.500", "choices": [10.5, 12.0, 12.5, 14.0]}
-{"prob_id": "prob_138", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3235.png", "question": "If ST = 8, TR = 4, and PT = 6, find QR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [6.0, 8.0, 9.0, 10.0]}
-{"prob_id": "prob_145", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2934.png", "question": "Find AE if AB = 12, AC = 16, and ED = 5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [12.0, 15.0, 16.0, 20.0]}
-{"prob_id": "prob_156", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_401.png", "question": "In \\odot R, find TV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.439", "choices": [9.22, 11.0, 12.0, 18.44]}
-{"prob_id": "prob_171", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3524.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.000", "choices": [1.0, 3.0, 5.0, 6.0]}
-{"prob_id": "prob_178", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_318.png", "question": "Find the area of the rectangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "129.904", "choices": [75.0, 112.5, 129.9, 225.0]}
-{"prob_id": "prob_182", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_947.png", "question": "Find the scale from B to B'. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.333", "choices": [0.75, 0.8333333333333334, 1.2, 1.3333333333333333]}
-{"prob_id": "prob_198", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1783.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.600", "choices": [9.0, 9.6, 12.0, 14.4]}
-{"prob_id": "prob_210", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_966.png", "question": "Find x so that BE and AD are perpendicular. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [5.0, 10.0, 20.0, 30.0]}
-{"prob_id": "prob_234", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_293.png", "question": "Quadrilateral EFGH is a rectangle. If EF = 4x-6 and HG = x+3, find EF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 12.0, 18.0, 20.0]}
-{"prob_id": "prob_260", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2667.png", "question": "Find the area of the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "264.000", "choices": [132.0, 264.0, 265.0, 528.0]}
-{"prob_id": "prob_269", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1314.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "63.000", "choices": [31.5, 63.0, 126.0, 252.0]}
-{"prob_id": "prob_292", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_249.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "57.995", "choices": [21.0, 34.0, 58.0, 67.0]}
-{"prob_id": "prob_293", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2312.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "76.000", "choices": [66.0, 68.0, 74.0, 76.0]}
-{"prob_id": "prob_296", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3907.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.798", "choices": [5.656854249492381, 6.928203230275509, 8.0, 9.797958971132712]}
-{"prob_id": "prob_307", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2189.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.416", "choices": [6.0, 8.485281374238571, 10.392304845413264, 13.416407864998739]}
-{"prob_id": "prob_323", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2067.png", "question": "In \\odot P, m \\angle MPL = 65 and NP \\perp PL. Find m \\widehat NM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [25.0, 45.0, 65.0, 90.0]}
-{"prob_id": "prob_377", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_8.png", "question": "Find the area of the trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "132.000", "choices": [72.0, 132.0, 144.0, 192.0]}
-{"prob_id": "prob_392", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_931.png", "question": "In \\odot P, the radius is 2 inches, find the length of \\widehat RS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.538", "choices": [2.27, 3.91, 4.54, 7.82]}
-{"prob_id": "prob_394", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1209.png", "question": "Find GH in the kite. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.209", "choices": [12.0, 15.0, 19.05255888325765, 19.209372712298546]}
-{"prob_id": "prob_397", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3975.png", "question": "Express the ratio of \\cos A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.600", "choices": [0.6, 0.75, 0.8, 1.33]}
-{"prob_id": "prob_401", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_924.png", "question": "Find m \\angle CAD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.000", "choices": [22.0, 44.0, 66.0, 92.0]}
-{"prob_id": "prob_414", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3714.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 3.0, 5.0, 6.0]}
-{"prob_id": "prob_490", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3757.png", "question": "Find the scale factor from Q to Q'. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 3.0, 4.0, 5.0]}
-{"prob_id": "prob_494", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2270.png", "question": "Find the variable of x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 7.0, 8.0, 9.0]}
-{"prob_id": "prob_506", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2431.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.000", "choices": [16.0, 17.0, 18.0, 19.0]}
-{"prob_id": "prob_512", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1546.png", "question": "Find the area of the trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "678.500", "choices": [506.0, 667.0, 678.5, 851.0]}
-{"prob_id": "prob_517", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_801.png", "question": "Find the area of the shaded sector. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.815", "choices": [0.9, 1.8, 10.8, 12.6]}
-{"prob_id": "prob_518", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1604.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.660", "choices": [7.0710678118654755, 8.660254037844386, 21.213203435596427, 25.980762113533157]}
-{"prob_id": "prob_522", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3209.png", "question": "Find PQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [3.0, 4.0, 6.0, 9.0]}
-{"prob_id": "prob_540", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1765.png", "question": "In \\odot M, FL = 24, HJ = 48, and m \\widehat HP = 65. Find FG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.000", "choices": [24.0, 32.0, 48.0, 65.0]}
-{"prob_id": "prob_619", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_534.png", "question": "Find GI if GH = 9, GK = 6, and KJ = 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [6.0, 9.0, 12.0, 15.0]}
-{"prob_id": "prob_662", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2737.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "45.000", "choices": [30.0, 45.0, 60.0, 90.0]}
-{"prob_id": "prob_697", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_664.png", "question": "JKLM is a rectangle. MLPR is a rhombus. m \\angle JMK = m \\angle RMP, m \\angle JMK = 55, and m \\angle MRP = 70. Find m \\angle KML. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [35.0, 70.0, 110.0, 140.0]}
-{"prob_id": "prob_700", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_731.png", "question": "m \\angle 4 = 101. Find the measure of \\angle 6. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "101.000", "choices": [69.0, 79.0, 89.0, 101.0]}
-{"prob_id": "prob_718", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2717.png", "question": "Find the area of the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "168.000", "choices": [38.0, 84.0, 168.0, 336.0]}
-{"prob_id": "prob_737", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1995.png", "question": "Find x if \\triangle JLM \\sim \\triangle QST. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.500", "choices": [1.5, 2.0, 3.0, 4.0]}
-{"prob_id": "prob_743", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2503.png", "question": "Find the area of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.511", "choices": [3.76, 7.51, 13.84, 15.02]}
-{"prob_id": "prob_749", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2983.png", "question": "Find x. Assume that any segment that appears to be tangent is tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [25.0, 27.5, 50.0, 105.0]}
-{"prob_id": "prob_772", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3675.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.171", "choices": [4.61, 5.17, 6.52, 8.46]}
-{"prob_id": "prob_777", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1402.png", "question": "Quadrilateral WXZY is a rectangle. Find the measure of \\angle 2 if m \\angle 1 = 30. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_799", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2733.png", "question": "Find TQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [6.0, 7.0, 12.0, 18.0]}
-{"prob_id": "prob_823", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3956.png", "question": "Each pair of polygons is similar. Find GF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.500", "choices": [7.5, 11.25, 20.7, 40.7]}
-{"prob_id": "prob_832", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1757.png", "question": "The square is circumscribed to the circle. Find the exact circumference of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.982", "choices": [21.991148575128552, 43.982297150257104, 65.97344572538566, 87.96459430051421]}
-{"prob_id": "prob_837", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_285.png", "question": "Find QP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 3.0, 5.0, 6.0]}
-{"prob_id": "prob_857", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2482.png", "question": "Find the length of \\widehat JK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.047", "choices": [0.52, 0.79, 1.05, 1.57]}
-{"prob_id": "prob_859", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_91.png", "question": "m \\angle 9 = 2x-4, m \\angle 10 = 2x+4. Find the measure of \\angle 10. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "94.000", "choices": [86.0, 94.0, 98.0, 104.0]}
-{"prob_id": "prob_869", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1220.png", "question": "The diagonals of rhombus FGHJ intersect at K. If GH = x+9 and JH = 5x-2, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.750", "choices": [2.75, 3.0, 5.5, 9.0]}
-{"prob_id": "prob_918", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3238.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [6.0, 9.0, 12.0, 15.0]}
-{"prob_id": "prob_932", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_171.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [3.0, 4.0, 5.0, 6.0]}
-{"prob_id": "prob_937", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1355.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [25.0, 50.0, 60.0, 100.0]}
-{"prob_id": "prob_939", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1301.png", "question": "Find m \\angle RST. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [55.0, 70.0, 75.0, 80.0]}
-{"prob_id": "prob_949", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1544.png", "question": "Find XZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [5.0, 17.0, 18.0, 34.0]}
-{"prob_id": "prob_955", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_668.png", "question": "Find y so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "31.000", "choices": [31.0, 51.0, 93.0, 129.0]}
-{"prob_id": "prob_960", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3830.png", "question": "Use parallelogram JKLM to find m \\angle JKL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [60.0, 70.0, 80.0, 90.0]}
-{"prob_id": "prob_984", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1412.png", "question": "In \\triangle PQR, ST \\parallel RQ. If PS = 12.5, SR = 5, and PT = 15, find TQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [5.0, 6.0, 6.5, 12.5]}
-{"prob_id": "prob_995", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1008.png", "question": "Cut four congruent triangles off the corners of a rectangle to make an octagon. What is the area of the octagon? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "528.000", "choices": [456.0, 528.0, 552.0, 564.0]}
-{"prob_id": "prob_1017", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3381.png", "question": "Find KL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [4.0, 5.0, 12.0, 15.0]}
-{"prob_id": "prob_1020", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_423.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "41.569", "choices": [24.0, 33.941125496954285, 41.569219381653056, 48.0]}
-{"prob_id": "prob_1021", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1240.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 4.0, 5.0, 9.0]}
-{"prob_id": "prob_1023", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_5.png", "question": "\\triangle LMN \\cong \\triangle QRS. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [10.0, 20.0, 40.0, 50.0]}
-{"prob_id": "prob_1035", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_191.png", "question": "In \\odot H, the diameter is 18, LM = 12, and m \\widehat LM = 84. Find HP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.708", "choices": [2.29, 3.35, 5.65, 6.71]}
-{"prob_id": "prob_1062", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3143.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [20.0, 21.0, 24.0, 25.0]}
-{"prob_id": "prob_1065", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_295.png", "question": "Find m \\angle CAM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [14.0, 28.0, 36.0, 90.0]}
-{"prob_id": "prob_1068", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1752.png", "question": "Find GD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [10.0, 12.0, 14.0, 20.0]}
-{"prob_id": "prob_1103", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3892.png", "question": "For trapezoid QRTU, V and S are midpoints of the legs. If QR = 4 and UT = 16, find VS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [5.0, 9.0, 10.0, 12.0]}
-{"prob_id": "prob_1107", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1796.png", "question": "Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 22.0, 25.0, 28.0]}
-{"prob_id": "prob_1143", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1734.png", "question": "Find the area of the shaded region. Assume that the polygon is regular unless otherwise stated. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "216.584", "choices": [216.6, 282.9, 464.8, 819.6]}
-{"prob_id": "prob_1175", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3285.png", "question": "m \\angle 1 = 123. Find the measure of \\angle 14. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "57.000", "choices": [47.0, 57.0, 67.0, 123.0]}
-{"prob_id": "prob_1187", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3830.png", "question": "Use parallelogram JKLM to find m \\angle KJL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 40.0, 50.0, 60.0]}
-{"prob_id": "prob_1205", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2944.png", "question": "Find the area of the trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "95.000", "choices": [80.0, 90.0, 95.0, 110.0]}
-{"prob_id": "prob_1227", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3256.png", "question": "Find JL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [7.0, 11.0, 12.0, 14.0]}
-{"prob_id": "prob_1232", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2395.png", "question": "If m \\widehat FE = 118, m \\widehat AB = 108, m \\angle EGB = 52, and m \\angle EFB = 30, find m \\widehat CF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.000", "choices": [30.0, 44.0, 108.0, 118.0]}
-{"prob_id": "prob_1267", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2070.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "21.617", "choices": [5.0, 8.1, 10.3, 21.6]}
-{"prob_id": "prob_1268", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1819.png", "question": "The diameters of \\odot A, \\odot B, and \\odot C are 10, 30 and 10 units, respectively. Find YW if AZ = CW and CW = 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 3.0, 10.0, 30.0]}
-{"prob_id": "prob_1278", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_926.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "58.905", "choices": [29.5, 58.9, 147.3, 589.0]}
-{"prob_id": "prob_1297", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2537.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "57.158", "choices": [33.0, 46.66904755831214, 57.157676649772945, 73.79024325749306]}
-{"prob_id": "prob_1298", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1288.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "552.000", "choices": [552.0, 575.0, 598.0, 720.0]}
-{"prob_id": "prob_1313", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2397.png", "question": "Use parallelogram JKLM to find m \\angle KLM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "71.000", "choices": [71.0, 79.0, 81.0, 89.0]}
-{"prob_id": "prob_1334", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3537.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.111", "choices": [6.5, 15.6, 22.1, 37.7]}
-{"prob_id": "prob_1338", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3111.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [1.7320508075688772, 3.0, 5.196152422706632, 6.0]}
-{"prob_id": "prob_1343", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3190.png", "question": "AB \\perp DC and GH \\perp FE. If \\triangle ACD \\sim \\triangle GEF, find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.200", "choices": [2.2, 3.6, 4.4, 6.3]}
-{"prob_id": "prob_1350", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3255.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.785", "choices": [4.2, 4.8, 7.9, 16.9]}
-{"prob_id": "prob_1364", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1819.png", "question": "The diameters of \\odot A, \\odot B, and \\odot C are 10, 30 and 10 units, respectively. Find ZX if AZ = CW and CW = 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 4.0, 5.0, 6.0]}
-{"prob_id": "prob_1401", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3122.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.142", "choices": [1.4, 7.1, 14.1, 15.6]}
-{"prob_id": "prob_1402", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1161.png", "question": "If pentagons ABCDE and PQRST are similar, find SR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.364", "choices": [1.8333333333333335, 4.363636363636363, 3.0, 14.666666666666666]}
-{"prob_id": "prob_1414", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2682.png", "question": "parallelogram MNPQ with m \\angle M = 10x and m \\angle N = 20x, find m \\angle M. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 45.0, 60.0, 120.0]}
-{"prob_id": "prob_1418", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3475.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "56.889", "choices": [35.2, 43.2, 53.5, 56.9]}
-{"prob_id": "prob_1420", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2531.png", "question": "If PR \\parallel KL, KN = 9, LN = 16, and PM = 2 KP, find KM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [5.0, 9.0, 12.0, 15.0]}
-{"prob_id": "prob_1435", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1085.png", "question": "Find m \\angle K. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "100.000", "choices": [6.0, 60.0, 100.0, 180.0]}
-{"prob_id": "prob_1439", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1396.png", "question": "For the pair of similar figures, the area of the blue figure is 8 in^{2} and the green figure is 32 in^{2}, find the scale factor from the blue to the green figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.500", "choices": [0.25, 0.5, 2.0, 4.0]}
-{"prob_id": "prob_1451", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3163.png", "question": "m \\angle 1 = 50 and m \\angle 3 = 60. Find the measure of \\angle 8. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [100.0, 110.0, 120.0, 130.0]}
-{"prob_id": "prob_1456", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3760.png", "question": "Find the measure of \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "68.000", "choices": [52.0, 56.0, 60.0, 68.0]}
-{"prob_id": "prob_1467", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3367.png", "question": "m \\angle 3 = 110 and m \\angle 12 = 55. Find the measure of \\angle 13. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [55.0, 65.0, 70.0, 110.0]}
-{"prob_id": "prob_1468", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3876.png", "question": "Find m \\angle 5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [50.0, 110.0, 130.0, 150.0]}
-{"prob_id": "prob_1494", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_714.png", "question": "Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.100", "choices": [3.5, 4.1, 4.5, 5.1]}
-{"prob_id": "prob_1506", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2370.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "71.000", "choices": [11.0, 31.0, 71.0, 133.0]}
-{"prob_id": "prob_1534", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_729.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.633", "choices": [5.0, 6.6332495807108, 10.0, 13.2664991614216]}
-{"prob_id": "prob_1539", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2633.png", "question": "Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.250", "choices": [3.75, 5.0, 6.25, 8.75]}
-{"prob_id": "prob_1569", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2447.png", "question": "What is \\cos B? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.385", "choices": [0.38, 0.42, 0.92, 2.4]}
-{"prob_id": "prob_1579", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_333.png", "question": "If PR \\parallel KL, KN = 9, LN = 16, PM = 2 KP, find MN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [7.0, 12.0, 15.0, 16.0]}
-{"prob_id": "prob_1588", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_642.png", "question": "Find ST. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.000", "choices": [7.0, 12.0, 19.0, 24.0]}
-{"prob_id": "prob_1610", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_724.png", "question": "Find x so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 8.0, 11.0, 19.0]}
-{"prob_id": "prob_1638", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3617.png", "question": "Find m \\angle BGE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [60.0, 120.0, 240.0, 360.0]}
-{"prob_id": "prob_1639", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3527.png", "question": "Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [30.0, 45.0, 60.0, 90.0]}
-{"prob_id": "prob_1648", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3029.png", "question": "Find the length of \\widehat AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.774", "choices": [7.63, 9.77, 11.13, 14.83]}
-{"prob_id": "prob_1664", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_967.png", "question": "Find the measure of \\angle 2. Assume that segments that appear tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "157.500", "choices": [85.0, 157.5, 230.0, 315.0]}
-{"prob_id": "prob_1686", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1966.png", "question": "Find \\sin S. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.600", "choices": [0.2, 0.4, 0.6, 0.8]}
-{"prob_id": "prob_1690", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_529.png", "question": "Find m \\angle 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "71.500", "choices": [51.0, 67.5, 71.5, 92.0]}
-{"prob_id": "prob_1705", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1905.png", "question": "In \\odot T, ZV = 1, and TW = 13. Find XY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [5.0, 10.0, 12.0, 13.0]}
-{"prob_id": "prob_1734", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1954.png", "question": "The segment is tangent to the circle. Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 3.0, 6.0, 9.0]}
-{"prob_id": "prob_1740", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3578.png", "question": "In \\odot F, m \\angle DFA = 50 and CF \\perp FB. Find m \\widehat ACE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "230.000", "choices": [75.0, 115.0, 150.0, 230.0]}
-{"prob_id": "prob_1758", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_763.png", "question": "Use parallelogram ABCD to find m \\angle DAB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "101.000", "choices": [20.0, 59.0, 72.0, 101.0]}
-{"prob_id": "prob_1764", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1416.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "163.000", "choices": [65.0, 132.0, 163.0, 180.0]}
-{"prob_id": "prob_1765", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1452.png", "question": "m \\angle BAC = 38, BC = DC = 5, find m \\angle DAC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [5.0, 10.0, 38.0, 40.0]}
-{"prob_id": "prob_1772", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3509.png", "question": "Find m \\angle W. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "108.000", "choices": [18.0, 27.0, 54.0, 108.0]}
-{"prob_id": "prob_1779", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2333.png", "question": "Find the value of the variable y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [10.0, 20.0, 30.0, 70.0]}
-{"prob_id": "prob_1780", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2631.png", "question": "The degree measure of \\widehat AC and \\widehat ADC are x and y respectively. If m \\angle ABC = 70, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "110.000", "choices": [90.0, 100.0, 110.0, 120.0]}
-{"prob_id": "prob_1812", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2700.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "76.000", "choices": [70.0, 72.0, 76.0, 78.0]}
-{"prob_id": "prob_1813", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_229.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [7.0, 9.899494936611665, 12.12435565298214, 14.0]}
-{"prob_id": "prob_1868", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2757.png", "question": "In rhombus ABCD, AB = 2x+3 and BC = 5x. Find AD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [1.0, 2.0, 4.0, 5.0]}
-{"prob_id": "prob_1898", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2684.png", "question": "Find KL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [7.0, 8.0, 12.0, 15.0]}
-{"prob_id": "prob_1906", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_978.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "178.191", "choices": [89.1, 178.2, 252.0, 356.4]}
-{"prob_id": "prob_1914", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3821.png", "question": "Find the measure of \\angle AFB on \\odot F with diameter AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "108.000", "choices": [72.0, 108.0, 120.0, 144.0]}
-{"prob_id": "prob_1934", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3991.png", "question": "Quadrilateral ABCD is a rectangle. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [5.0, 12.0, 24.0, 25.0]}
-{"prob_id": "prob_1959", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2523.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.536", "choices": [3.5355339059327378, 5.0, 7.0710678118654755, 10.0]}
-{"prob_id": "prob_1961", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3250.png", "question": "Find m \\angle ABC if m \\angle CDA = 61. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "140.000", "choices": [55.0, 69.0, 85.0, 140.0]}
-{"prob_id": "prob_1972", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1260.png", "question": "AB is a diameter, AC = 8 inches, and BC = 15 inches. Find the radius of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.500", "choices": [7.5, 8.0, 8.5, 17.0]}
-{"prob_id": "prob_2000", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3322.png", "question": "Quadrilateral ABDC is a rectangle. m \\angle 2 = 40. Find m \\angle 8. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "100.000", "choices": [40.0, 50.0, 80.0, 100.0]}
-{"prob_id": "prob_2010", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2456.png", "question": "Triangle LMN is equilateral, and MP bisects LN. Find the measure of MN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [9.0, 10.0, 11.0, 12.0]}
-{"prob_id": "prob_2027", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2732.png", "question": "Find QS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [5.0, 15.0, 20.0, 25.0]}
-{"prob_id": "prob_2030", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1745.png", "question": "In \\odot O, EC and AB are diameters, and m \\angle BOD = m \\angle DOE = m \\angle EOF = m \\angle FOA. Find m \\widehat AD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "135.000", "choices": [45.0, 135.0, 180.0, 360.0]}
-{"prob_id": "prob_2032", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1740.png", "question": "Quadrilateral DEFG is a rectangle. If m \\angle EDF = 5x-3 and m \\angle DFG = 3x+7, find m \\angle EDF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [22.0, 45.0, 68.0, 90.0]}
-{"prob_id": "prob_2039", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2304.png", "question": "Each pair of polygons is similar. Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 12.0, 15.0, 20.0]}
-{"prob_id": "prob_2045", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3009.png", "question": "Find RS if \\triangle QRS is an equilateral triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [0.5, 1.0, 1.5, 2.0]}
-{"prob_id": "prob_2061", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3708.png", "question": "Find the measure of the altitude drawn to the hypotenuse. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.928", "choices": [3.4641016151377544, 4.898979485566356, 6.928203230275509, 9.797958971132712]}
-{"prob_id": "prob_2065", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2216.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "93.000", "choices": [35.0, 52.0, 77.0, 93.0]}
-{"prob_id": "prob_2070", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_527.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.748", "choices": [11.0, 15.556349186104047, 17.74823934929885, 25.553864678361276]}
-{"prob_id": "prob_2084", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2751.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [2.0, 5.0, 6.0, 9.0]}
-{"prob_id": "prob_2116", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_982.png", "question": "EB \\parallel DC. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.500", "choices": [5.0, 7.5, 9.5, 10.0]}
-{"prob_id": "prob_2128", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_244.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.700", "choices": [35.7, 49.0, 71.4, 104.0]}
-{"prob_id": "prob_2141", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_566.png", "question": "Use parallelogram MNPR to find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [8.0, 20.0, 24.0, 32.0]}
-{"prob_id": "prob_2164", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3891.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.433", "choices": [21.1, 22.4, 23.4, 42.2]}
-{"prob_id": "prob_2174", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1335.png", "question": "Find y so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [11.0, 14.0, 77.0, 98.0]}
-{"prob_id": "prob_2180", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3204.png", "question": "Find the length of \\widehat JK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.744", "choices": [6.87, 13.74, 20.62, 27.49]}
-{"prob_id": "prob_2191", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2775.png", "question": "If m \\angle 5 = 7x-5 and m \\angle 4 = 2x+23, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [5.6, 18.0, 20.0, 22.0]}
-{"prob_id": "prob_2241", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2932.png", "question": "Find m \\angle 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "33.000", "choices": [33.0, 43.0, 57.0, 123.0]}
-{"prob_id": "prob_2273", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_499.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [20.0, 30.0, 40.0, 50.0]}
-{"prob_id": "prob_2287", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3110.png", "question": "Find AB if \\triangle ABC is an isosceles triangle with AB = BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [3.0, 4.0, 7.0, 11.0]}
-{"prob_id": "prob_2289", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2360.png", "question": "If DB = 24, AE = 3, and EC = 18, find AD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [3.0, 4.0, 6.0, 8.0]}
-{"prob_id": "prob_2295", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1851.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 4.5, 5.0, 6.0]}
-{"prob_id": "prob_2301", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1143.png", "question": "In \\odot B, CE = 13.5. Find BD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.294", "choices": [3.71, 4.29, 4.53, 6.75]}
-{"prob_id": "prob_2342", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3510.png", "question": "Find DE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [3.0, 4.0, 6.0, 9.0]}
-{"prob_id": "prob_2358", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1477.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.730", "choices": [10.7, 19.6, 30.4, 50.0]}
-{"prob_id": "prob_2371", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2048.png", "question": "Find z in the given parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.500", "choices": [4.0, 4.5, 5.0, 9.5]}
-{"prob_id": "prob_2385", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_810.png", "question": "For the pair of similar figures, the area of the blue figure is 36 yd^{2}, find the area of the green figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [9.0, 18.0, 72.0, 144.0]}
-{"prob_id": "prob_2394", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3643.png", "question": "Circle J has a radius of 10 units, \\odot K has a radius of 8 units, and BC = 5.4 units. Find JK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.600", "choices": [12.6, 14.6, 20.6, 30.6]}
-{"prob_id": "prob_2417", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1725.png", "question": "If \\triangle LMN \\sim \\triangle QRS, QR = 35, RS = 37, SQ = 12, and NL = 5, find the perimeter of \\triangle LMN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [35.0, 42.0, 63.0, 84.0]}
-{"prob_id": "prob_2424", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1497.png", "question": "What is the area of \\parallelogram ABCD? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.000", "choices": [24.0, 30.0, 48.0, 60.0]}
-{"prob_id": "prob_2425", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1809.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 4.0, 6.0, 7.0]}
-{"prob_id": "prob_2464", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1745.png", "question": "In \\odot O, EC and AB are diameters, and m \\angle BOD = m \\angle DOE = m \\angle EOF = m \\angle FOA. Find m \\widehat AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 90.0, 180.0, 360.0]}
-{"prob_id": "prob_2472", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3863.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [5.0, 7.0, 13.0, 14.0]}
-{"prob_id": "prob_2484", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_924.png", "question": "Find m \\angle ABC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [22.0, 24.0, 42.0, 44.0]}
-{"prob_id": "prob_2527", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2240.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "123.000", "choices": [97.0, 99.0, 110.0, 123.0]}
-{"prob_id": "prob_2547", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_293.png", "question": "Quadrilateral EFGH is a rectangle. If FK = 32 feet, find EG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "64.000", "choices": [13.0, 30.0, 57.0, 64.0]}
-{"prob_id": "prob_2550", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3051.png", "question": "Find m \\angle W. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "76.000", "choices": [38.0, 38.0, 76.0, 152.0]}
-{"prob_id": "prob_2588", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2171.png", "question": "\\odot P \\cong \\odot Q. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [7.0, 11.0, 22.0, 44.0]}
-{"prob_id": "prob_2601", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3107.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "180.000", "choices": [165.0, 180.0, 195.0, 210.0]}
-{"prob_id": "prob_2613", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_546.png", "question": "Find w in the given parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 4.0, 5.0, 13.0]}
-{"prob_id": "prob_2640", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1825.png", "question": "Find m \\angle D. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [58.0, 64.0, 80.0, 82.0]}
-{"prob_id": "prob_2647", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3965.png", "question": "Lines l, m, and n are perpendicular bisectors of \\triangle PQR and meet at T. If TQ = 2x, PT = 3y-1, and TR = 8, find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 4.0, 5.0, 6.0]}
-{"prob_id": "prob_2654", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_690.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.485", "choices": [1.4142135623730951, 4.242640687119286, 8.485281374238571, 12.727922061357857]}
-{"prob_id": "prob_2705", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2242.png", "question": "\\triangle EFG is equilateral, and EH bisects \\angle E. Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [15.0, 30.0, 45.0, 60.0]}
-{"prob_id": "prob_2711", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_475.png", "question": "Find the measure of \\angle 1. Assume that segments that appear tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "129.000", "choices": [51.0, 78.0, 102.0, 129.0]}
-{"prob_id": "prob_2730", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3367.png", "question": "m \\angle 3 = 110 and m \\angle 12 = 55. Find the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "110.000", "choices": [55.0, 110.0, 125.0, 135.0]}
-{"prob_id": "prob_2737", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3643.png", "question": "Circle J has a radius of 10 units, \\odot K has a radius of 8 units, and BC = 5.4 units. Find CK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.600", "choices": [2.4, 2.6, 2.8, 4.0]}
-{"prob_id": "prob_2767", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2364.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.777", "choices": [22.627416997969522, 27.712812921102035, 32.0, 35.77708763999664]}
-{"prob_id": "prob_2780", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1846.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.180", "choices": [5.0, 8.660254037844386, 10.0, 11.180339887498949]}
-{"prob_id": "prob_2794", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_258.png", "question": "Find PS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [7.0, 9.0, 14.0, 16.0]}
-{"prob_id": "prob_2813", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1689.png", "question": "Quadrilateral ABCD is a rhombus. If AB = 2x+3 and BC = x+7, find CD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [4.0, 11.0, 19.0, 20.0]}
-{"prob_id": "prob_2816", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_185.png", "question": "Use the Pythagorean Theorem to find the length of the hypotenuse. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.000", "choices": [5.0, 10.908712114635714, 12.0, 13.0]}
-{"prob_id": "prob_2822", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1765.png", "question": "In \\odot M, FL = 24, HJ = 48, and m \\widehat HP = 65. Find NJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [24.0, 32.0, 48.0, 65.0]}
-{"prob_id": "prob_2826", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3163.png", "question": "m \\angle 1 = 50 and m \\angle 3 = 60. Find the measure of \\angle 6. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [50.0, 60.0, 70.0, 80.0]}
-{"prob_id": "prob_2862", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2379.png", "question": "\\triangle LMN \\cong \\triangle QRS. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 5.0, 7.0, 18.0]}
-{"prob_id": "prob_2863", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2422.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.276", "choices": [3.4, 7.0, 8.1, 9.3]}
-{"prob_id": "prob_2871", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1663.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "91.924", "choices": [65.0, 91.9, 112.6, 130.0]}
-{"prob_id": "prob_2907", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2112.png", "question": "Find m \\widehat QTS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "248.000", "choices": [109.0, 212.0, 248.0, 254.0]}
-{"prob_id": "prob_2938", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_135.png", "question": "Find the area of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.383", "choices": [3.9, 11.7, 23.4, 46.8]}
-{"prob_id": "prob_3002", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_621.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.667", "choices": [1.6666666666666667, 2.3333333333333335, 4.0, 6.0]}
-{"prob_id": "prob_3010", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3225.png", "question": "Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [5.5, 7.0, 8.0, 10.0]}
-{"prob_id": "prob_3011", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2756.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "64.000", "choices": [60.0, 62.0, 64.0, 66.0]}
-{"prob_id": "prob_3025", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1626.png", "question": "If IJ / XJ = HJ / YJ, m \\angle WXJ = 130 and m \\angle WZG = 20, find m \\angle J. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [40.0, 55.0, 60.0, 70.0]}
-{"prob_id": "prob_3037", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2445.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.809", "choices": [18.8, 23.2, 25.9, 44.0]}
-{"prob_id": "prob_3070", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3840.png", "question": "In RSTV, RS = 6, VT = 3 and RX is twice the length of XV. Find XY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [3.0, 4.0, 6.0, 9.0]}
-{"prob_id": "prob_3093", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_104.png", "question": "Each pair of polygons is similar. Find AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.600", "choices": [7.0, 7.6, 12.0, 19.0]}
-{"prob_id": "prob_3104", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1989.png", "question": "Find the measure of \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "95.000", "choices": [85.0, 90.0, 95.0, 105.0]}
-{"prob_id": "prob_3124", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_712.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "27.440", "choices": [13.3, 20.99, 27.44, 49.5]}
-{"prob_id": "prob_3128", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3774.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.205", "choices": [7.2, 8.0, 12.0, 15.0]}
-{"prob_id": "prob_3136", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_791.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.333", "choices": [10.0, 10.666666666666666, 13.333333333333334, 16.666666666666668]}
-{"prob_id": "prob_3153", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3517.png", "question": "A square is inscribed in a circle of area 18\\pi square units. Find the length of a side of the square. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [3.0, 4.242640687119286, 6.0, 8.485281374238571]}
-{"prob_id": "prob_3158", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2488.png", "question": "Find the scale factor from W to W'. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.333", "choices": [0.3333333333333333, 0.6666666666666666, 0.75, 1.5]}
-{"prob_id": "prob_3170", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2381.png", "question": "What is the measure of \\angle B if m \\angle A = 10? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 35.0, 47.5, 90.0]}
-{"prob_id": "prob_3188", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_734.png", "question": "Find BC if AB = 6, AF = 8, BC = x, CD = y, DE = 2y-3, and FE = x+\\frac{10}{3}. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [9.0, 10.0, 13.3, 15.0]}
-{"prob_id": "prob_3203", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_483.png", "question": "Find x in the parallelogram. Area = 148 m^{2}. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.500", "choices": [17.5, 18.5, 19.5, 20.5]}
-{"prob_id": "prob_3243", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3572.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.646", "choices": [2.6457513110645907, 4.242640687119286, 5.196152422706632, 7.348469228349534]}
-{"prob_id": "prob_3252", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_326.png", "question": "A square is inscribed in a circle having a radius of 6 inches. Find the length of the side of the square. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.485", "choices": [2.1213203435596424, 4.242640687119286, 8.485281374238571, 16.970562748477143]}
-{"prob_id": "prob_3258", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3592.png", "question": "m \\angle 11 = 62 and m \\angle 14 = 38. Find the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [38.0, 42.0, 62.0, 80.0]}
-{"prob_id": "prob_3297", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1420.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1440.000", "choices": [972.0, 1080.0, 1440.0, 2412.0]}
-{"prob_id": "prob_3328", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1010.png", "question": "Find the measure of \\angle 7 if m \\angle 4 = m \\angle 5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "89.000", "choices": [63.0, 64.0, 69.0, 89.0]}
-{"prob_id": "prob_3365", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1054.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.492", "choices": [7.745966692414834, 8.246211251235321, 15.491933384829668, 16.492422502470642]}
-{"prob_id": "prob_3372", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1806.png", "question": "Find x for equilateral triangle SRT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [3.0, 6.0, 9.0, 12.0]}
-{"prob_id": "prob_3377", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1390.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "108.000", "choices": [39.0, 84.0, 108.0, 129.0]}
-{"prob_id": "prob_3390", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3155.png", "question": "\\angle 1 and \\angle 2 form a linear pair and m \\angle 2 = 67. Find the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "113.000", "choices": [67.0, 113.0, 123.0, 133.0]}
-{"prob_id": "prob_3396", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_153.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.440", "choices": [5.0, 6.0, 7.4, 10.0]}
-{"prob_id": "prob_3436", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2936.png", "question": "\\triangle RSV \\cong \\triangle TVS. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [11.0, 11.5, 12.0, 12.5]}
-{"prob_id": "prob_3468", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3311.png", "question": "\\triangle KLN and \\triangle LMN are isosceles and m \\angle JKN = 130. Find the measure of \\angle J. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "106.000", "choices": [105.0, 106.0, 108.0, 111.0]}
-{"prob_id": "prob_3479", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_613.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "315.000", "choices": [294.0, 315.0, 336.0, 357.0]}
-{"prob_id": "prob_3498", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3686.png", "question": "Use a calculator to find the measure of \\angle J. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.005", "choices": [33.0, 40.0, 50.0, 57.0]}
-{"prob_id": "prob_3506", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2526.png", "question": "AD is perpendicular to BC and AB is perpendicular to AC. What is BC? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [7.0710678118654755, 8.660254037844386, 20.0, 25.0]}
-{"prob_id": "prob_3545", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1919.png", "question": "If ABCD is a rhombus, and m \\angle ABC = 70, what is m \\angle 1? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [45.0, 55.0, 70.0, 125.0]}
-{"prob_id": "prob_3569", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3805.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_3581", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2397.png", "question": "Use parallelogram JKLM to find m \\angle JML. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "109.000", "choices": [50.0, 71.0, 109.0, 144.0]}
-{"prob_id": "prob_3583", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_466.png", "question": "AB = DF. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [1.0, 2.0, 3.0, 4.0]}
-{"prob_id": "prob_3628", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1860.png", "question": "Find x so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [2.0, 17.0, 34.0, 68.0]}
-{"prob_id": "prob_3638", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1839.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 9.0, 12.25, 24.0]}
-{"prob_id": "prob_3664", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1031.png", "question": "Express the ratio of \\cos P. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.471", "choices": [0.47, 0.53, 0.88, 1.88]}
-{"prob_id": "prob_3665", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3296.png", "question": "m \\angle WXY = m \\angle TXY. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [2.0, 4.0, 5.0, 10.0]}
-{"prob_id": "prob_3668", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2652.png", "question": "Use parallelogram PQRS to find QP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 5.0, 8.0, 15.0]}
-{"prob_id": "prob_3692", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3746.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [1.8, 5.0, 46.0, 90.0]}
-{"prob_id": "prob_3705", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2491.png", "question": "a = 14, b = 48, and c = 50, find \\cos A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.960", "choices": [0.14, 0.48, 0.5, 0.96]}
-{"prob_id": "prob_3738", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2831.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.588", "choices": [9.0, 15.588457268119894, 18.0, 31.17691453623979]}
-{"prob_id": "prob_3760", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1365.png", "question": "Find the measure of the altitude drawn to the hypotenuse. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.330", "choices": [14.0, 18.33030277982336, 24.0, 336.0]}
-{"prob_id": "prob_3821", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3821.png", "question": "Find the measure of \\angle CFD on \\odot F with diameter AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "123.000", "choices": [115.0, 119.0, 120.0, 123.0]}
-{"prob_id": "prob_3885", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1956.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [22.0, 44.0, 60.0, 120.0]}
-{"prob_id": "prob_3894", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2466.png", "question": "Find JQ if Q is the incenter of \\triangle JLN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.795", "choices": [16.5, 18.79, 20.32, 25.5]}
-{"prob_id": "prob_3917", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_293.png", "question": "Quadrilateral EFGH is a rectangle. If m \\angle HGE = 13, find m \\angle FGE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "77.000", "choices": [13.0, 46.0, 57.0, 77.0]}
-{"prob_id": "prob_3919", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1052.png", "question": "Find the area of the regular polygon figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "101.823", "choices": [12.7, 25.5, 101.8, 203.6]}
-{"prob_id": "prob_3935", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1519.png", "question": "Trapezoid GHJK has an area of 75 square meters. Find the height. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [2.5, 3.0, 5.0, 7.5]}
-{"prob_id": "prob_3949", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3612.png", "question": "Given the square. Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.971", "choices": [8.485281374238571, 16.970562748477143, 20.784609690826528, 24.0]}
-{"prob_id": "prob_3970", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3418.png", "question": "\\triangle RST \\cong \\triangle ABC. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [8.0, 10.0, 13.0, 21.0]}
-{"prob_id": "prob_3984", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_514.png", "question": "Find m \\widehat JLK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "232.000", "choices": [116.0, 184.0, 232.0, 298.0]}
-{"prob_id": "prob_3987", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2123.png", "question": "Find the measure of \\angle Z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "33.749", "choices": [29.1, 33.7, 56.3, 60.9]}
-{"prob_id": "prob_3992", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3740.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.191", "choices": [19.5, 30.2, 60.4, 120.8]}
-{"prob_id": "prob_4026", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_986.png", "question": "m \\angle 1 = 4p+15, m \\angle 3 = 3p-10 and m \\angle 4 = 6r+5. Find the value of p. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [15.0, 20.0, 25.0, 30.0]}
-{"prob_id": "prob_4030", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1156.png", "question": "Use parallelogram ABCD to find m \\angle AFD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "97.000", "choices": [3.0, 34.0, 49.0, 97.0]}
-{"prob_id": "prob_4032", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_342.png", "question": "\\triangle WXY \\cong \\triangle WXZ. Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [3.0, 4.0, 5.0, 7.0]}
-{"prob_id": "prob_4043", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2380.png", "question": "Let GH be the median of trapezoid RSBA. Find GH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "62.000", "choices": [27.0, 54.0, 62.0, 86.0]}
-{"prob_id": "prob_4044", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_9.png", "question": "In rhombus ABCD, m \\angle DAB = 2 m \\angle ADC and CB = 6. Find m \\angle ADB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_4046", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3682.png", "question": "m \\angle 2 = 2x, m \\angle 3 = x. Find m \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 45.0, 60.0, 90.0]}
-{"prob_id": "prob_4056", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2974.png", "question": "Find m \\angle ABC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "51.000", "choices": [42.0, 51.0, 56.0, 148.0]}
-{"prob_id": "prob_4067", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1743.png", "question": "Find the measure of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "33.000", "choices": [32.0, 33.0, 45.0, 55.0]}
-{"prob_id": "prob_4093", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2554.png", "question": "Express the ratio of \\cos X. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.280", "choices": [0.28, 0.29, 0.96, 3.43]}
-{"prob_id": "prob_4144", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1031.png", "question": "Express the ratio of \\sin P. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.882", "choices": [0.47, 0.53, 0.88, 1.88]}
-{"prob_id": "prob_4158", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2343.png", "question": "\\angle ABC is intersected by parallel lines l and m. What is the measure of \\angle ABC? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "71.000", "choices": [33.0, 38.0, 61.0, 71.0]}
-{"prob_id": "prob_4187", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2961.png", "question": "Find m \\angle A of quadrilateral ABCD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "135.000", "choices": [45.0, 90.0, 135.0, 180.0]}
-{"prob_id": "prob_4188", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3531.png", "question": "Find DE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [4.0, 6.0, 7.0, 10.0]}
-{"prob_id": "prob_4216", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1494.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.077", "choices": [4.358898943540674, 5.0, 13.076696830622023, 14.0]}
-{"prob_id": "prob_4227", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_661.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.500", "choices": [14.4, 18.0, 22.5, 24.0]}
-{"prob_id": "prob_4233", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1967.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.200", "choices": [9.2, 10.2, 11.2, 12.2]}
-{"prob_id": "prob_4238", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1408.png", "question": "Find m \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [28.0, 38.0, 52.0, 62.0]}
-{"prob_id": "prob_4250", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1562.png", "question": "Find x so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [1.0, 2.0, 3.0, 4.0]}
-{"prob_id": "prob_4251", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3150.png", "question": "ABCD \\sim AEFG. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [2.0, 3.0, 5.0, 6.0]}
-{"prob_id": "prob_4255", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1345.png", "question": "Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.000", "choices": [23.0, 24.0, 25.0, 27.0]}
-{"prob_id": "prob_4258", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2218.png", "question": "Find the area of the regular polygon figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "64.952", "choices": [10.8, 21.7, 65.0, 129.9]}
-{"prob_id": "prob_4267", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3005.png", "question": "Find the area of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "285.000", "choices": [256.5, 285.0, 389.5, 405.0]}
-{"prob_id": "prob_4285", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2980.png", "question": "MC = 7, RM = 4, and AT = 16. Find MS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.500", "choices": [2.0, 3.5, 4.0, 7.0]}
-{"prob_id": "prob_4310", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3135.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.667", "choices": [0.21428571428571427, 4.666666666666667, 12.0, 16.0]}
-{"prob_id": "prob_4325", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1197.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.583", "choices": [2.0, 5.6, 7.6, 8.0]}
-{"prob_id": "prob_4338", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3781.png", "question": "If XN = 6, XM = 2, and XY = 10, find NZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [12.0, 16.0, 24.0, 32.0]}
-{"prob_id": "prob_4343", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3251.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [10.0, 20.0, 30.0, 42.0]}
-{"prob_id": "prob_4348", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2757.png", "question": "In rhombus ABCD, AB = 2x+3 and BC = 5x. Find m \\angle AEB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 60.0, 90.0, 180.0]}
-{"prob_id": "prob_4357", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2456.png", "question": "Triangle LMN is equilateral, and MP bisects LN. Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [15.0, 16.0, 17.0, 18.0]}
-{"prob_id": "prob_4380", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1163.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.000", "choices": [1.0, 2.0, 3.0, 4.0]}
-{"prob_id": "prob_4402", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3885.png", "question": "The rectangle is inscribed into the circle. Find the exact circumference of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "31.416", "choices": [25.132741228718345, 31.41592653589793, 50.26548245743669, 62.83185307179586]}
-{"prob_id": "prob_4403", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_531.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 6.0, 8.0, 16.0]}
-{"prob_id": "prob_4433", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2325.png", "question": "Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "39.000", "choices": [39.0, 42.0, 48.0, 51.0]}
-{"prob_id": "prob_4471", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_547.png", "question": "UJ = 9, VJ = 3, and ZT = 18. Find SV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [3.0, 6.0, 9.0, 12.0]}
-{"prob_id": "prob_4480", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1103.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 40.0, 50.0, 60.0]}
-{"prob_id": "prob_4483", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1260.png", "question": "AB is a diameter, AC = 8 inches, and BC = 15 inches. Find the circumference of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "53.407", "choices": [26.703537555513243, 47.12388980384689, 50.26548245743669, 53.40707511102649]}
-{"prob_id": "prob_4485", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1257.png", "question": "Find h in the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [11.0, 15.556349186104047, 19.05255888325765, 22.0]}
-{"prob_id": "prob_4522", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2491.png", "question": "a = 14, b = 48, and c = 50, find \\sin A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.280", "choices": [0.14, 0.28, 0.48, 0.5]}
-{"prob_id": "prob_4532", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2567.png", "question": "Find the area of the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "132.000", "choices": [33.0, 66.0, 132.0, 264.0]}
-{"prob_id": "prob_4555", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3624.png", "question": "Find m \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "66.000", "choices": [38.0, 60.0, 66.0, 72.0]}
-{"prob_id": "prob_4565", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3170.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "69.755", "choices": [69.0, 69.8, 76.4, 77.2]}
-{"prob_id": "prob_4568", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_910.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "74.000", "choices": [56.0, 68.0, 74.0, 84.0]}
-{"prob_id": "prob_4577", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2326.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.392", "choices": [1.7320508075688772, 6.0, 10.392304845413264, 18.0]}
-{"prob_id": "prob_4591", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2611.png", "question": "Find the value of t in the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [6.0, 7.0, 8.0, 13.0]}
-{"prob_id": "prob_4605", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1553.png", "question": "GH = KJ. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [27.0, 54.0, 55.0, 83.0]}
-{"prob_id": "prob_4633", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_60.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "68.000", "choices": [68.0, 78.0, 79.0, 136.0]}
-{"prob_id": "prob_4635", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_422.png", "question": "Find the value of m \\angle FCE if line p \\parallel line q. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "105.000", "choices": [105.0, 110.0, 115.0, 120.0]}
-{"prob_id": "prob_4636", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2998.png", "question": "Find m \\angle B. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "61.000", "choices": [29.0, 58.0, 61.0, 122.0]}
-{"prob_id": "prob_4638", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1814.png", "question": "m \\angle 12 = 64. Find the measure of \\angle 7. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "64.000", "choices": [54.0, 64.0, 74.0, 84.0]}
-{"prob_id": "prob_4643", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_23.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [10.0, 17.32050807568877, 20.0, 30.0]}
-{"prob_id": "prob_4693", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2816.png", "question": "For trapezoid QRST, A and B are midpoints of the legs. Find m \\angle S. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "135.000", "choices": [45.0, 60.0, 120.0, 135.0]}
-{"prob_id": "prob_4733", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1334.png", "question": "AC is a diagonal of rhombus ABCD. If m \\angle CDE is 116, what is m \\angle ACD? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "58.000", "choices": [58.0, 90.0, 116.0, 180.0]}
-{"prob_id": "prob_4774", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3318.png", "question": "In rhombus LMPQ, m \\angle QLM = 2x^{2}-10, m \\angle QPM = 8x, and MP = 10. Find the perimeter of LMPQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [10.0, 40.0, 70.0, 140.0]}
-{"prob_id": "prob_4803", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2776.png", "question": "Find the measure of JK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "31.000", "choices": [15.5, 31.0, 62.0, 124.0]}
-{"prob_id": "prob_4807", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1141.png", "question": "The area of trapezoid JKLM is 138 square feet. The area of trapezoid QTSR is 5.52 square feet. If trapezoid JKLM \\sim trapezoid QTSR, find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.000", "choices": [0.2, 1.0, 25.0, 125.0]}
-{"prob_id": "prob_4848", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1918.png", "question": "Find m \\angle R. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "58.000", "choices": [58.0, 60.0, 122.0, 124.0]}
-{"prob_id": "prob_4878", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1362.png", "question": "Find the value of the variable t. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 4.0, 5.0, 6.0]}
-{"prob_id": "prob_4881", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2099.png", "question": "Find BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [6.0, 9.0, 15.0, 60.0]}
-{"prob_id": "prob_4913", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1402.png", "question": "Quadrilateral WXZY is a rectangle. Find the measure of \\angle 5 if m \\angle 1 = 30. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [15.0, 30.0, 45.0, 60.0]}
-{"prob_id": "prob_4942", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1010.png", "question": "Find the measure of \\angle 3 if m \\angle 4 = m \\angle 5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "116.000", "choices": [116.0, 126.0, 136.0, 146.0]}
-{"prob_id": "prob_4947", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_960.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.240", "choices": [9.0, 9.6, 10.2, 10.8]}
-{"prob_id": "prob_4955", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2420.png", "question": "Find m \\angle 2 if m \\widehat BC = 30 and m \\widehat AD = 20. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "155.000", "choices": [20.0, 25.0, 30.0, 155.0]}
-{"prob_id": "prob_4965", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1204.png", "question": "Circle O has a radius of 13 inches. Radius OB is perpendicular to chord CD which is 24 inches long. Find OX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 12.0, 13.0, 26.0]}
-{"prob_id": "prob_4978", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1156.png", "question": "Use parallelogram ABCD to find m \\angle CDF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.000", "choices": [34.0, 43.0, 47.0, 77.0]}
-{"prob_id": "prob_4985", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3322.png", "question": "Quadrilateral ABDC is a rectangle. m \\angle 2 = 40. Find m \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [10.0, 40.0, 50.0, 90.0]}
-{"prob_id": "prob_5004", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_600.png", "question": "Find the area of \\parallelogram JKLM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [12.0, 22.4, 24.0, 48.0]}
-{"prob_id": "prob_5021", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3806.png", "question": "AD and CG are diameters of \\odot B. Find m \\widehat AG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [35.0, 40.0, 45.0, 55.0]}
-{"prob_id": "prob_5025", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3189.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.215", "choices": [15.1, 30.2, 60.4, 912.9]}
-{"prob_id": "prob_5028", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_83.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [1.0, 2.0, 4.0, 8.0]}
-{"prob_id": "prob_5031", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2961.png", "question": "Find m \\angle C of quadrilateral ABCD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 90.0, 135.0, 180.0]}
-{"prob_id": "prob_5039", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_172.png", "question": "Equilateral pentagon PQRST is inscribed in \\odot U. Find m \\angle PSR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "72.000", "choices": [36.0, 72.0, 120.0, 144.0]}
-{"prob_id": "prob_5065", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1349.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.500", "choices": [9.5, 10.5, 12.5, 13.5]}
-{"prob_id": "prob_5102", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3031.png", "question": "The area of the shaded region is 66 cm^{2}. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.964", "choices": [4.6, 6.5, 13.0, 26.0]}
-{"prob_id": "prob_5109", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_727.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 6.5, 7.0, 7.5]}
-{"prob_id": "prob_5112", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1764.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "528.000", "choices": [428.0, 528.0, 572.0, 624.0]}
-{"prob_id": "prob_5122", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2865.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.857", "choices": [5.13, 5.46, 15.96, 43.86]}
-{"prob_id": "prob_5138", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2544.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.000", "choices": [23.0, 30.0, 67.0, 90.0]}
-{"prob_id": "prob_5140", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_500.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [24.0, 56.0, 65.0, 115.0]}
-{"prob_id": "prob_5148", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1962.png", "question": "If AB = 12, AC = 16, and ED = 5, find AE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [10.0, 12.0, 15.0, 16.0]}
-{"prob_id": "prob_5171", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_925.png", "question": "Find BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [4.0, 6.0, 7.0, 8.0]}
-{"prob_id": "prob_5211", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2346.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.063", "choices": [7.1, 14.1, 22.1, 30.0]}
-{"prob_id": "prob_5227", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3112.png", "question": "Find XY of isosceles \\triangle XYZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [2.0, 7.0, 8.0, 14.0]}
-{"prob_id": "prob_5240", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2756.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "207.846", "choices": [120.0, 124.7, 207.8, 240.0]}
-{"prob_id": "prob_5245", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3404.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [6.0, 8.0, 12.0, 15.0]}
-{"prob_id": "prob_5254", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3811.png", "question": "In \\odot Z, m \\angle WZX = m \\angle XZY, m \\angle VZU = 4x, m \\angle UZY = 2x+24, and VY and WU are diameters. Find m \\widehat WUX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "308.000", "choices": [52.0, 104.0, 154.0, 308.0]}
-{"prob_id": "prob_5276", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1353.png", "question": "Use parallelogram JKLM to find m \\angle KJL if JK = 2b+3 and JM = 3a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 70.0, 80.0, 100.0]}
-{"prob_id": "prob_5280", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1402.png", "question": "Quadrilateral WXZY is a rectangle. Find the measure of \\angle 3 if m \\angle 1 = 30. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 45.0, 60.0, 90.0]}
-{"prob_id": "prob_5287", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1999.png", "question": "Trapezoid GHJK has an area of 188.35 square feet. Find GK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "26.799", "choices": [5.1, 21.6, 22.8, 26.8]}
-{"prob_id": "prob_5309", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3781.png", "question": "If XM = 4, XN = 6, and NZ = 9, find XY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [4.0, 6.0, 9.0, 10.0]}
-{"prob_id": "prob_5347", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2444.png", "question": "Find m \\angle 9. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [60.0, 120.0, 240.0, 300.0]}
-{"prob_id": "prob_5354", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2734.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.722", "choices": [8.5, 12.020815280171309, 14.722431864335457, 17.0]}
-{"prob_id": "prob_5370", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3018.png", "question": "In \\triangle DEF, m \\angle E = 108, m \\angle F = 26, and f = 20. Find d. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.819", "choices": [26.0, 32.82, 60.0, 65.0]}
-{"prob_id": "prob_5374", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_743.png", "question": "Chords AC and DF are equidistant from the center. If the radius of \\odot G is 26, find AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.000", "choices": [5.0, 10.0, 13.0, 48.0]}
-{"prob_id": "prob_5381", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_576.png", "question": "Circles G, J, and K all intersect at L. If GH = 10, find JL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 10.0, 10.0, 25.0]}
-{"prob_id": "prob_5394", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3566.png", "question": "In \\odot S, m \\widehat PQR = 98. Find m \\widehat PQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "49.000", "choices": [45.0, 49.0, 90.0, 98.0]}
-{"prob_id": "prob_5399", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_251.png", "question": "If CE = t-2. EB = t+1, CD = 2, and CA = 10, find CE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.000", "choices": [1.0, 2.0, 3.0, 4.0]}
-{"prob_id": "prob_5409", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1747.png", "question": "Find \\cos C. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.800", "choices": [0.6, 0.75, 0.8, 1.25]}
-{"prob_id": "prob_5453", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1949.png", "question": "Find m \\angle A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_5456", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1406.png", "question": "Find x. Area = 357 in^{2}. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "21.000", "choices": [21.0, 22.0, 23.0, 24.0]}
-{"prob_id": "prob_5496", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_281.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [30.0, 35.0, 70.0, 140.0]}
-{"prob_id": "prob_5502", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_804.png", "question": "Find x in the given parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [38.0, 75.0, 76.0, 109.0]}
-{"prob_id": "prob_5514", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_54.png", "question": "Find BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 8.0, 12.0, 16.0]}
-{"prob_id": "prob_5515", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2249.png", "question": "\\triangle BCD \\cong \\triangle WXY. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 3.0, 4.0, 5.0]}
-{"prob_id": "prob_5520", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2278.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.639", "choices": [8.0, 10.16, 10.24, 16.64]}
-{"prob_id": "prob_5530", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_587.png", "question": "The perimeter of this polygon is 60 centimeters. Find the length of the side of the polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [12.0, 15.0, 30.0, 60.0]}
-{"prob_id": "prob_5546", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_908.png", "question": "Find the area of the shaded region formed by the circle and regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "76.395", "choices": [76.4, 237.8, 266.6, 314.2]}
-{"prob_id": "prob_5548", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_523.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 3.0, 4.0, 6.0]}
-{"prob_id": "prob_5571", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3021.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [11.0, 12.0, 13.0, 14.0]}
-{"prob_id": "prob_5598", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1992.png", "question": "In regular hexagon UVWXYZ. Find WY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.785", "choices": [12.0, 14.696938456699067, 20.784609690826528, 36.0]}
-{"prob_id": "prob_5610", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_851.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "53.000", "choices": [37.0, 45.0, 53.0, 63.0]}
-{"prob_id": "prob_5618", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1204.png", "question": "Circle O has a radius of 13 inches. Radius OB is perpendicular to chord CD which is 24 inches long. If m \\widehat CD = 134, find m \\widehat CB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "67.000", "choices": [24.0, 33.0, 67.0, 134.0]}
-{"prob_id": "prob_5630", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_881.png", "question": "Find EG if G is the incenter of \\triangle ABC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [4.0, 5.0, 12.0, 13.0]}
-{"prob_id": "prob_5634", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3411.png", "question": "m \\angle 9 = 75. Find the measure of \\angle 6. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "105.000", "choices": [75.0, 85.0, 95.0, 105.0]}
-{"prob_id": "prob_5637", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1284.png", "question": "In \\odot X, AB = CD = 30, and m \\widehat CZ = 40. Find m \\widehat CD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [30.0, 40.0, 60.0, 80.0]}
-{"prob_id": "prob_5657", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3992.png", "question": "Find the area of the shaded sector. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "182.605", "choices": [24.3, 91.3, 182.6, 524.3]}
-{"prob_id": "prob_5669", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2593.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.321", "choices": [6.928203230275509, 10.392304845413264, 13.856406460551018, 17.32050807568877]}
-{"prob_id": "prob_5697", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2281.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [30.0, 34.0, 60.0, 68.0]}
-{"prob_id": "prob_5743", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2823.png", "question": "If LK = 4, MP = 3, PQ = 6, KJ = 2, RS = 6, and LP = 2, find JH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [2.0, 3.0, 4.0, 6.0]}
-{"prob_id": "prob_5758", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_982.png", "question": "EB \\parallel DC. Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.500", "choices": [5.0, 7.5, 9.5, 10.0]}
-{"prob_id": "prob_5769", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_557.png", "question": "Find the measure of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "76.000", "choices": [49.0, 55.0, 57.0, 76.0]}
-{"prob_id": "prob_5785", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2784.png", "question": "Use parallelogram ABCD to find m \\angle ADC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "128.000", "choices": [42.0, 52.0, 72.0, 128.0]}
-{"prob_id": "prob_5793", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1821.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.899", "choices": [3.4641016151377544, 4.0, 4.898979485566356, 6.0]}
-{"prob_id": "prob_5813", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1907.png", "question": "Find the measure of \\widehat YXZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "166.000", "choices": [145.0, 166.0, 194.0, 215.0]}
-{"prob_id": "prob_5823", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3450.png", "question": "HK and IG are diameters of \\odot L. Find m \\widehat IHJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "270.000", "choices": [59.0, 135.0, 270.0, 301.0]}
-{"prob_id": "prob_5833", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2962.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.695", "choices": [3.9, 11.8, 28.7, 30.7]}
-{"prob_id": "prob_5850", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3664.png", "question": "If WXYZ is a kite, find WP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.472", "choices": [4.47213595499958, 16.0, 20.0, 36.0]}
-{"prob_id": "prob_5886", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1096.png", "question": "Use rectangle LMNP, parallelogram LKMJ. If LN = 10, LJ = 2x+1, and PJ = 3x-1, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 4.0, 5.0, 10.0]}
-{"prob_id": "prob_5900", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2802.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "97.529", "choices": [97.53, 103.0, 108.0, 113.0]}
-{"prob_id": "prob_5914", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2057.png", "question": "CP is an altitude, CQ is the angle bisector of \\angle ACB, and R is the midpoint of AB. Find m \\angle ACQ if m \\angle ACB = 123-x and m \\angle QCB = 42+x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [40.0, 45.0, 50.0, 55.0]}
-{"prob_id": "prob_5980", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1024.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "144.000", "choices": [25.0, 50.0, 72.0, 144.0]}
-{"prob_id": "prob_5988", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_955.png", "question": "In \\odot P, JK = 10 and m \\widehat JLK = 134. Find m \\widehat JL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "67.000", "choices": [46.0, 67.0, 92.0, 134.0]}
-{"prob_id": "prob_5991", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_256.png", "question": "m \\angle 3 = 43. Find the measure of \\angle 11. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.000", "choices": [43.0, 53.0, 63.0, 137.0]}
-{"prob_id": "prob_5997", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1765.png", "question": "In \\odot M, FL = 24, HJ = 48, and m \\widehat HP = 65. Find m \\widehat HJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "130.000", "choices": [65.0, 120.0, 130.0, 155.0]}
-{"prob_id": "prob_6007", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_695.png", "question": "Find BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.000", "choices": [5.0, 9.0, 12.0, 13.0]}
-{"prob_id": "prob_6014", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_9.png", "question": "In rhombus ABCD, m \\angle DAB = 2 m \\angle ADC and CB = 6. Find m \\angle ACD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [45.0, 60.0, 90.0, 180.0]}
-{"prob_id": "prob_6056", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3728.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.856", "choices": [11.313708498984761, 13.856406460551018, 16.0, 24.0]}
-{"prob_id": "prob_6057", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2304.png", "question": "Each pair of polygons is similar. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [8.0, 12.0, 15.0, 20.0]}
-{"prob_id": "prob_6079", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3292.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "52.547", "choices": [49.5, 52.5, 55.5, 58.5]}
-{"prob_id": "prob_6129", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3000.png", "question": "Find the perimeter of \\triangle BCD, if \\triangle BCD \\sim \\triangle FDE, CD = 12, FD = 5, FE = 4, and DE = 8. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.500", "choices": [21.3, 25.5, 29.8, 34.0]}
-{"prob_id": "prob_6130", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_366.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "78.000", "choices": [32.0, 39.0, 46.0, 78.0]}
-{"prob_id": "prob_6164", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_534.png", "question": "Find KJ if GJ = 8, GH = 12, and HI = 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 4.0, 6.0, 8.0]}
-{"prob_id": "prob_6172", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3688.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 90.0, 180.0, 360.0]}
-{"prob_id": "prob_6189", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_620.png", "question": "Use a Pythagorean Triple to find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [66.0, 68.0, 70.0, 72.0]}
-{"prob_id": "prob_6192", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_866.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 120.0, 240.0]}
-{"prob_id": "prob_6202", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2144.png", "question": "ABCD is a rhombus. If PB = 12, AB = 15, and m \\angle ABD = 24. Find m \\angle BDA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [24.0, 55.0, 90.0, 120.0]}
-{"prob_id": "prob_6203", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2288.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [8.0, 9.0, 12.0, 15.0]}
-{"prob_id": "prob_6226", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1716.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.856", "choices": [3.4641016151377544, 6.928203230275509, 10.392304845413264, 13.856406460551018]}
-{"prob_id": "prob_6229", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2899.png", "question": "Find h in the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [4.62, 5.66, 6.93, 8.0]}
-{"prob_id": "prob_6249", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1402.png", "question": "Quadrilateral WXZY is a rectangle. Find the measure of \\angle 6 if m \\angle 1 = 30. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 45.0, 60.0, 90.0]}
-{"prob_id": "prob_6259", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3744.png", "question": "Find the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "109.000", "choices": [54.5, 90.0, 109.0, 218.0]}
-{"prob_id": "prob_6266", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1777.png", "question": "Find CD if AC = x-3, BE = 20, AB = 16, and CD = x+5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [32.0, 35.0, 36.0, 40.0]}
-{"prob_id": "prob_6279", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2680.png", "question": "Find the measure of \\angle A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "41.810", "choices": [33.7, 41.8, 48.2, 56.3]}
-{"prob_id": "prob_6281", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_25.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.500", "choices": [37.5, 47.0, 52.5, 133.0]}
-{"prob_id": "prob_6293", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1066.png", "question": "Tangent MP is drawn to \\odot O. Find x if MO = 20. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [5.0, 8.94427190999916, 12.0, 16.0]}
-{"prob_id": "prob_6297", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2855.png", "question": "KL is tangent to \\odot M at K. Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.450", "choices": [6.0, 9.45, 18.9, 37.8]}
-{"prob_id": "prob_6303", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1396.png", "question": "For the pair of similar figures, the area of the blue figure is 8 in^{2} and the green figure is 32 in^{2}, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [1.0, 2.0, 8.0, 16.0]}
-{"prob_id": "prob_6313", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1391.png", "question": "QT bisects \\angle SQR. If m \\angle SQR = 6x+8 and m \\angle TQR = 4x-14, find m \\angle SQT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "58.000", "choices": [18.0, 32.0, 36.0, 58.0]}
-{"prob_id": "prob_6334", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_424.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.274", "choices": [9.4, 18.8, 28.3, 37.7]}
-{"prob_id": "prob_6343", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3038.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [14.0, 24.24871130596428, 28.0, 42.0]}
-{"prob_id": "prob_6347", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3934.png", "question": "Find the area of the trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "180.000", "choices": [45.0, 90.0, 180.0, 360.0]}
-{"prob_id": "prob_6356", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_566.png", "question": "Use parallelogram MNPR to find m \\angle MNP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "71.000", "choices": [33.0, 38.0, 71.0, 109.0]}
-{"prob_id": "prob_6393", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_848.png", "question": "Use parallelogram ABCD to find AD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [6.0, 12.0, 18.0, 30.0]}
-{"prob_id": "prob_6423", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1122.png", "question": "Find x in the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.000", "choices": [37.0, 41.0, 78.0, 115.0]}
-{"prob_id": "prob_6427", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2928.png", "question": "m \\angle 4 = 2y+32 and m \\angle 5 = 3y-3. Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [18.0, 35.0, 55.0, 72.0]}
-{"prob_id": "prob_6429", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1626.png", "question": "If IJ / XJ = HJ / YJ, m \\angle WXJ = 130 and m \\angle WZG = 20, find m \\angle YIZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [40.0, 50.0, 65.0, 110.0]}
-{"prob_id": "prob_6432", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1800.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.400", "choices": [0.8, 1.0, 1.4, 1.6]}
-{"prob_id": "prob_6434", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_347.png", "question": "Find the measure of \\angle 2 if AB \\perp BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "68.000", "choices": [64.0, 68.0, 72.0, 76.0]}
-{"prob_id": "prob_6440", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1739.png", "question": "Find m \\angle H. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "97.000", "choices": [97.0, 102.0, 107.0, 122.0]}
-{"prob_id": "prob_6442", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_943.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [30.0, 35.0, 45.0, 85.0]}
-{"prob_id": "prob_6452", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_763.png", "question": "Use parallelogram ABCD to find m \\angle ACD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.000", "choices": [20.0, 29.0, 49.0, 59.0]}
-{"prob_id": "prob_6457", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_606.png", "question": "m \\angle 1 = 58, m \\angle 2 = 47, and m \\angle 3 = 26. Find the measure of \\angle 9. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "49.000", "choices": [39.0, 47.0, 49.0, 58.0]}
-{"prob_id": "prob_6468", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_418.png", "question": "Point D is the center of the circle. What is m \\angle ABC? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [30.0, 45.0, 60.0, 90.0]}
-{"prob_id": "prob_6473", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2593.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [4.0, 6.0, 8.0, 10.0]}
-{"prob_id": "prob_6479", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2009.png", "question": "Find x if AE = 3, AB = 2, BC = 6, and ED = 2x-3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [5.0, 6.0, 8.0, 9.0]}
-{"prob_id": "prob_6481", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_594.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.000", "choices": [22.0, 40.0, 44.0, 48.0]}
-{"prob_id": "prob_6515", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_154.png", "question": "Find x so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.000", "choices": [13.0, 26.0, 39.0, 52.0]}
-{"prob_id": "prob_6530", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2031.png", "question": "P is the incenter of \\triangle AEC. Find m \\angle DEP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.500", "choices": [28.5, 30.0, 31.0, 33.0]}
-{"prob_id": "prob_6531", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1063.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 7.0710678118654755, 8.660254037844386, 10.0]}
-{"prob_id": "prob_6556", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_114.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.414", "choices": [17.4, 22.1, 22.3, 45.9]}
-{"prob_id": "prob_6561", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_347.png", "question": "Find the measure of \\angle 3 if AB \\perp BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "76.000", "choices": [64.0, 68.0, 72.0, 76.0]}
-{"prob_id": "prob_6587", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2823.png", "question": "If LK = 4, MP = 3, PQ = 6, KJ = 2, RS = 6, and LP = 2, find ML. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 3.0, 4.0, 6.0]}
-{"prob_id": "prob_6594", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_172.png", "question": "Equilateral pentagon PQRST is inscribed in \\odot U. Find m \\widehat QR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "72.000", "choices": [36.0, 72.0, 120.0, 144.0]}
-{"prob_id": "prob_6596", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2382.png", "question": "Find m \\angle JKL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.000", "choices": [35.0, 37.0, 53.0, 73.0]}
-{"prob_id": "prob_6620", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2011.png", "question": "Find WR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [6.0, 8.0, 10.0, 12.0]}
-{"prob_id": "prob_6640", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2191.png", "question": "For trapezoid TRSV, M and N are midpoints of the legs. If TR = 32 and MN = 25, find VS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [18.0, 36.0, 50.0, 64.0]}
-{"prob_id": "prob_6666", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2868.png", "question": "Find BD if BF bisects \\angle ABC and AC \\parallel ED, BA = 6, BC = 7.5, AC = 9, and DE = 9. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.500", "choices": [12.0, 13.5, 15.0, 18.0]}
-{"prob_id": "prob_6678", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2651.png", "question": "The diameter of \\odot S is 30 units, the diameter of \\odot R is 20 units, and DS = 9 units. Find RC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 6.0, 9.0, 12.0]}
-{"prob_id": "prob_6733", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_706.png", "question": "Circle A has diameters DF and PG. If DF = 10, find DA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 10.0, 20.0, 25.0]}
-{"prob_id": "prob_6747", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2868.png", "question": "Find CF if BF bisects \\angle ABC and AC \\parallel ED, BA = 6, BC = 7.5, AC = 9, and DE = 9. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 4.5, 5.0, 7.5]}
-{"prob_id": "prob_6780", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1819.png", "question": "The diameters of \\odot A, \\odot B, and \\odot C are 10, 30 and 10 units, respectively. Find AC if AZ = CW and CW = 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [2.0, 10.0, 30.0, 34.0]}
-{"prob_id": "prob_6827", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3882.png", "question": "Find AD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.500", "choices": [5.5, 6.0, 7.5, 9.0]}
-{"prob_id": "prob_6864", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2638.png", "question": "If the area of the rhombus is 169 square millimeters, what is x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.000", "choices": [6.5, 13.0, 26.0, 52.0]}
-{"prob_id": "prob_6880", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2314.png", "question": "Quadrilateral WXYZ is inscribed in \\odot V. Find m \\angle X. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [85.0, 95.0, 115.0, 120.0]}
-{"prob_id": "prob_6887", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2067.png", "question": "In \\odot P, m \\angle MPL = 65 and NP \\perp PL. Find m \\widehat NJK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "155.000", "choices": [25.0, 75.0, 90.0, 155.0]}
-{"prob_id": "prob_6918", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_432.png", "question": "In \\odot F, FH = FL and FK = 17. Find JG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [15.0, 16.0, 17.0, 30.0]}
-{"prob_id": "prob_6923", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3872.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [5.0, 6.0, 7.0, 8.0]}
-{"prob_id": "prob_6937", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1585.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 4.0, 5.0, 6.0]}
-{"prob_id": "prob_6948", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3393.png", "question": "Find m \\widehat LP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "150.000", "choices": [114.0, 144.0, 150.0, 156.0]}
-{"prob_id": "prob_6986", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1745.png", "question": "In \\odot O, EC and AB are diameters, and m \\angle BOD = m \\angle DOE = m \\angle EOF = m \\angle FOA. Find m \\widehat AE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 90.0, 180.0, 360.0]}
-{"prob_id": "prob_6988", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3214.png", "question": "Find the height of the parallelogram given its area with 2000 square units. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [30.0, 40.0, 50.0, 60.0]}
-{"prob_id": "prob_7014", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_576.png", "question": "Circles G, J, and K all intersect at L. If GH = 10, find FH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [5.0, 10.0, 20.0, 25.0]}
-{"prob_id": "prob_7024", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_835.png", "question": "For trapezoid ABDC, S and T are midpoints of the legs. If AB = x+4, CD = 3x+2, and ST = 9, find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [3.0, 5.0, 7.0, 9.0]}
-{"prob_id": "prob_7049", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3322.png", "question": "Quadrilateral ABDC is a rectangle. If m \\angle 1 = 38, find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "52.000", "choices": [33.0, 38.0, 52.0, 87.0]}
-{"prob_id": "prob_7071", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1943.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.321", "choices": [5.0, 10.0, 17.32050807568877, 20.0]}
-{"prob_id": "prob_7077", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_678.png", "question": "Find m \\widehat XZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "88.000", "choices": [56.0, 68.0, 88.0, 92.0]}
-{"prob_id": "prob_7105", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1595.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.583", "choices": [3.4641016151377544, 4.123105625617661, 4.58257569495584, 5.385164807134504]}
-{"prob_id": "prob_7119", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1853.png", "question": "In \\triangle PQR, ZQ = 3a-11, ZP = a+5, PY = 2c-1, YR = 4c-11, m \\angle PRZ = 4b-17, m \\angle ZRQ = 3b-4, m \\angle QYR = 7b+6, and m \\angle PXR = 2a+10. If RZ is an angle bisector, find m \\angle PRZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [20.0, 25.0, 30.0, 35.0]}
-{"prob_id": "prob_7128", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2351.png", "question": "Find the side length DE in isosceles triangle DEF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [2.0, 8.0, 11.0, 20.0]}
-{"prob_id": "prob_7135", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3776.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.167", "choices": [10.285714285714286, 14.0, 15.833333333333334, 16.166666666666668]}
-{"prob_id": "prob_7156", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_942.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [60.0, 80.0, 90.0, 120.0]}
-{"prob_id": "prob_7159", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_788.png", "question": "Quadrilateral ABCD is inscribed in \\odot Z such that m \\angle BZA = 104, m \\widehat CB = 94, and AB \\parallel DC. Find m \\angle ZAC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [9.0, 36.0, 94.0, 144.0]}
-{"prob_id": "prob_7165", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1789.png", "question": "Find the perimeter of \\triangle RUW if \\triangle RUW \\sim \\triangle STV, ST = 24, VS = 12, VT = 18 and UW = 21. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "63.000", "choices": [63.0, 68.0, 70.0, 75.0]}
-{"prob_id": "prob_7166", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2980.png", "question": "MC = 7, RM = 4, and AT = 16. Find MB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [6.0, 8.0, 10.0, 12.0]}
-{"prob_id": "prob_7188", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_945.png", "question": "GJ is a diameter of \\odot K. Find m \\widehat GLJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "180.000", "choices": [90.0, 120.0, 180.0, 360.0]}
-{"prob_id": "prob_7204", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_699.png", "question": "If AE = m-2, EC = m+4, AD = 4, and AB = 20, find m. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [3.0, 4.0, 5.0, 6.0]}
-{"prob_id": "prob_7218", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3834.png", "question": "If c = 5, find a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.500", "choices": [2.5, 5.0, 7.5, 10.0]}
-{"prob_id": "prob_7237", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_835.png", "question": "For trapezoid ABDC, S and T are midpoints of the legs. If CD = 14, ST = 10, and AB = 2x, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 3.0, 10.0, 14.0]}
-{"prob_id": "prob_7242", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_474.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.265", "choices": [12.6, 25.1, 48.0, 50.27]}
-{"prob_id": "prob_7246", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2224.png", "question": "A regular polygon is inscribed in a circle. Find the measure of the central angle \\angle KRL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_7248", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_101.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 8.0, 10.0, 12.0]}
-{"prob_id": "prob_7254", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2502.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.641", "choices": [34.6, 36.0, 40.0, 48.0]}
-{"prob_id": "prob_7282", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_442.png", "question": "Find m \\angle Z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "110.000", "choices": [80.0, 108.0, 110.0, 112.0]}
-{"prob_id": "prob_7295", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3174.png", "question": "Find the value of the variable y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [30.0, 50.0, 60.0, 80.0]}
-{"prob_id": "prob_7304", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_821.png", "question": "Find a, if FG = 18, GH = 42, and FK = 15. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "57.000", "choices": [15.0, 18.0, 42.0, 57.0]}
-{"prob_id": "prob_7306", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3059.png", "question": "Find m \\angle H. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "31.000", "choices": [26.0, 31.0, 62.0, 88.0]}
-{"prob_id": "prob_7315", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3038.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [14.0, 24.24871130596428, 28.0, 34.29285639896449]}
-{"prob_id": "prob_7323", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_974.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "95.247", "choices": [80.49844718999243, 95.24704719832526, 119.39849245279439, 129.79984591670362]}
-{"prob_id": "prob_7331", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2267.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 8.0, 10.0, 12.0]}
-{"prob_id": "prob_7349", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3539.png", "question": "Find the value of the variable x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "54.000", "choices": [36.0, 54.0, 60.0, 108.0]}
-{"prob_id": "prob_7363", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2250.png", "question": "Find m \\angle RCM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.000", "choices": [27.0, 43.0, 47.0, 67.0]}
-{"prob_id": "prob_7365", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3997.png", "question": "\\angle 6 and \\angle 8 are complementary, m \\angle 8 = 47. Find the measure of \\angle 7. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [43.0, 47.0, 86.0, 90.0]}
-{"prob_id": "prob_7379", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_201.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [25.0, 40.0, 65.0, 115.0]}
-{"prob_id": "prob_7402", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1690.png", "question": "Find the area of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "54.000", "choices": [27.0, 36.0, 54.0, 108.0]}
-{"prob_id": "prob_7419", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_547.png", "question": "UJ = 9, VJ = 3, and ZT = 18. Find SJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [3.0, 6.0, 9.0, 12.0]}
-{"prob_id": "prob_7443", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3900.png", "question": "BD bisects \\angle ABF. If m \\angle FBC = 2x+25 and m \\angle ABF = 10x-1, find m \\angle DBF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "64.500", "choices": [25.5, 50.0, 54.0, 64.5]}
-{"prob_id": "prob_7448", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1356.png", "question": "Find x so that line m \\parallel line n. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [10.0, 20.0, 31.0, 40.0]}
-{"prob_id": "prob_7462", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3603.png", "question": "Find a in the given parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [2.0, 8.0, 9.0, 10.0]}
-{"prob_id": "prob_7472", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3740.png", "question": "Find the circumference of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.478", "choices": [18.6, 19.5, 37.7, 39.0]}
-{"prob_id": "prob_7473", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1949.png", "question": "Find m \\angle B. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_7500", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3501.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.889", "choices": [11.313708498984761, 13.856406460551018, 17.88854381999832, 21.166010488516726]}
-{"prob_id": "prob_7536", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2841.png", "question": "Find the perimeter of \\triangle DEF, if \\triangle DEF \\sim \\triangle CBF, perimeter of \\triangle CBF = 27, DF = 3, and FC = 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.250", "choices": [20.25, 21.0, 27.0, 36.0]}
-{"prob_id": "prob_7549", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2770.png", "question": "Find y so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 16.0, 20.0, 24.0]}
-{"prob_id": "prob_7553", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_974.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.697", "choices": [6.0, 7.348469228349534, 12.0, 14.696938456699067]}
-{"prob_id": "prob_7554", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3610.png", "question": "Find \\sin N. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.923", "choices": [0.38, 0.42, 0.92, 2.4]}
-{"prob_id": "prob_7557", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2740.png", "question": "Express the ratio of \\tan L. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.417", "choices": [0.38, 0.42, 0.92, 2.4]}
-{"prob_id": "prob_7561", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1583.png", "question": "Find x so that line a \\parallel line b. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [2.5, 14.0, 15.0, 16.0]}
-{"prob_id": "prob_7586", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1590.png", "question": "Find m \\angle S. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [28.0, 30.0, 32.0, 34.0]}
-{"prob_id": "prob_7601", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3952.png", "question": "Find \\tan X. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.400", "choices": [0.4166666666666667, 0.9230769230769231, 1.4166666666666667, 2.4]}
-{"prob_id": "prob_7633", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1602.png", "question": "Find the measure of \\angle T. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "21.801", "choices": [21.8, 23.6, 66.4, 68.2]}
-{"prob_id": "prob_7645", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1903.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.657", "choices": [4.0, 5.656854249492381, 6.928203230275509, 8.0]}
-{"prob_id": "prob_7699", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2560.png", "question": "m \\angle 4 = 42. Find m \\angle 7. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "138.000", "choices": [42.0, 48.0, 132.0, 138.0]}
-{"prob_id": "prob_7726", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_814.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.000", "choices": [22.0, 32.0, 40.0, 42.0]}
-{"prob_id": "prob_7731", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2137.png", "question": "m \\widehat AC = 160 and m \\angle BEC = 38. What is m \\angle AEB? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "42.000", "choices": [42.0, 61.0, 80.0, 84.0]}
-{"prob_id": "prob_7741", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_46.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [12.0, 16.0, 51.0, 65.0]}
-{"prob_id": "prob_7742", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_562.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [3.0, 4.0, 5.0, 6.0]}
-{"prob_id": "prob_7746", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_628.png", "question": "Find TX if EX = 24 and DE = 7. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.000", "choices": [7.0, 24.0, 25.0, 32.0]}
-{"prob_id": "prob_7757", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_298.png", "question": "PQRS is a rhombus inscribed in a circle. Find m \\widehat SP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [30.0, 45.0, 60.0, 90.0]}
-{"prob_id": "prob_7776", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3904.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.500", "choices": [22.5, 23.0, 23.5, 24.0]}
-{"prob_id": "prob_7807", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2859.png", "question": "Find x so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 5.0, 12.0, 18.0]}
-{"prob_id": "prob_7826", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_584.png", "question": "\\triangle JKL \\sim \\triangle WYZ. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "21.000", "choices": [13.0, 21.0, 32.0, 44.0]}
-{"prob_id": "prob_7829", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1131.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.500", "choices": [7.5, 10.0, 12.5, 15.0]}
-{"prob_id": "prob_7837", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_254.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.166", "choices": [8.082903768654761, 16.165807537309522, 24.24871130596428, 28.0]}
-{"prob_id": "prob_7845", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3784.png", "question": "XY and XZ are midsegments of \\triangle RST. Find ST. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [7.0, 13.0, 14.0, 20.0]}
-{"prob_id": "prob_7852", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3610.png", "question": "Solve for \\cos N. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.385", "choices": [0.38, 0.42, 0.92, 2.4]}
-{"prob_id": "prob_7881", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1305.png", "question": "Quadrilateral WXYZ is a rectangle. If ZP = 4x-9 and PY = 2x+5, find ZX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [9.0, 10.0, 19.0, 38.0]}
-{"prob_id": "prob_7905", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_803.png", "question": "Find the length of \\widehat ZY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.854", "choices": [3.93, 6.0, 7.85, 15.71]}
-{"prob_id": "prob_7915", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3258.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.000", "choices": [0.5, 1.0, 1.5, 2.0]}
-{"prob_id": "prob_7918", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3943.png", "question": "Find the perimeter of \\triangle WZX, if \\triangle WZX \\sim \\triangle SRT, ST = 6, WX = 5, and the perimeter of \\triangle SRT = 15. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.500", "choices": [12.5, 13.0, 15.0, 18.0]}
-{"prob_id": "prob_7942", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2313.png", "question": "The segment is tangent to the circle. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [16.0, 18.0, 30.0, 34.0]}
-{"prob_id": "prob_7995", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_452.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.777", "choices": [5.8, 6.5, 14.2, 44.3]}
-{"prob_id": "prob_8005", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_442.png", "question": "Find m \\angle Y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [80.0, 108.0, 110.0, 114.0]}
-{"prob_id": "prob_8008", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3377.png", "question": "In \\triangle CDF, K is the centroid and DK = 16. Find CD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [9.0, 12.0, 18.0, 18.0]}
-{"prob_id": "prob_8022", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3288.png", "question": "For the pair of similar figures, the area of the blue figure is 400 mm^{2} and the green figure is 64 mm^{2}, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [6.4, 16.0, 100.0, 250.0]}
-{"prob_id": "prob_8029", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3610.png", "question": "Determine \\tan M. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.417", "choices": [0.38, 0.42, 0.92, 2.4]}
-{"prob_id": "prob_8087", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1089.png", "question": "Find the area of the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "136.000", "choices": [68.0, 136.0, 272.0, 544.0]}
-{"prob_id": "prob_8131", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1838.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.500", "choices": [3.5, 7.0, 10.5, 21.0]}
-{"prob_id": "prob_8136", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_412.png", "question": "\\triangle ABC \\sim \\triangle FDG. Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [8.0, 10.0, 12.0, 15.0]}
-{"prob_id": "prob_8152", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1210.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "157.080", "choices": [104.7, 157.1, 235.6, 314.2]}
-{"prob_id": "prob_8160", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_981.png", "question": "Find m \\angle VXW. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [25.0, 65.0, 115.0, 180.0]}
-{"prob_id": "prob_8163", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3589.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.091", "choices": [22.045407685048602, 44.090815370097204, 54.0, 62.35382907247958]}
-{"prob_id": "prob_8172", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3675.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.746", "choices": [4.88, 5.96, 6.75, 8.42]}
-{"prob_id": "prob_8177", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2900.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.798", "choices": [3.4641016151377544, 4.898979485566356, 6.928203230275509, 9.797958971132712]}
-{"prob_id": "prob_8207", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1788.png", "question": "Square ABDC is inscribed in \\odot K. Find the measure of the central angle \\angle CFD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 60.0, 90.0, 180.0]}
-{"prob_id": "prob_8214", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3201.png", "question": "Find the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [25.0, 55.0, 65.0, 75.0]}
-{"prob_id": "prob_8215", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3874.png", "question": "Find the perimeter of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.731", "choices": [5.84, 6.65, 8.21, 8.73]}
-{"prob_id": "prob_8251", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1584.png", "question": "The segment is tangent to the circle. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.485", "choices": [7.5, 8.5, 9.2, 13.0]}
-{"prob_id": "prob_8269", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2250.png", "question": "Find m \\angle NCL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [60.0, 120.0, 240.0, 360.0]}
-{"prob_id": "prob_8270", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3034.png", "question": "Use parallelogram WXYZ to find m \\angle XYZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "105.000", "choices": [30.0, 75.0, 105.0, 180.0]}
-{"prob_id": "prob_8277", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3590.png", "question": "Q is the centroid and BE = 9. Find BQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [3.0, 6.0, 9.0, 12.0]}
-{"prob_id": "prob_8290", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_566.png", "question": "Use parallelogram MNPR to find m \\angle RNP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [38.0, 52.0, 52.0, 62.0]}
-{"prob_id": "prob_8294", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3586.png", "question": "Find QM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [4.0, 8.0, 12.0, 16.0]}
-{"prob_id": "prob_8310", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_167.png", "question": "Use parallelogram to find b. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [7.0, 11.0, 21.0, 33.0]}
-{"prob_id": "prob_8311", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3039.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [12.0, 15.0, 18.0, 21.0]}
-{"prob_id": "prob_8330", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2056.png", "question": "Polygon ABCD \\sim polygon AEFG, m \\angle AGF = 108, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26. Find m \\angle ADC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "108.000", "choices": [14.0, 72.0, 108.0, 120.0]}
-{"prob_id": "prob_8360", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3682.png", "question": "m \\angle 2 = 2x, m \\angle 3 = x. Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 45.0, 60.0, 90.0]}
-{"prob_id": "prob_8398", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3795.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [7.0, 9.0, 12.0, 15.0]}
-{"prob_id": "prob_8422", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_703.png", "question": "Find m \\angle MPQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "101.000", "choices": [45.0, 56.0, 79.0, 101.0]}
-{"prob_id": "prob_8428", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1193.png", "question": "Find the measure of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [23.0, 24.0, 28.0, 33.0]}
-{"prob_id": "prob_8438", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3820.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "125.000", "choices": [55.0, 115.0, 125.0, 135.0]}
-{"prob_id": "prob_8439", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_606.png", "question": "m \\angle 1 = 58, m \\angle 2 = 47, and m \\angle 3 = 26. Find the measure of \\angle 5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "47.000", "choices": [43.0, 47.0, 58.0, 73.0]}
-{"prob_id": "prob_8448", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1535.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "169.741", "choices": [56.6, 138.6, 169.7, 196.0]}
-{"prob_id": "prob_8486", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2478.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "79.000", "choices": [21.0, 27.0, 52.0, 79.0]}
-{"prob_id": "prob_8503", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1524.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.806", "choices": [6.0, 8.0, 10.0, 12.806248474865697]}
-{"prob_id": "prob_8507", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3163.png", "question": "m \\angle 1 = 50 and m \\angle 3 = 60. Find the measure of \\angle 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [40.0, 50.0, 60.0, 70.0]}
-{"prob_id": "prob_8515", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2996.png", "question": "The two polygons are similar. Find UT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.500", "choices": [12.0, 20.5, 22.5, 35.0]}
-{"prob_id": "prob_8530", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3803.png", "question": "Find PT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.667", "choices": [6.0, 6.666666666666667, 7.0, 7.333333333333333]}
-{"prob_id": "prob_8543", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_335.png", "question": "Find the area of the trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2256.000", "choices": [191.5, 1128.0, 2256.0, 4512.0]}
-{"prob_id": "prob_8548", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2928.png", "question": "m \\angle 3 = x-12 and m \\angle 6 = 72. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "84.000", "choices": [6.0, 18.0, 72.0, 84.0]}
-{"prob_id": "prob_8552", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_636.png", "question": "Find the value of the variable x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "125.000", "choices": [55.0, 115.0, 125.0, 135.0]}
-{"prob_id": "prob_8575", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2469.png", "question": "Find m \\angle R. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.088", "choices": [29.1, 43.7, 54.8, 56.1]}
-{"prob_id": "prob_8577", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1765.png", "question": "In \\odot M, FL = 24, HJ = 48, and m \\widehat HP = 65. Find m \\widehat PJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [37.5, 65.0, 85.0, 130.0]}
-{"prob_id": "prob_8593", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1395.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [10.0, 20.0, 30.0, 40.0]}
-{"prob_id": "prob_8605", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_78.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [8.0, 13.856406460551018, 24.0, 27.712812921102035]}
-{"prob_id": "prob_8618", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3104.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.750", "choices": [10.25, 12.75, 18.75, 25.5]}
-{"prob_id": "prob_8622", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1284.png", "question": "In \\odot X, AB = CD = 30, and m \\widehat CZ = 40. Find ND. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [10.0, 15.0, 20.0, 30.0]}
-{"prob_id": "prob_8626", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_242.png", "question": "Find m \\angle WYZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.000", "choices": [4.0, 16.0, 23.0, 32.0]}
-{"prob_id": "prob_8631", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2248.png", "question": "Given that the perimeter of \\triangle ABC = 25, find x. Assume that segments that appear tangent to circles are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 6.0, 7.0, 9.0]}
-{"prob_id": "prob_8650", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3371.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "36.373", "choices": [21.0, 29.698484809834998, 36.373066958946424, 42.0]}
-{"prob_id": "prob_8662", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2572.png", "question": "Find the area of the kite. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "336.000", "choices": [168.0, 336.0, 672.0, 1344.0]}
-{"prob_id": "prob_8665", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1417.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.657", "choices": [5.656854249492381, 6.928203230275509, 8.0, 8.94427190999916]}
-{"prob_id": "prob_8683", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_292.png", "question": "Find x so that GJ \\parallel FK. GH = x+3.5, HJ = x-8.5, FH = 21, HK = 7. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.500", "choices": [12.0, 12.5, 14.5, 17.5]}
-{"prob_id": "prob_8724", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2984.png", "question": "Find the length of \\widehat WN if \\triangle IWN is equilateral and WN = 5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.236", "choices": [1.8849555921538759, 5.235987755982989, 15.707963267948966, 31.41592653589793]}
-{"prob_id": "prob_8768", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2798.png", "question": "in \\triangle XYZ, P is the centroid, KP = 3, and XJ = 8. Find YJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [3.0, 6.0, 8.0, 9.0]}
-{"prob_id": "prob_8781", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_611.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "31.069", "choices": [24.0, 31.1, 38.1, 52.3]}
-{"prob_id": "prob_8863", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3465.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [10.0, 30.0, 90.0, 120.0]}
-{"prob_id": "prob_8868", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_664.png", "question": "JKLM is a rectangle. MLPR is a rhombus. m \\angle JMK = m \\angle RMP, m \\angle JMK = 55, and m \\angle MRP = 70. Find m \\angle KLP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "160.000", "choices": [20.0, 110.0, 140.0, 160.0]}
-{"prob_id": "prob_8885", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1019.png", "question": "If CW = WF and ED = 30, what is DF? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [15.0, 30.0, 45.0, 60.0]}
-{"prob_id": "prob_8896", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3171.png", "question": "Find the area of the shaded region. Assume that the polygon is regular. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1208.081", "choices": [1208.1, 1669.9, 3444.7, 4263.4]}
-{"prob_id": "prob_8900", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2869.png", "question": "Find PN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [25.0, 30.0, 50.0, 60.0]}
-{"prob_id": "prob_8907", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2363.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [10.0, 11.0, 12.0, 13.0]}
-{"prob_id": "prob_8929", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2582.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.207", "choices": [37.2, 40.6, 49.4, 52.8]}
-{"prob_id": "prob_8939", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3373.png", "question": "Find the length of AC in the isosceles triangle ABC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [1.5, 7.0, 11.0, 12.5]}
-{"prob_id": "prob_8943", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_566.png", "question": "Use parallelogram MNPR to find m \\angle RMN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "109.000", "choices": [33.0, 38.0, 71.0, 109.0]}
-{"prob_id": "prob_8952", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2065.png", "question": "MN \\parallel BC. Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [6.0, 9.0, 12.0, 15.0]}
+{"prob_id": "prob_1", "image_path": "images/img_3160.png", "question": "Line m is the perpendicular bisector of XZ, WZ = 14.9. Find WX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.900", "choices": [7.45, 14.9, 22.4, 25.3]}
+{"prob_id": "prob_17", "image_path": "images/img_3834.png", "question": "If c = 5, find b. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.330", "choices": [1.7320508075688772, 2.598076211353316, 3.4641016151377544, 4.330127018922193]}
+{"prob_id": "prob_21", "image_path": "images/img_1683.png", "question": "Find m \\angle 6. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [25.0, 28.0, 35.0, 55.0]}
+{"prob_id": "prob_27", "image_path": "images/img_423.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.000", "choices": [24.0, 33.941125496954285, 41.569219381653056, 48.0]}
+{"prob_id": "prob_31", "image_path": "images/img_2339.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [35.0, 70.0, 75.0, 82.0]}
+{"prob_id": "prob_40", "image_path": "images/img_1740.png", "question": "Quadrilateral DEFG is a rectangle. If m \\angle EFD = 2x-3 and m \\angle DFG = x+12, find m \\angle EFD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "51.000", "choices": [51.0, 55.0, 67.0, 102.0]}
+{"prob_id": "prob_51", "image_path": "images/img_1340.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "113.000", "choices": [90.0, 113.0, 123.0, 157.0]}
+{"prob_id": "prob_74", "image_path": "images/img_3559.png", "question": "\\triangle ABC \\sim \\triangle DEF. BG is a median of \\triangle ABC, and EH is a median of \\triangle DEF. Find EH if BC = 30, BG = 15, and EF = 15. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.500", "choices": [7.5, 15.0, 22.5, 30.0]}
+{"prob_id": "prob_87", "image_path": "images/img_883.png", "question": "If AB \\parallel DC, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [32.5, 65.0, 105.0, 115.0]}
+{"prob_id": "prob_89", "image_path": "images/img_3755.png", "question": "If RL = 5, RT = 9, and WS = 6, find RW. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.500", "choices": [5.4, 6.0, 6.6, 7.5]}
+{"prob_id": "prob_90", "image_path": "images/img_1226.png", "question": "Find XW. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [6.0, 12.0, 18.0, 24.0]}
+{"prob_id": "prob_94", "image_path": "images/img_121.png", "question": "If FGHJ is a kite, find m \\angle GFJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [72.0, 80.0, 128.0, 190.0]}
+{"prob_id": "prob_116", "image_path": "images/img_3692.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.500", "choices": [10.5, 12.0, 12.5, 14.0]}
+{"prob_id": "prob_138", "image_path": "images/img_3235.png", "question": "If ST = 8, TR = 4, and PT = 6, find QR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [6.0, 8.0, 9.0, 10.0]}
+{"prob_id": "prob_145", "image_path": "images/img_2934.png", "question": "Find AE if AB = 12, AC = 16, and ED = 5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [12.0, 15.0, 16.0, 20.0]}
+{"prob_id": "prob_156", "image_path": "images/img_401.png", "question": "In \\odot R, find TV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.439", "choices": [9.22, 11.0, 12.0, 18.44]}
+{"prob_id": "prob_171", "image_path": "images/img_3524.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.000", "choices": [1.0, 3.0, 5.0, 6.0]}
+{"prob_id": "prob_178", "image_path": "images/img_318.png", "question": "Find the area of the rectangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "129.904", "choices": [75.0, 112.5, 129.9, 225.0]}
+{"prob_id": "prob_182", "image_path": "images/img_947.png", "question": "Find the scale from B to B'. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.333", "choices": [0.75, 0.8333333333333334, 1.2, 1.3333333333333333]}
+{"prob_id": "prob_198", "image_path": "images/img_1783.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.600", "choices": [9.0, 9.6, 12.0, 14.4]}
+{"prob_id": "prob_210", "image_path": "images/img_966.png", "question": "Find x so that BE and AD are perpendicular. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [5.0, 10.0, 20.0, 30.0]}
+{"prob_id": "prob_234", "image_path": "images/img_293.png", "question": "Quadrilateral EFGH is a rectangle. If EF = 4x-6 and HG = x+3, find EF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 12.0, 18.0, 20.0]}
+{"prob_id": "prob_260", "image_path": "images/img_2667.png", "question": "Find the area of the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "264.000", "choices": [132.0, 264.0, 265.0, 528.0]}
+{"prob_id": "prob_269", "image_path": "images/img_1314.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "63.000", "choices": [31.5, 63.0, 126.0, 252.0]}
+{"prob_id": "prob_292", "image_path": "images/img_249.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "57.995", "choices": [21.0, 34.0, 58.0, 67.0]}
+{"prob_id": "prob_293", "image_path": "images/img_2312.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "76.000", "choices": [66.0, 68.0, 74.0, 76.0]}
+{"prob_id": "prob_296", "image_path": "images/img_3907.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.798", "choices": [5.656854249492381, 6.928203230275509, 8.0, 9.797958971132712]}
+{"prob_id": "prob_307", "image_path": "images/img_2189.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.416", "choices": [6.0, 8.485281374238571, 10.392304845413264, 13.416407864998739]}
+{"prob_id": "prob_323", "image_path": "images/img_2067.png", "question": "In \\odot P, m \\angle MPL = 65 and NP \\perp PL. Find m \\widehat NM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [25.0, 45.0, 65.0, 90.0]}
+{"prob_id": "prob_377", "image_path": "images/img_8.png", "question": "Find the area of the trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "132.000", "choices": [72.0, 132.0, 144.0, 192.0]}
+{"prob_id": "prob_392", "image_path": "images/img_931.png", "question": "In \\odot P, the radius is 2 inches, find the length of \\widehat RS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.538", "choices": [2.27, 3.91, 4.54, 7.82]}
+{"prob_id": "prob_394", "image_path": "images/img_1209.png", "question": "Find GH in the kite. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.209", "choices": [12.0, 15.0, 19.05255888325765, 19.209372712298546]}
+{"prob_id": "prob_397", "image_path": "images/img_3975.png", "question": "Express the ratio of \\cos A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.600", "choices": [0.6, 0.75, 0.8, 1.33]}
+{"prob_id": "prob_401", "image_path": "images/img_924.png", "question": "Find m \\angle CAD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.000", "choices": [22.0, 44.0, 66.0, 92.0]}
+{"prob_id": "prob_414", "image_path": "images/img_3714.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 3.0, 5.0, 6.0]}
+{"prob_id": "prob_490", "image_path": "images/img_3757.png", "question": "Find the scale factor from Q to Q'. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 3.0, 4.0, 5.0]}
+{"prob_id": "prob_494", "image_path": "images/img_2270.png", "question": "Find the variable of x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 7.0, 8.0, 9.0]}
+{"prob_id": "prob_506", "image_path": "images/img_2431.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.000", "choices": [16.0, 17.0, 18.0, 19.0]}
+{"prob_id": "prob_512", "image_path": "images/img_1546.png", "question": "Find the area of the trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "678.500", "choices": [506.0, 667.0, 678.5, 851.0]}
+{"prob_id": "prob_517", "image_path": "images/img_801.png", "question": "Find the area of the shaded sector. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.815", "choices": [0.9, 1.8, 10.8, 12.6]}
+{"prob_id": "prob_518", "image_path": "images/img_1604.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.660", "choices": [7.0710678118654755, 8.660254037844386, 21.213203435596427, 25.980762113533157]}
+{"prob_id": "prob_522", "image_path": "images/img_3209.png", "question": "Find PQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [3.0, 4.0, 6.0, 9.0]}
+{"prob_id": "prob_540", "image_path": "images/img_1765.png", "question": "In \\odot M, FL = 24, HJ = 48, and m \\widehat HP = 65. Find FG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.000", "choices": [24.0, 32.0, 48.0, 65.0]}
+{"prob_id": "prob_619", "image_path": "images/img_534.png", "question": "Find GI if GH = 9, GK = 6, and KJ = 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [6.0, 9.0, 12.0, 15.0]}
+{"prob_id": "prob_662", "image_path": "images/img_2737.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "45.000", "choices": [30.0, 45.0, 60.0, 90.0]}
+{"prob_id": "prob_697", "image_path": "images/img_664.png", "question": "JKLM is a rectangle. MLPR is a rhombus. m \\angle JMK = m \\angle RMP, m \\angle JMK = 55, and m \\angle MRP = 70. Find m \\angle KML. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [35.0, 70.0, 110.0, 140.0]}
+{"prob_id": "prob_700", "image_path": "images/img_731.png", "question": "m \\angle 4 = 101. Find the measure of \\angle 6. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "101.000", "choices": [69.0, 79.0, 89.0, 101.0]}
+{"prob_id": "prob_718", "image_path": "images/img_2717.png", "question": "Find the area of the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "168.000", "choices": [38.0, 84.0, 168.0, 336.0]}
+{"prob_id": "prob_737", "image_path": "images/img_1995.png", "question": "Find x if \\triangle JLM \\sim \\triangle QST. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.500", "choices": [1.5, 2.0, 3.0, 4.0]}
+{"prob_id": "prob_743", "image_path": "images/img_2503.png", "question": "Find the area of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.511", "choices": [3.76, 7.51, 13.84, 15.02]}
+{"prob_id": "prob_749", "image_path": "images/img_2983.png", "question": "Find x. Assume that any segment that appears to be tangent is tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [25.0, 27.5, 50.0, 105.0]}
+{"prob_id": "prob_772", "image_path": "images/img_3675.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.171", "choices": [4.61, 5.17, 6.52, 8.46]}
+{"prob_id": "prob_777", "image_path": "images/img_1402.png", "question": "Quadrilateral WXZY is a rectangle. Find the measure of \\angle 2 if m \\angle 1 = 30. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_799", "image_path": "images/img_2733.png", "question": "Find TQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [6.0, 7.0, 12.0, 18.0]}
+{"prob_id": "prob_823", "image_path": "images/img_3956.png", "question": "Each pair of polygons is similar. Find GF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.500", "choices": [7.5, 11.25, 20.7, 40.7]}
+{"prob_id": "prob_832", "image_path": "images/img_1757.png", "question": "The square is circumscribed to the circle. Find the exact circumference of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.982", "choices": [21.991148575128552, 43.982297150257104, 65.97344572538566, 87.96459430051421]}
+{"prob_id": "prob_837", "image_path": "images/img_285.png", "question": "Find QP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 3.0, 5.0, 6.0]}
+{"prob_id": "prob_857", "image_path": "images/img_2482.png", "question": "Find the length of \\widehat JK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.047", "choices": [0.52, 0.79, 1.05, 1.57]}
+{"prob_id": "prob_859", "image_path": "images/img_91.png", "question": "m \\angle 9 = 2x-4, m \\angle 10 = 2x+4. Find the measure of \\angle 10. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "94.000", "choices": [86.0, 94.0, 98.0, 104.0]}
+{"prob_id": "prob_869", "image_path": "images/img_1220.png", "question": "The diagonals of rhombus FGHJ intersect at K. If GH = x+9 and JH = 5x-2, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.750", "choices": [2.75, 3.0, 5.5, 9.0]}
+{"prob_id": "prob_918", "image_path": "images/img_3238.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [6.0, 9.0, 12.0, 15.0]}
+{"prob_id": "prob_932", "image_path": "images/img_171.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [3.0, 4.0, 5.0, 6.0]}
+{"prob_id": "prob_937", "image_path": "images/img_1355.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [25.0, 50.0, 60.0, 100.0]}
+{"prob_id": "prob_939", "image_path": "images/img_1301.png", "question": "Find m \\angle RST. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [55.0, 70.0, 75.0, 80.0]}
+{"prob_id": "prob_949", "image_path": "images/img_1544.png", "question": "Find XZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [5.0, 17.0, 18.0, 34.0]}
+{"prob_id": "prob_955", "image_path": "images/img_668.png", "question": "Find y so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "31.000", "choices": [31.0, 51.0, 93.0, 129.0]}
+{"prob_id": "prob_960", "image_path": "images/img_3830.png", "question": "Use parallelogram JKLM to find m \\angle JKL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [60.0, 70.0, 80.0, 90.0]}
+{"prob_id": "prob_984", "image_path": "images/img_1412.png", "question": "In \\triangle PQR, ST \\parallel RQ. If PS = 12.5, SR = 5, and PT = 15, find TQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [5.0, 6.0, 6.5, 12.5]}
+{"prob_id": "prob_995", "image_path": "images/img_1008.png", "question": "Cut four congruent triangles off the corners of a rectangle to make an octagon. What is the area of the octagon? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "528.000", "choices": [456.0, 528.0, 552.0, 564.0]}
+{"prob_id": "prob_1017", "image_path": "images/img_3381.png", "question": "Find KL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [4.0, 5.0, 12.0, 15.0]}
+{"prob_id": "prob_1020", "image_path": "images/img_423.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "41.569", "choices": [24.0, 33.941125496954285, 41.569219381653056, 48.0]}
+{"prob_id": "prob_1021", "image_path": "images/img_1240.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 4.0, 5.0, 9.0]}
+{"prob_id": "prob_1023", "image_path": "images/img_5.png", "question": "\\triangle LMN \\cong \\triangle QRS. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [10.0, 20.0, 40.0, 50.0]}
+{"prob_id": "prob_1035", "image_path": "images/img_191.png", "question": "In \\odot H, the diameter is 18, LM = 12, and m \\widehat LM = 84. Find HP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.708", "choices": [2.29, 3.35, 5.65, 6.71]}
+{"prob_id": "prob_1062", "image_path": "images/img_3143.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [20.0, 21.0, 24.0, 25.0]}
+{"prob_id": "prob_1065", "image_path": "images/img_295.png", "question": "Find m \\angle CAM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [14.0, 28.0, 36.0, 90.0]}
+{"prob_id": "prob_1068", "image_path": "images/img_1752.png", "question": "Find GD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [10.0, 12.0, 14.0, 20.0]}
+{"prob_id": "prob_1103", "image_path": "images/img_3892.png", "question": "For trapezoid QRTU, V and S are midpoints of the legs. If QR = 4 and UT = 16, find VS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [5.0, 9.0, 10.0, 12.0]}
+{"prob_id": "prob_1107", "image_path": "images/img_1796.png", "question": "Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 22.0, 25.0, 28.0]}
+{"prob_id": "prob_1143", "image_path": "images/img_1734.png", "question": "Find the area of the shaded region. Assume that the polygon is regular unless otherwise stated. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "216.584", "choices": [216.6, 282.9, 464.8, 819.6]}
+{"prob_id": "prob_1175", "image_path": "images/img_3285.png", "question": "m \\angle 1 = 123. Find the measure of \\angle 14. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "57.000", "choices": [47.0, 57.0, 67.0, 123.0]}
+{"prob_id": "prob_1187", "image_path": "images/img_3830.png", "question": "Use parallelogram JKLM to find m \\angle KJL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 40.0, 50.0, 60.0]}
+{"prob_id": "prob_1205", "image_path": "images/img_2944.png", "question": "Find the area of the trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "95.000", "choices": [80.0, 90.0, 95.0, 110.0]}
+{"prob_id": "prob_1227", "image_path": "images/img_3256.png", "question": "Find JL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [7.0, 11.0, 12.0, 14.0]}
+{"prob_id": "prob_1232", "image_path": "images/img_2395.png", "question": "If m \\widehat FE = 118, m \\widehat AB = 108, m \\angle EGB = 52, and m \\angle EFB = 30, find m \\widehat CF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.000", "choices": [30.0, 44.0, 108.0, 118.0]}
+{"prob_id": "prob_1267", "image_path": "images/img_2070.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "21.617", "choices": [5.0, 8.1, 10.3, 21.6]}
+{"prob_id": "prob_1268", "image_path": "images/img_1819.png", "question": "The diameters of \\odot A, \\odot B, and \\odot C are 10, 30 and 10 units, respectively. Find YW if AZ = CW and CW = 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 3.0, 10.0, 30.0]}
+{"prob_id": "prob_1278", "image_path": "images/img_926.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "58.905", "choices": [29.5, 58.9, 147.3, 589.0]}
+{"prob_id": "prob_1297", "image_path": "images/img_2537.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "57.158", "choices": [33.0, 46.66904755831214, 57.157676649772945, 73.79024325749306]}
+{"prob_id": "prob_1298", "image_path": "images/img_1288.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "552.000", "choices": [552.0, 575.0, 598.0, 720.0]}
+{"prob_id": "prob_1313", "image_path": "images/img_2397.png", "question": "Use parallelogram JKLM to find m \\angle KLM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "71.000", "choices": [71.0, 79.0, 81.0, 89.0]}
+{"prob_id": "prob_1334", "image_path": "images/img_3537.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.111", "choices": [6.5, 15.6, 22.1, 37.7]}
+{"prob_id": "prob_1338", "image_path": "images/img_3111.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [1.7320508075688772, 3.0, 5.196152422706632, 6.0]}
+{"prob_id": "prob_1343", "image_path": "images/img_3190.png", "question": "AB \\perp DC and GH \\perp FE. If \\triangle ACD \\sim \\triangle GEF, find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.200", "choices": [2.2, 3.6, 4.4, 6.3]}
+{"prob_id": "prob_1350", "image_path": "images/img_3255.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.785", "choices": [4.2, 4.8, 7.9, 16.9]}
+{"prob_id": "prob_1364", "image_path": "images/img_1819.png", "question": "The diameters of \\odot A, \\odot B, and \\odot C are 10, 30 and 10 units, respectively. Find ZX if AZ = CW and CW = 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 4.0, 5.0, 6.0]}
+{"prob_id": "prob_1401", "image_path": "images/img_3122.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.142", "choices": [1.4, 7.1, 14.1, 15.6]}
+{"prob_id": "prob_1402", "image_path": "images/img_1161.png", "question": "If pentagons ABCDE and PQRST are similar, find SR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.364", "choices": [1.8333333333333335, 4.363636363636363, 3.0, 14.666666666666666]}
+{"prob_id": "prob_1414", "image_path": "images/img_2682.png", "question": "parallelogram MNPQ with m \\angle M = 10x and m \\angle N = 20x, find m \\angle M. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 45.0, 60.0, 120.0]}
+{"prob_id": "prob_1418", "image_path": "images/img_3475.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "56.889", "choices": [35.2, 43.2, 53.5, 56.9]}
+{"prob_id": "prob_1420", "image_path": "images/img_2531.png", "question": "If PR \\parallel KL, KN = 9, LN = 16, and PM = 2 KP, find KM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [5.0, 9.0, 12.0, 15.0]}
+{"prob_id": "prob_1435", "image_path": "images/img_1085.png", "question": "Find m \\angle K. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "100.000", "choices": [6.0, 60.0, 100.0, 180.0]}
+{"prob_id": "prob_1439", "image_path": "images/img_1396.png", "question": "For the pair of similar figures, the area of the blue figure is 8 in^{2} and the green figure is 32 in^{2}, find the scale factor from the blue to the green figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.500", "choices": [0.25, 0.5, 2.0, 4.0]}
+{"prob_id": "prob_1451", "image_path": "images/img_3163.png", "question": "m \\angle 1 = 50 and m \\angle 3 = 60. Find the measure of \\angle 8. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [100.0, 110.0, 120.0, 130.0]}
+{"prob_id": "prob_1456", "image_path": "images/img_3760.png", "question": "Find the measure of \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "68.000", "choices": [52.0, 56.0, 60.0, 68.0]}
+{"prob_id": "prob_1467", "image_path": "images/img_3367.png", "question": "m \\angle 3 = 110 and m \\angle 12 = 55. Find the measure of \\angle 13. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [55.0, 65.0, 70.0, 110.0]}
+{"prob_id": "prob_1468", "image_path": "images/img_3876.png", "question": "Find m \\angle 5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [50.0, 110.0, 130.0, 150.0]}
+{"prob_id": "prob_1494", "image_path": "images/img_714.png", "question": "Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.100", "choices": [3.5, 4.1, 4.5, 5.1]}
+{"prob_id": "prob_1506", "image_path": "images/img_2370.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "71.000", "choices": [11.0, 31.0, 71.0, 133.0]}
+{"prob_id": "prob_1534", "image_path": "images/img_729.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.633", "choices": [5.0, 6.6332495807108, 10.0, 13.2664991614216]}
+{"prob_id": "prob_1539", "image_path": "images/img_2633.png", "question": "Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.250", "choices": [3.75, 5.0, 6.25, 8.75]}
+{"prob_id": "prob_1569", "image_path": "images/img_2447.png", "question": "What is \\cos B? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.385", "choices": [0.38, 0.42, 0.92, 2.4]}
+{"prob_id": "prob_1579", "image_path": "images/img_333.png", "question": "If PR \\parallel KL, KN = 9, LN = 16, PM = 2 KP, find MN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [7.0, 12.0, 15.0, 16.0]}
+{"prob_id": "prob_1588", "image_path": "images/img_642.png", "question": "Find ST. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.000", "choices": [7.0, 12.0, 19.0, 24.0]}
+{"prob_id": "prob_1610", "image_path": "images/img_724.png", "question": "Find x so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 8.0, 11.0, 19.0]}
+{"prob_id": "prob_1638", "image_path": "images/img_3617.png", "question": "Find m \\angle BGE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [60.0, 120.0, 240.0, 360.0]}
+{"prob_id": "prob_1639", "image_path": "images/img_3527.png", "question": "Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [30.0, 45.0, 60.0, 90.0]}
+{"prob_id": "prob_1648", "image_path": "images/img_3029.png", "question": "Find the length of \\widehat AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.774", "choices": [7.63, 9.77, 11.13, 14.83]}
+{"prob_id": "prob_1664", "image_path": "images/img_967.png", "question": "Find the measure of \\angle 2. Assume that segments that appear tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "157.500", "choices": [85.0, 157.5, 230.0, 315.0]}
+{"prob_id": "prob_1686", "image_path": "images/img_1966.png", "question": "Find \\sin S. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.600", "choices": [0.2, 0.4, 0.6, 0.8]}
+{"prob_id": "prob_1690", "image_path": "images/img_529.png", "question": "Find m \\angle 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "71.500", "choices": [51.0, 67.5, 71.5, 92.0]}
+{"prob_id": "prob_1705", "image_path": "images/img_1905.png", "question": "In \\odot T, ZV = 1, and TW = 13. Find XY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [5.0, 10.0, 12.0, 13.0]}
+{"prob_id": "prob_1734", "image_path": "images/img_1954.png", "question": "The segment is tangent to the circle. Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 3.0, 6.0, 9.0]}
+{"prob_id": "prob_1740", "image_path": "images/img_3578.png", "question": "In \\odot F, m \\angle DFA = 50 and CF \\perp FB. Find m \\widehat ACE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "230.000", "choices": [75.0, 115.0, 150.0, 230.0]}
+{"prob_id": "prob_1758", "image_path": "images/img_763.png", "question": "Use parallelogram ABCD to find m \\angle DAB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "101.000", "choices": [20.0, 59.0, 72.0, 101.0]}
+{"prob_id": "prob_1764", "image_path": "images/img_1416.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "163.000", "choices": [65.0, 132.0, 163.0, 180.0]}
+{"prob_id": "prob_1765", "image_path": "images/img_1452.png", "question": "m \\angle BAC = 38, BC = DC = 5, find m \\angle DAC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [5.0, 10.0, 38.0, 40.0]}
+{"prob_id": "prob_1772", "image_path": "images/img_3509.png", "question": "Find m \\angle W. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "108.000", "choices": [18.0, 27.0, 54.0, 108.0]}
+{"prob_id": "prob_1779", "image_path": "images/img_2333.png", "question": "Find the value of the variable y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [10.0, 20.0, 30.0, 70.0]}
+{"prob_id": "prob_1780", "image_path": "images/img_2631.png", "question": "The degree measure of \\widehat AC and \\widehat ADC are x and y respectively. If m \\angle ABC = 70, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "110.000", "choices": [90.0, 100.0, 110.0, 120.0]}
+{"prob_id": "prob_1812", "image_path": "images/img_2700.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "76.000", "choices": [70.0, 72.0, 76.0, 78.0]}
+{"prob_id": "prob_1813", "image_path": "images/img_229.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [7.0, 9.899494936611665, 12.12435565298214, 14.0]}
+{"prob_id": "prob_1868", "image_path": "images/img_2757.png", "question": "In rhombus ABCD, AB = 2x+3 and BC = 5x. Find AD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [1.0, 2.0, 4.0, 5.0]}
+{"prob_id": "prob_1898", "image_path": "images/img_2684.png", "question": "Find KL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [7.0, 8.0, 12.0, 15.0]}
+{"prob_id": "prob_1906", "image_path": "images/img_978.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "178.191", "choices": [89.1, 178.2, 252.0, 356.4]}
+{"prob_id": "prob_1914", "image_path": "images/img_3821.png", "question": "Find the measure of \\angle AFB on \\odot F with diameter AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "108.000", "choices": [72.0, 108.0, 120.0, 144.0]}
+{"prob_id": "prob_1934", "image_path": "images/img_3991.png", "question": "Quadrilateral ABCD is a rectangle. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [5.0, 12.0, 24.0, 25.0]}
+{"prob_id": "prob_1959", "image_path": "images/img_2523.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.536", "choices": [3.5355339059327378, 5.0, 7.0710678118654755, 10.0]}
+{"prob_id": "prob_1961", "image_path": "images/img_3250.png", "question": "Find m \\angle ABC if m \\angle CDA = 61. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "140.000", "choices": [55.0, 69.0, 85.0, 140.0]}
+{"prob_id": "prob_1972", "image_path": "images/img_1260.png", "question": "AB is a diameter, AC = 8 inches, and BC = 15 inches. Find the radius of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.500", "choices": [7.5, 8.0, 8.5, 17.0]}
+{"prob_id": "prob_2000", "image_path": "images/img_3322.png", "question": "Quadrilateral ABDC is a rectangle. m \\angle 2 = 40. Find m \\angle 8. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "100.000", "choices": [40.0, 50.0, 80.0, 100.0]}
+{"prob_id": "prob_2010", "image_path": "images/img_2456.png", "question": "Triangle LMN is equilateral, and MP bisects LN. Find the measure of MN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [9.0, 10.0, 11.0, 12.0]}
+{"prob_id": "prob_2027", "image_path": "images/img_2732.png", "question": "Find QS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [5.0, 15.0, 20.0, 25.0]}
+{"prob_id": "prob_2030", "image_path": "images/img_1745.png", "question": "In \\odot O, EC and AB are diameters, and m \\angle BOD = m \\angle DOE = m \\angle EOF = m \\angle FOA. Find m \\widehat AD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "135.000", "choices": [45.0, 135.0, 180.0, 360.0]}
+{"prob_id": "prob_2032", "image_path": "images/img_1740.png", "question": "Quadrilateral DEFG is a rectangle. If m \\angle EDF = 5x-3 and m \\angle DFG = 3x+7, find m \\angle EDF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [22.0, 45.0, 68.0, 90.0]}
+{"prob_id": "prob_2039", "image_path": "images/img_2304.png", "question": "Each pair of polygons is similar. Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 12.0, 15.0, 20.0]}
+{"prob_id": "prob_2045", "image_path": "images/img_3009.png", "question": "Find RS if \\triangle QRS is an equilateral triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [0.5, 1.0, 1.5, 2.0]}
+{"prob_id": "prob_2061", "image_path": "images/img_3708.png", "question": "Find the measure of the altitude drawn to the hypotenuse. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.928", "choices": [3.4641016151377544, 4.898979485566356, 6.928203230275509, 9.797958971132712]}
+{"prob_id": "prob_2065", "image_path": "images/img_2216.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "93.000", "choices": [35.0, 52.0, 77.0, 93.0]}
+{"prob_id": "prob_2070", "image_path": "images/img_527.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.748", "choices": [11.0, 15.556349186104047, 17.74823934929885, 25.553864678361276]}
+{"prob_id": "prob_2084", "image_path": "images/img_2751.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [2.0, 5.0, 6.0, 9.0]}
+{"prob_id": "prob_2116", "image_path": "images/img_982.png", "question": "EB \\parallel DC. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.500", "choices": [5.0, 7.5, 9.5, 10.0]}
+{"prob_id": "prob_2128", "image_path": "images/img_244.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.700", "choices": [35.7, 49.0, 71.4, 104.0]}
+{"prob_id": "prob_2141", "image_path": "images/img_566.png", "question": "Use parallelogram MNPR to find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [8.0, 20.0, 24.0, 32.0]}
+{"prob_id": "prob_2164", "image_path": "images/img_3891.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.433", "choices": [21.1, 22.4, 23.4, 42.2]}
+{"prob_id": "prob_2174", "image_path": "images/img_1335.png", "question": "Find y so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [11.0, 14.0, 77.0, 98.0]}
+{"prob_id": "prob_2180", "image_path": "images/img_3204.png", "question": "Find the length of \\widehat JK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.744", "choices": [6.87, 13.74, 20.62, 27.49]}
+{"prob_id": "prob_2191", "image_path": "images/img_2775.png", "question": "If m \\angle 5 = 7x-5 and m \\angle 4 = 2x+23, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [5.6, 18.0, 20.0, 22.0]}
+{"prob_id": "prob_2241", "image_path": "images/img_2932.png", "question": "Find m \\angle 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "33.000", "choices": [33.0, 43.0, 57.0, 123.0]}
+{"prob_id": "prob_2273", "image_path": "images/img_499.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [20.0, 30.0, 40.0, 50.0]}
+{"prob_id": "prob_2287", "image_path": "images/img_3110.png", "question": "Find AB if \\triangle ABC is an isosceles triangle with AB = BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [3.0, 4.0, 7.0, 11.0]}
+{"prob_id": "prob_2289", "image_path": "images/img_2360.png", "question": "If DB = 24, AE = 3, and EC = 18, find AD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [3.0, 4.0, 6.0, 8.0]}
+{"prob_id": "prob_2295", "image_path": "images/img_1851.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 4.5, 5.0, 6.0]}
+{"prob_id": "prob_2301", "image_path": "images/img_1143.png", "question": "In \\odot B, CE = 13.5. Find BD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.294", "choices": [3.71, 4.29, 4.53, 6.75]}
+{"prob_id": "prob_2342", "image_path": "images/img_3510.png", "question": "Find DE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [3.0, 4.0, 6.0, 9.0]}
+{"prob_id": "prob_2358", "image_path": "images/img_1477.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.730", "choices": [10.7, 19.6, 30.4, 50.0]}
+{"prob_id": "prob_2371", "image_path": "images/img_2048.png", "question": "Find z in the given parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.500", "choices": [4.0, 4.5, 5.0, 9.5]}
+{"prob_id": "prob_2385", "image_path": "images/img_810.png", "question": "For the pair of similar figures, the area of the blue figure is 36 yd^{2}, find the area of the green figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [9.0, 18.0, 72.0, 144.0]}
+{"prob_id": "prob_2394", "image_path": "images/img_3643.png", "question": "Circle J has a radius of 10 units, \\odot K has a radius of 8 units, and BC = 5.4 units. Find JK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.600", "choices": [12.6, 14.6, 20.6, 30.6]}
+{"prob_id": "prob_2417", "image_path": "images/img_1725.png", "question": "If \\triangle LMN \\sim \\triangle QRS, QR = 35, RS = 37, SQ = 12, and NL = 5, find the perimeter of \\triangle LMN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [35.0, 42.0, 63.0, 84.0]}
+{"prob_id": "prob_2424", "image_path": "images/img_1497.png", "question": "What is the area of \\parallelogram ABCD? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.000", "choices": [24.0, 30.0, 48.0, 60.0]}
+{"prob_id": "prob_2425", "image_path": "images/img_1809.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 4.0, 6.0, 7.0]}
+{"prob_id": "prob_2464", "image_path": "images/img_1745.png", "question": "In \\odot O, EC and AB are diameters, and m \\angle BOD = m \\angle DOE = m \\angle EOF = m \\angle FOA. Find m \\widehat AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 90.0, 180.0, 360.0]}
+{"prob_id": "prob_2472", "image_path": "images/img_3863.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [5.0, 7.0, 13.0, 14.0]}
+{"prob_id": "prob_2484", "image_path": "images/img_924.png", "question": "Find m \\angle ABC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [22.0, 24.0, 42.0, 44.0]}
+{"prob_id": "prob_2527", "image_path": "images/img_2240.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "123.000", "choices": [97.0, 99.0, 110.0, 123.0]}
+{"prob_id": "prob_2547", "image_path": "images/img_293.png", "question": "Quadrilateral EFGH is a rectangle. If FK = 32 feet, find EG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "64.000", "choices": [13.0, 30.0, 57.0, 64.0]}
+{"prob_id": "prob_2550", "image_path": "images/img_3051.png", "question": "Find m \\angle W. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "76.000", "choices": [38.0, 38.0, 76.0, 152.0]}
+{"prob_id": "prob_2588", "image_path": "images/img_2171.png", "question": "\\odot P \\cong \\odot Q. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [7.0, 11.0, 22.0, 44.0]}
+{"prob_id": "prob_2601", "image_path": "images/img_3107.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "180.000", "choices": [165.0, 180.0, 195.0, 210.0]}
+{"prob_id": "prob_2613", "image_path": "images/img_546.png", "question": "Find w in the given parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 4.0, 5.0, 13.0]}
+{"prob_id": "prob_2640", "image_path": "images/img_1825.png", "question": "Find m \\angle D. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [58.0, 64.0, 80.0, 82.0]}
+{"prob_id": "prob_2647", "image_path": "images/img_3965.png", "question": "Lines l, m, and n are perpendicular bisectors of \\triangle PQR and meet at T. If TQ = 2x, PT = 3y-1, and TR = 8, find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 4.0, 5.0, 6.0]}
+{"prob_id": "prob_2654", "image_path": "images/img_690.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.485", "choices": [1.4142135623730951, 4.242640687119286, 8.485281374238571, 12.727922061357857]}
+{"prob_id": "prob_2705", "image_path": "images/img_2242.png", "question": "\\triangle EFG is equilateral, and EH bisects \\angle E. Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [15.0, 30.0, 45.0, 60.0]}
+{"prob_id": "prob_2711", "image_path": "images/img_475.png", "question": "Find the measure of \\angle 1. Assume that segments that appear tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "129.000", "choices": [51.0, 78.0, 102.0, 129.0]}
+{"prob_id": "prob_2730", "image_path": "images/img_3367.png", "question": "m \\angle 3 = 110 and m \\angle 12 = 55. Find the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "110.000", "choices": [55.0, 110.0, 125.0, 135.0]}
+{"prob_id": "prob_2737", "image_path": "images/img_3643.png", "question": "Circle J has a radius of 10 units, \\odot K has a radius of 8 units, and BC = 5.4 units. Find CK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.600", "choices": [2.4, 2.6, 2.8, 4.0]}
+{"prob_id": "prob_2767", "image_path": "images/img_2364.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.777", "choices": [22.627416997969522, 27.712812921102035, 32.0, 35.77708763999664]}
+{"prob_id": "prob_2780", "image_path": "images/img_1846.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.180", "choices": [5.0, 8.660254037844386, 10.0, 11.180339887498949]}
+{"prob_id": "prob_2794", "image_path": "images/img_258.png", "question": "Find PS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [7.0, 9.0, 14.0, 16.0]}
+{"prob_id": "prob_2813", "image_path": "images/img_1689.png", "question": "Quadrilateral ABCD is a rhombus. If AB = 2x+3 and BC = x+7, find CD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [4.0, 11.0, 19.0, 20.0]}
+{"prob_id": "prob_2816", "image_path": "images/img_185.png", "question": "Use the Pythagorean Theorem to find the length of the hypotenuse. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.000", "choices": [5.0, 10.908712114635714, 12.0, 13.0]}
+{"prob_id": "prob_2822", "image_path": "images/img_1765.png", "question": "In \\odot M, FL = 24, HJ = 48, and m \\widehat HP = 65. Find NJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [24.0, 32.0, 48.0, 65.0]}
+{"prob_id": "prob_2826", "image_path": "images/img_3163.png", "question": "m \\angle 1 = 50 and m \\angle 3 = 60. Find the measure of \\angle 6. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [50.0, 60.0, 70.0, 80.0]}
+{"prob_id": "prob_2862", "image_path": "images/img_2379.png", "question": "\\triangle LMN \\cong \\triangle QRS. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 5.0, 7.0, 18.0]}
+{"prob_id": "prob_2863", "image_path": "images/img_2422.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.276", "choices": [3.4, 7.0, 8.1, 9.3]}
+{"prob_id": "prob_2871", "image_path": "images/img_1663.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "91.924", "choices": [65.0, 91.9, 112.6, 130.0]}
+{"prob_id": "prob_2907", "image_path": "images/img_2112.png", "question": "Find m \\widehat QTS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "248.000", "choices": [109.0, 212.0, 248.0, 254.0]}
+{"prob_id": "prob_2938", "image_path": "images/img_135.png", "question": "Find the area of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.383", "choices": [3.9, 11.7, 23.4, 46.8]}
+{"prob_id": "prob_3002", "image_path": "images/img_621.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.667", "choices": [1.6666666666666667, 2.3333333333333335, 4.0, 6.0]}
+{"prob_id": "prob_3010", "image_path": "images/img_3225.png", "question": "Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [5.5, 7.0, 8.0, 10.0]}
+{"prob_id": "prob_3011", "image_path": "images/img_2756.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "64.000", "choices": [60.0, 62.0, 64.0, 66.0]}
+{"prob_id": "prob_3025", "image_path": "images/img_1626.png", "question": "If IJ / XJ = HJ / YJ, m \\angle WXJ = 130 and m \\angle WZG = 20, find m \\angle J. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [40.0, 55.0, 60.0, 70.0]}
+{"prob_id": "prob_3037", "image_path": "images/img_2445.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.809", "choices": [18.8, 23.2, 25.9, 44.0]}
+{"prob_id": "prob_3070", "image_path": "images/img_3840.png", "question": "In RSTV, RS = 6, VT = 3 and RX is twice the length of XV. Find XY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [3.0, 4.0, 6.0, 9.0]}
+{"prob_id": "prob_3093", "image_path": "images/img_104.png", "question": "Each pair of polygons is similar. Find AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.600", "choices": [7.0, 7.6, 12.0, 19.0]}
+{"prob_id": "prob_3104", "image_path": "images/img_1989.png", "question": "Find the measure of \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "95.000", "choices": [85.0, 90.0, 95.0, 105.0]}
+{"prob_id": "prob_3124", "image_path": "images/img_712.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "27.440", "choices": [13.3, 20.99, 27.44, 49.5]}
+{"prob_id": "prob_3128", "image_path": "images/img_3774.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.205", "choices": [7.2, 8.0, 12.0, 15.0]}
+{"prob_id": "prob_3136", "image_path": "images/img_791.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.333", "choices": [10.0, 10.666666666666666, 13.333333333333334, 16.666666666666668]}
+{"prob_id": "prob_3153", "image_path": "images/img_3517.png", "question": "A square is inscribed in a circle of area 18\\pi square units. Find the length of a side of the square. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [3.0, 4.242640687119286, 6.0, 8.485281374238571]}
+{"prob_id": "prob_3158", "image_path": "images/img_2488.png", "question": "Find the scale factor from W to W'. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.333", "choices": [0.3333333333333333, 0.6666666666666666, 0.75, 1.5]}
+{"prob_id": "prob_3170", "image_path": "images/img_2381.png", "question": "What is the measure of \\angle B if m \\angle A = 10? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 35.0, 47.5, 90.0]}
+{"prob_id": "prob_3188", "image_path": "images/img_734.png", "question": "Find BC if AB = 6, AF = 8, BC = x, CD = y, DE = 2y-3, and FE = x+\\frac{10}{3}. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [9.0, 10.0, 13.3, 15.0]}
+{"prob_id": "prob_3203", "image_path": "images/img_483.png", "question": "Find x in the parallelogram. Area = 148 m^{2}. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.500", "choices": [17.5, 18.5, 19.5, 20.5]}
+{"prob_id": "prob_3243", "image_path": "images/img_3572.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.646", "choices": [2.6457513110645907, 4.242640687119286, 5.196152422706632, 7.348469228349534]}
+{"prob_id": "prob_3252", "image_path": "images/img_326.png", "question": "A square is inscribed in a circle having a radius of 6 inches. Find the length of the side of the square. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.485", "choices": [2.1213203435596424, 4.242640687119286, 8.485281374238571, 16.970562748477143]}
+{"prob_id": "prob_3258", "image_path": "images/img_3592.png", "question": "m \\angle 11 = 62 and m \\angle 14 = 38. Find the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [38.0, 42.0, 62.0, 80.0]}
+{"prob_id": "prob_3297", "image_path": "images/img_1420.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1440.000", "choices": [972.0, 1080.0, 1440.0, 2412.0]}
+{"prob_id": "prob_3328", "image_path": "images/img_1010.png", "question": "Find the measure of \\angle 7 if m \\angle 4 = m \\angle 5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "89.000", "choices": [63.0, 64.0, 69.0, 89.0]}
+{"prob_id": "prob_3365", "image_path": "images/img_1054.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.492", "choices": [7.745966692414834, 8.246211251235321, 15.491933384829668, 16.492422502470642]}
+{"prob_id": "prob_3372", "image_path": "images/img_1806.png", "question": "Find x for equilateral triangle SRT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [3.0, 6.0, 9.0, 12.0]}
+{"prob_id": "prob_3377", "image_path": "images/img_1390.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "108.000", "choices": [39.0, 84.0, 108.0, 129.0]}
+{"prob_id": "prob_3390", "image_path": "images/img_3155.png", "question": "\\angle 1 and \\angle 2 form a linear pair and m \\angle 2 = 67. Find the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "113.000", "choices": [67.0, 113.0, 123.0, 133.0]}
+{"prob_id": "prob_3396", "image_path": "images/img_153.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.440", "choices": [5.0, 6.0, 7.4, 10.0]}
+{"prob_id": "prob_3436", "image_path": "images/img_2936.png", "question": "\\triangle RSV \\cong \\triangle TVS. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [11.0, 11.5, 12.0, 12.5]}
+{"prob_id": "prob_3468", "image_path": "images/img_3311.png", "question": "\\triangle KLN and \\triangle LMN are isosceles and m \\angle JKN = 130. Find the measure of \\angle J. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "106.000", "choices": [105.0, 106.0, 108.0, 111.0]}
+{"prob_id": "prob_3479", "image_path": "images/img_613.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "315.000", "choices": [294.0, 315.0, 336.0, 357.0]}
+{"prob_id": "prob_3498", "image_path": "images/img_3686.png", "question": "Use a calculator to find the measure of \\angle J. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.005", "choices": [33.0, 40.0, 50.0, 57.0]}
+{"prob_id": "prob_3506", "image_path": "images/img_2526.png", "question": "AD is perpendicular to BC and AB is perpendicular to AC. What is BC? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [7.0710678118654755, 8.660254037844386, 20.0, 25.0]}
+{"prob_id": "prob_3545", "image_path": "images/img_1919.png", "question": "If ABCD is a rhombus, and m \\angle ABC = 70, what is m \\angle 1? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [45.0, 55.0, 70.0, 125.0]}
+{"prob_id": "prob_3569", "image_path": "images/img_3805.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_3581", "image_path": "images/img_2397.png", "question": "Use parallelogram JKLM to find m \\angle JML. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "109.000", "choices": [50.0, 71.0, 109.0, 144.0]}
+{"prob_id": "prob_3583", "image_path": "images/img_466.png", "question": "AB = DF. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [1.0, 2.0, 3.0, 4.0]}
+{"prob_id": "prob_3628", "image_path": "images/img_1860.png", "question": "Find x so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [2.0, 17.0, 34.0, 68.0]}
+{"prob_id": "prob_3638", "image_path": "images/img_1839.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 9.0, 12.25, 24.0]}
+{"prob_id": "prob_3664", "image_path": "images/img_1031.png", "question": "Express the ratio of \\cos P. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.471", "choices": [0.47, 0.53, 0.88, 1.88]}
+{"prob_id": "prob_3665", "image_path": "images/img_3296.png", "question": "m \\angle WXY = m \\angle TXY. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [2.0, 4.0, 5.0, 10.0]}
+{"prob_id": "prob_3668", "image_path": "images/img_2652.png", "question": "Use parallelogram PQRS to find QP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 5.0, 8.0, 15.0]}
+{"prob_id": "prob_3692", "image_path": "images/img_3746.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [1.8, 5.0, 46.0, 90.0]}
+{"prob_id": "prob_3705", "image_path": "images/img_2491.png", "question": "a = 14, b = 48, and c = 50, find \\cos A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.960", "choices": [0.14, 0.48, 0.5, 0.96]}
+{"prob_id": "prob_3738", "image_path": "images/img_2831.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.588", "choices": [9.0, 15.588457268119894, 18.0, 31.17691453623979]}
+{"prob_id": "prob_3760", "image_path": "images/img_1365.png", "question": "Find the measure of the altitude drawn to the hypotenuse. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.330", "choices": [14.0, 18.33030277982336, 24.0, 336.0]}
+{"prob_id": "prob_3821", "image_path": "images/img_3821.png", "question": "Find the measure of \\angle CFD on \\odot F with diameter AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "123.000", "choices": [115.0, 119.0, 120.0, 123.0]}
+{"prob_id": "prob_3885", "image_path": "images/img_1956.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [22.0, 44.0, 60.0, 120.0]}
+{"prob_id": "prob_3894", "image_path": "images/img_2466.png", "question": "Find JQ if Q is the incenter of \\triangle JLN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.795", "choices": [16.5, 18.79, 20.32, 25.5]}
+{"prob_id": "prob_3917", "image_path": "images/img_293.png", "question": "Quadrilateral EFGH is a rectangle. If m \\angle HGE = 13, find m \\angle FGE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "77.000", "choices": [13.0, 46.0, 57.0, 77.0]}
+{"prob_id": "prob_3919", "image_path": "images/img_1052.png", "question": "Find the area of the regular polygon figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "101.823", "choices": [12.7, 25.5, 101.8, 203.6]}
+{"prob_id": "prob_3935", "image_path": "images/img_1519.png", "question": "Trapezoid GHJK has an area of 75 square meters. Find the height. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [2.5, 3.0, 5.0, 7.5]}
+{"prob_id": "prob_3949", "image_path": "images/img_3612.png", "question": "Given the square. Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.971", "choices": [8.485281374238571, 16.970562748477143, 20.784609690826528, 24.0]}
+{"prob_id": "prob_3970", "image_path": "images/img_3418.png", "question": "\\triangle RST \\cong \\triangle ABC. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [8.0, 10.0, 13.0, 21.0]}
+{"prob_id": "prob_3984", "image_path": "images/img_514.png", "question": "Find m \\widehat JLK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "232.000", "choices": [116.0, 184.0, 232.0, 298.0]}
+{"prob_id": "prob_3987", "image_path": "images/img_2123.png", "question": "Find the measure of \\angle Z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "33.749", "choices": [29.1, 33.7, 56.3, 60.9]}
+{"prob_id": "prob_3992", "image_path": "images/img_3740.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.191", "choices": [19.5, 30.2, 60.4, 120.8]}
+{"prob_id": "prob_4026", "image_path": "images/img_986.png", "question": "m \\angle 1 = 4p+15, m \\angle 3 = 3p-10 and m \\angle 4 = 6r+5. Find the value of p. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [15.0, 20.0, 25.0, 30.0]}
+{"prob_id": "prob_4030", "image_path": "images/img_1156.png", "question": "Use parallelogram ABCD to find m \\angle AFD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "97.000", "choices": [3.0, 34.0, 49.0, 97.0]}
+{"prob_id": "prob_4032", "image_path": "images/img_342.png", "question": "\\triangle WXY \\cong \\triangle WXZ. Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [3.0, 4.0, 5.0, 7.0]}
+{"prob_id": "prob_4043", "image_path": "images/img_2380.png", "question": "Let GH be the median of trapezoid RSBA. Find GH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "62.000", "choices": [27.0, 54.0, 62.0, 86.0]}
+{"prob_id": "prob_4044", "image_path": "images/img_9.png", "question": "In rhombus ABCD, m \\angle DAB = 2 m \\angle ADC and CB = 6. Find m \\angle ADB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_4046", "image_path": "images/img_3682.png", "question": "m \\angle 2 = 2x, m \\angle 3 = x. Find m \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 45.0, 60.0, 90.0]}
+{"prob_id": "prob_4056", "image_path": "images/img_2974.png", "question": "Find m \\angle ABC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "51.000", "choices": [42.0, 51.0, 56.0, 148.0]}
+{"prob_id": "prob_4067", "image_path": "images/img_1743.png", "question": "Find the measure of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "33.000", "choices": [32.0, 33.0, 45.0, 55.0]}
+{"prob_id": "prob_4093", "image_path": "images/img_2554.png", "question": "Express the ratio of \\cos X. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.280", "choices": [0.28, 0.29, 0.96, 3.43]}
+{"prob_id": "prob_4144", "image_path": "images/img_1031.png", "question": "Express the ratio of \\sin P. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.882", "choices": [0.47, 0.53, 0.88, 1.88]}
+{"prob_id": "prob_4158", "image_path": "images/img_2343.png", "question": "\\angle ABC is intersected by parallel lines l and m. What is the measure of \\angle ABC? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "71.000", "choices": [33.0, 38.0, 61.0, 71.0]}
+{"prob_id": "prob_4187", "image_path": "images/img_2961.png", "question": "Find m \\angle A of quadrilateral ABCD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "135.000", "choices": [45.0, 90.0, 135.0, 180.0]}
+{"prob_id": "prob_4188", "image_path": "images/img_3531.png", "question": "Find DE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [4.0, 6.0, 7.0, 10.0]}
+{"prob_id": "prob_4216", "image_path": "images/img_1494.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.077", "choices": [4.358898943540674, 5.0, 13.076696830622023, 14.0]}
+{"prob_id": "prob_4227", "image_path": "images/img_661.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.500", "choices": [14.4, 18.0, 22.5, 24.0]}
+{"prob_id": "prob_4233", "image_path": "images/img_1967.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.200", "choices": [9.2, 10.2, 11.2, 12.2]}
+{"prob_id": "prob_4238", "image_path": "images/img_1408.png", "question": "Find m \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [28.0, 38.0, 52.0, 62.0]}
+{"prob_id": "prob_4250", "image_path": "images/img_1562.png", "question": "Find x so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [1.0, 2.0, 3.0, 4.0]}
+{"prob_id": "prob_4251", "image_path": "images/img_3150.png", "question": "ABCD \\sim AEFG. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [2.0, 3.0, 5.0, 6.0]}
+{"prob_id": "prob_4255", "image_path": "images/img_1345.png", "question": "Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.000", "choices": [23.0, 24.0, 25.0, 27.0]}
+{"prob_id": "prob_4258", "image_path": "images/img_2218.png", "question": "Find the area of the regular polygon figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "64.952", "choices": [10.8, 21.7, 65.0, 129.9]}
+{"prob_id": "prob_4267", "image_path": "images/img_3005.png", "question": "Find the area of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "285.000", "choices": [256.5, 285.0, 389.5, 405.0]}
+{"prob_id": "prob_4285", "image_path": "images/img_2980.png", "question": "MC = 7, RM = 4, and AT = 16. Find MS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.500", "choices": [2.0, 3.5, 4.0, 7.0]}
+{"prob_id": "prob_4310", "image_path": "images/img_3135.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.667", "choices": [0.21428571428571427, 4.666666666666667, 12.0, 16.0]}
+{"prob_id": "prob_4325", "image_path": "images/img_1197.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.583", "choices": [2.0, 5.6, 7.6, 8.0]}
+{"prob_id": "prob_4338", "image_path": "images/img_3781.png", "question": "If XN = 6, XM = 2, and XY = 10, find NZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [12.0, 16.0, 24.0, 32.0]}
+{"prob_id": "prob_4343", "image_path": "images/img_3251.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [10.0, 20.0, 30.0, 42.0]}
+{"prob_id": "prob_4348", "image_path": "images/img_2757.png", "question": "In rhombus ABCD, AB = 2x+3 and BC = 5x. Find m \\angle AEB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 60.0, 90.0, 180.0]}
+{"prob_id": "prob_4357", "image_path": "images/img_2456.png", "question": "Triangle LMN is equilateral, and MP bisects LN. Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [15.0, 16.0, 17.0, 18.0]}
+{"prob_id": "prob_4380", "image_path": "images/img_1163.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.000", "choices": [1.0, 2.0, 3.0, 4.0]}
+{"prob_id": "prob_4402", "image_path": "images/img_3885.png", "question": "The rectangle is inscribed into the circle. Find the exact circumference of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "31.416", "choices": [25.132741228718345, 31.41592653589793, 50.26548245743669, 62.83185307179586]}
+{"prob_id": "prob_4403", "image_path": "images/img_531.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 6.0, 8.0, 16.0]}
+{"prob_id": "prob_4433", "image_path": "images/img_2325.png", "question": "Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "39.000", "choices": [39.0, 42.0, 48.0, 51.0]}
+{"prob_id": "prob_4471", "image_path": "images/img_547.png", "question": "UJ = 9, VJ = 3, and ZT = 18. Find SV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [3.0, 6.0, 9.0, 12.0]}
+{"prob_id": "prob_4480", "image_path": "images/img_1103.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 40.0, 50.0, 60.0]}
+{"prob_id": "prob_4483", "image_path": "images/img_1260.png", "question": "AB is a diameter, AC = 8 inches, and BC = 15 inches. Find the circumference of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "53.407", "choices": [26.703537555513243, 47.12388980384689, 50.26548245743669, 53.40707511102649]}
+{"prob_id": "prob_4485", "image_path": "images/img_1257.png", "question": "Find h in the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [11.0, 15.556349186104047, 19.05255888325765, 22.0]}
+{"prob_id": "prob_4522", "image_path": "images/img_2491.png", "question": "a = 14, b = 48, and c = 50, find \\sin A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.280", "choices": [0.14, 0.28, 0.48, 0.5]}
+{"prob_id": "prob_4532", "image_path": "images/img_2567.png", "question": "Find the area of the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "132.000", "choices": [33.0, 66.0, 132.0, 264.0]}
+{"prob_id": "prob_4555", "image_path": "images/img_3624.png", "question": "Find m \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "66.000", "choices": [38.0, 60.0, 66.0, 72.0]}
+{"prob_id": "prob_4565", "image_path": "images/img_3170.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "69.755", "choices": [69.0, 69.8, 76.4, 77.2]}
+{"prob_id": "prob_4568", "image_path": "images/img_910.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "74.000", "choices": [56.0, 68.0, 74.0, 84.0]}
+{"prob_id": "prob_4577", "image_path": "images/img_2326.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.392", "choices": [1.7320508075688772, 6.0, 10.392304845413264, 18.0]}
+{"prob_id": "prob_4591", "image_path": "images/img_2611.png", "question": "Find the value of t in the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [6.0, 7.0, 8.0, 13.0]}
+{"prob_id": "prob_4605", "image_path": "images/img_1553.png", "question": "GH = KJ. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [27.0, 54.0, 55.0, 83.0]}
+{"prob_id": "prob_4633", "image_path": "images/img_60.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "68.000", "choices": [68.0, 78.0, 79.0, 136.0]}
+{"prob_id": "prob_4635", "image_path": "images/img_422.png", "question": "Find the value of m \\angle FCE if line p \\parallel line q. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "105.000", "choices": [105.0, 110.0, 115.0, 120.0]}
+{"prob_id": "prob_4636", "image_path": "images/img_2998.png", "question": "Find m \\angle B. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "61.000", "choices": [29.0, 58.0, 61.0, 122.0]}
+{"prob_id": "prob_4638", "image_path": "images/img_1814.png", "question": "m \\angle 12 = 64. Find the measure of \\angle 7. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "64.000", "choices": [54.0, 64.0, 74.0, 84.0]}
+{"prob_id": "prob_4643", "image_path": "images/img_23.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [10.0, 17.32050807568877, 20.0, 30.0]}
+{"prob_id": "prob_4693", "image_path": "images/img_2816.png", "question": "For trapezoid QRST, A and B are midpoints of the legs. Find m \\angle S. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "135.000", "choices": [45.0, 60.0, 120.0, 135.0]}
+{"prob_id": "prob_4733", "image_path": "images/img_1334.png", "question": "AC is a diagonal of rhombus ABCD. If m \\angle CDE is 116, what is m \\angle ACD? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "58.000", "choices": [58.0, 90.0, 116.0, 180.0]}
+{"prob_id": "prob_4774", "image_path": "images/img_3318.png", "question": "In rhombus LMPQ, m \\angle QLM = 2x^{2}-10, m \\angle QPM = 8x, and MP = 10. Find the perimeter of LMPQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [10.0, 40.0, 70.0, 140.0]}
+{"prob_id": "prob_4803", "image_path": "images/img_2776.png", "question": "Find the measure of JK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "31.000", "choices": [15.5, 31.0, 62.0, 124.0]}
+{"prob_id": "prob_4807", "image_path": "images/img_1141.png", "question": "The area of trapezoid JKLM is 138 square feet. The area of trapezoid QTSR is 5.52 square feet. If trapezoid JKLM \\sim trapezoid QTSR, find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.000", "choices": [0.2, 1.0, 25.0, 125.0]}
+{"prob_id": "prob_4848", "image_path": "images/img_1918.png", "question": "Find m \\angle R. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "58.000", "choices": [58.0, 60.0, 122.0, 124.0]}
+{"prob_id": "prob_4878", "image_path": "images/img_1362.png", "question": "Find the value of the variable t. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 4.0, 5.0, 6.0]}
+{"prob_id": "prob_4881", "image_path": "images/img_2099.png", "question": "Find BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [6.0, 9.0, 15.0, 60.0]}
+{"prob_id": "prob_4913", "image_path": "images/img_1402.png", "question": "Quadrilateral WXZY is a rectangle. Find the measure of \\angle 5 if m \\angle 1 = 30. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [15.0, 30.0, 45.0, 60.0]}
+{"prob_id": "prob_4942", "image_path": "images/img_1010.png", "question": "Find the measure of \\angle 3 if m \\angle 4 = m \\angle 5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "116.000", "choices": [116.0, 126.0, 136.0, 146.0]}
+{"prob_id": "prob_4947", "image_path": "images/img_960.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.240", "choices": [9.0, 9.6, 10.2, 10.8]}
+{"prob_id": "prob_4955", "image_path": "images/img_2420.png", "question": "Find m \\angle 2 if m \\widehat BC = 30 and m \\widehat AD = 20. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "155.000", "choices": [20.0, 25.0, 30.0, 155.0]}
+{"prob_id": "prob_4965", "image_path": "images/img_1204.png", "question": "Circle O has a radius of 13 inches. Radius OB is perpendicular to chord CD which is 24 inches long. Find OX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 12.0, 13.0, 26.0]}
+{"prob_id": "prob_4978", "image_path": "images/img_1156.png", "question": "Use parallelogram ABCD to find m \\angle CDF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.000", "choices": [34.0, 43.0, 47.0, 77.0]}
+{"prob_id": "prob_4985", "image_path": "images/img_3322.png", "question": "Quadrilateral ABDC is a rectangle. m \\angle 2 = 40. Find m \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [10.0, 40.0, 50.0, 90.0]}
+{"prob_id": "prob_5004", "image_path": "images/img_600.png", "question": "Find the area of \\parallelogram JKLM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [12.0, 22.4, 24.0, 48.0]}
+{"prob_id": "prob_5021", "image_path": "images/img_3806.png", "question": "AD and CG are diameters of \\odot B. Find m \\widehat AG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [35.0, 40.0, 45.0, 55.0]}
+{"prob_id": "prob_5025", "image_path": "images/img_3189.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.215", "choices": [15.1, 30.2, 60.4, 912.9]}
+{"prob_id": "prob_5028", "image_path": "images/img_83.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [1.0, 2.0, 4.0, 8.0]}
+{"prob_id": "prob_5031", "image_path": "images/img_2961.png", "question": "Find m \\angle C of quadrilateral ABCD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 90.0, 135.0, 180.0]}
+{"prob_id": "prob_5039", "image_path": "images/img_172.png", "question": "Equilateral pentagon PQRST is inscribed in \\odot U. Find m \\angle PSR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "72.000", "choices": [36.0, 72.0, 120.0, 144.0]}
+{"prob_id": "prob_5065", "image_path": "images/img_1349.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.500", "choices": [9.5, 10.5, 12.5, 13.5]}
+{"prob_id": "prob_5102", "image_path": "images/img_3031.png", "question": "The area of the shaded region is 66 cm^{2}. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.964", "choices": [4.6, 6.5, 13.0, 26.0]}
+{"prob_id": "prob_5109", "image_path": "images/img_727.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 6.5, 7.0, 7.5]}
+{"prob_id": "prob_5112", "image_path": "images/img_1764.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "528.000", "choices": [428.0, 528.0, 572.0, 624.0]}
+{"prob_id": "prob_5122", "image_path": "images/img_2865.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.857", "choices": [5.13, 5.46, 15.96, 43.86]}
+{"prob_id": "prob_5138", "image_path": "images/img_2544.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.000", "choices": [23.0, 30.0, 67.0, 90.0]}
+{"prob_id": "prob_5140", "image_path": "images/img_500.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [24.0, 56.0, 65.0, 115.0]}
+{"prob_id": "prob_5148", "image_path": "images/img_1962.png", "question": "If AB = 12, AC = 16, and ED = 5, find AE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [10.0, 12.0, 15.0, 16.0]}
+{"prob_id": "prob_5171", "image_path": "images/img_925.png", "question": "Find BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [4.0, 6.0, 7.0, 8.0]}
+{"prob_id": "prob_5211", "image_path": "images/img_2346.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.063", "choices": [7.1, 14.1, 22.1, 30.0]}
+{"prob_id": "prob_5227", "image_path": "images/img_3112.png", "question": "Find XY of isosceles \\triangle XYZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [2.0, 7.0, 8.0, 14.0]}
+{"prob_id": "prob_5240", "image_path": "images/img_2756.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "207.846", "choices": [120.0, 124.7, 207.8, 240.0]}
+{"prob_id": "prob_5245", "image_path": "images/img_3404.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [6.0, 8.0, 12.0, 15.0]}
+{"prob_id": "prob_5254", "image_path": "images/img_3811.png", "question": "In \\odot Z, m \\angle WZX = m \\angle XZY, m \\angle VZU = 4x, m \\angle UZY = 2x+24, and VY and WU are diameters. Find m \\widehat WUX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "308.000", "choices": [52.0, 104.0, 154.0, 308.0]}
+{"prob_id": "prob_5276", "image_path": "images/img_1353.png", "question": "Use parallelogram JKLM to find m \\angle KJL if JK = 2b+3 and JM = 3a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 70.0, 80.0, 100.0]}
+{"prob_id": "prob_5280", "image_path": "images/img_1402.png", "question": "Quadrilateral WXZY is a rectangle. Find the measure of \\angle 3 if m \\angle 1 = 30. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 45.0, 60.0, 90.0]}
+{"prob_id": "prob_5287", "image_path": "images/img_1999.png", "question": "Trapezoid GHJK has an area of 188.35 square feet. Find GK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "26.799", "choices": [5.1, 21.6, 22.8, 26.8]}
+{"prob_id": "prob_5309", "image_path": "images/img_3781.png", "question": "If XM = 4, XN = 6, and NZ = 9, find XY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [4.0, 6.0, 9.0, 10.0]}
+{"prob_id": "prob_5347", "image_path": "images/img_2444.png", "question": "Find m \\angle 9. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [60.0, 120.0, 240.0, 300.0]}
+{"prob_id": "prob_5354", "image_path": "images/img_2734.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.722", "choices": [8.5, 12.020815280171309, 14.722431864335457, 17.0]}
+{"prob_id": "prob_5370", "image_path": "images/img_3018.png", "question": "In \\triangle DEF, m \\angle E = 108, m \\angle F = 26, and f = 20. Find d. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.819", "choices": [26.0, 32.82, 60.0, 65.0]}
+{"prob_id": "prob_5374", "image_path": "images/img_743.png", "question": "Chords AC and DF are equidistant from the center. If the radius of \\odot G is 26, find AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.000", "choices": [5.0, 10.0, 13.0, 48.0]}
+{"prob_id": "prob_5381", "image_path": "images/img_576.png", "question": "Circles G, J, and K all intersect at L. If GH = 10, find JL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 10.0, 10.0, 25.0]}
+{"prob_id": "prob_5394", "image_path": "images/img_3566.png", "question": "In \\odot S, m \\widehat PQR = 98. Find m \\widehat PQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "49.000", "choices": [45.0, 49.0, 90.0, 98.0]}
+{"prob_id": "prob_5399", "image_path": "images/img_251.png", "question": "If CE = t-2. EB = t+1, CD = 2, and CA = 10, find CE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.000", "choices": [1.0, 2.0, 3.0, 4.0]}
+{"prob_id": "prob_5409", "image_path": "images/img_1747.png", "question": "Find \\cos C. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.800", "choices": [0.6, 0.75, 0.8, 1.25]}
+{"prob_id": "prob_5453", "image_path": "images/img_1949.png", "question": "Find m \\angle A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_5456", "image_path": "images/img_1406.png", "question": "Find x. Area = 357 in^{2}. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "21.000", "choices": [21.0, 22.0, 23.0, 24.0]}
+{"prob_id": "prob_5496", "image_path": "images/img_281.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [30.0, 35.0, 70.0, 140.0]}
+{"prob_id": "prob_5502", "image_path": "images/img_804.png", "question": "Find x in the given parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [38.0, 75.0, 76.0, 109.0]}
+{"prob_id": "prob_5514", "image_path": "images/img_54.png", "question": "Find BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 8.0, 12.0, 16.0]}
+{"prob_id": "prob_5515", "image_path": "images/img_2249.png", "question": "\\triangle BCD \\cong \\triangle WXY. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 3.0, 4.0, 5.0]}
+{"prob_id": "prob_5520", "image_path": "images/img_2278.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.639", "choices": [8.0, 10.16, 10.24, 16.64]}
+{"prob_id": "prob_5530", "image_path": "images/img_587.png", "question": "The perimeter of this polygon is 60 centimeters. Find the length of the side of the polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [12.0, 15.0, 30.0, 60.0]}
+{"prob_id": "prob_5546", "image_path": "images/img_908.png", "question": "Find the area of the shaded region formed by the circle and regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "76.395", "choices": [76.4, 237.8, 266.6, 314.2]}
+{"prob_id": "prob_5548", "image_path": "images/img_523.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 3.0, 4.0, 6.0]}
+{"prob_id": "prob_5571", "image_path": "images/img_3021.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [11.0, 12.0, 13.0, 14.0]}
+{"prob_id": "prob_5598", "image_path": "images/img_1992.png", "question": "In regular hexagon UVWXYZ. Find WY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.785", "choices": [12.0, 14.696938456699067, 20.784609690826528, 36.0]}
+{"prob_id": "prob_5610", "image_path": "images/img_851.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "53.000", "choices": [37.0, 45.0, 53.0, 63.0]}
+{"prob_id": "prob_5618", "image_path": "images/img_1204.png", "question": "Circle O has a radius of 13 inches. Radius OB is perpendicular to chord CD which is 24 inches long. If m \\widehat CD = 134, find m \\widehat CB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "67.000", "choices": [24.0, 33.0, 67.0, 134.0]}
+{"prob_id": "prob_5630", "image_path": "images/img_881.png", "question": "Find EG if G is the incenter of \\triangle ABC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [4.0, 5.0, 12.0, 13.0]}
+{"prob_id": "prob_5634", "image_path": "images/img_3411.png", "question": "m \\angle 9 = 75. Find the measure of \\angle 6. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "105.000", "choices": [75.0, 85.0, 95.0, 105.0]}
+{"prob_id": "prob_5637", "image_path": "images/img_1284.png", "question": "In \\odot X, AB = CD = 30, and m \\widehat CZ = 40. Find m \\widehat CD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [30.0, 40.0, 60.0, 80.0]}
+{"prob_id": "prob_5657", "image_path": "images/img_3992.png", "question": "Find the area of the shaded sector. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "182.605", "choices": [24.3, 91.3, 182.6, 524.3]}
+{"prob_id": "prob_5669", "image_path": "images/img_2593.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.321", "choices": [6.928203230275509, 10.392304845413264, 13.856406460551018, 17.32050807568877]}
+{"prob_id": "prob_5697", "image_path": "images/img_2281.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [30.0, 34.0, 60.0, 68.0]}
+{"prob_id": "prob_5743", "image_path": "images/img_2823.png", "question": "If LK = 4, MP = 3, PQ = 6, KJ = 2, RS = 6, and LP = 2, find JH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [2.0, 3.0, 4.0, 6.0]}
+{"prob_id": "prob_5758", "image_path": "images/img_982.png", "question": "EB \\parallel DC. Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.500", "choices": [5.0, 7.5, 9.5, 10.0]}
+{"prob_id": "prob_5769", "image_path": "images/img_557.png", "question": "Find the measure of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "76.000", "choices": [49.0, 55.0, 57.0, 76.0]}
+{"prob_id": "prob_5785", "image_path": "images/img_2784.png", "question": "Use parallelogram ABCD to find m \\angle ADC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "128.000", "choices": [42.0, 52.0, 72.0, 128.0]}
+{"prob_id": "prob_5793", "image_path": "images/img_1821.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.899", "choices": [3.4641016151377544, 4.0, 4.898979485566356, 6.0]}
+{"prob_id": "prob_5813", "image_path": "images/img_1907.png", "question": "Find the measure of \\widehat YXZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "166.000", "choices": [145.0, 166.0, 194.0, 215.0]}
+{"prob_id": "prob_5823", "image_path": "images/img_3450.png", "question": "HK and IG are diameters of \\odot L. Find m \\widehat IHJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "270.000", "choices": [59.0, 135.0, 270.0, 301.0]}
+{"prob_id": "prob_5833", "image_path": "images/img_2962.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.695", "choices": [3.9, 11.8, 28.7, 30.7]}
+{"prob_id": "prob_5850", "image_path": "images/img_3664.png", "question": "If WXYZ is a kite, find WP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.472", "choices": [4.47213595499958, 16.0, 20.0, 36.0]}
+{"prob_id": "prob_5886", "image_path": "images/img_1096.png", "question": "Use rectangle LMNP, parallelogram LKMJ. If LN = 10, LJ = 2x+1, and PJ = 3x-1, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 4.0, 5.0, 10.0]}
+{"prob_id": "prob_5900", "image_path": "images/img_2802.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "97.529", "choices": [97.53, 103.0, 108.0, 113.0]}
+{"prob_id": "prob_5914", "image_path": "images/img_2057.png", "question": "CP is an altitude, CQ is the angle bisector of \\angle ACB, and R is the midpoint of AB. Find m \\angle ACQ if m \\angle ACB = 123-x and m \\angle QCB = 42+x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [40.0, 45.0, 50.0, 55.0]}
+{"prob_id": "prob_5980", "image_path": "images/img_1024.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "144.000", "choices": [25.0, 50.0, 72.0, 144.0]}
+{"prob_id": "prob_5988", "image_path": "images/img_955.png", "question": "In \\odot P, JK = 10 and m \\widehat JLK = 134. Find m \\widehat JL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "67.000", "choices": [46.0, 67.0, 92.0, 134.0]}
+{"prob_id": "prob_5991", "image_path": "images/img_256.png", "question": "m \\angle 3 = 43. Find the measure of \\angle 11. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.000", "choices": [43.0, 53.0, 63.0, 137.0]}
+{"prob_id": "prob_5997", "image_path": "images/img_1765.png", "question": "In \\odot M, FL = 24, HJ = 48, and m \\widehat HP = 65. Find m \\widehat HJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "130.000", "choices": [65.0, 120.0, 130.0, 155.0]}
+{"prob_id": "prob_6007", "image_path": "images/img_695.png", "question": "Find BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.000", "choices": [5.0, 9.0, 12.0, 13.0]}
+{"prob_id": "prob_6014", "image_path": "images/img_9.png", "question": "In rhombus ABCD, m \\angle DAB = 2 m \\angle ADC and CB = 6. Find m \\angle ACD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [45.0, 60.0, 90.0, 180.0]}
+{"prob_id": "prob_6056", "image_path": "images/img_3728.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.856", "choices": [11.313708498984761, 13.856406460551018, 16.0, 24.0]}
+{"prob_id": "prob_6057", "image_path": "images/img_2304.png", "question": "Each pair of polygons is similar. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [8.0, 12.0, 15.0, 20.0]}
+{"prob_id": "prob_6079", "image_path": "images/img_3292.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "52.547", "choices": [49.5, 52.5, 55.5, 58.5]}
+{"prob_id": "prob_6129", "image_path": "images/img_3000.png", "question": "Find the perimeter of \\triangle BCD, if \\triangle BCD \\sim \\triangle FDE, CD = 12, FD = 5, FE = 4, and DE = 8. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.500", "choices": [21.3, 25.5, 29.8, 34.0]}
+{"prob_id": "prob_6130", "image_path": "images/img_366.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "78.000", "choices": [32.0, 39.0, 46.0, 78.0]}
+{"prob_id": "prob_6164", "image_path": "images/img_534.png", "question": "Find KJ if GJ = 8, GH = 12, and HI = 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 4.0, 6.0, 8.0]}
+{"prob_id": "prob_6172", "image_path": "images/img_3688.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 90.0, 180.0, 360.0]}
+{"prob_id": "prob_6189", "image_path": "images/img_620.png", "question": "Use a Pythagorean Triple to find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [66.0, 68.0, 70.0, 72.0]}
+{"prob_id": "prob_6192", "image_path": "images/img_866.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 120.0, 240.0]}
+{"prob_id": "prob_6202", "image_path": "images/img_2144.png", "question": "ABCD is a rhombus. If PB = 12, AB = 15, and m \\angle ABD = 24. Find m \\angle BDA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [24.0, 55.0, 90.0, 120.0]}
+{"prob_id": "prob_6203", "image_path": "images/img_2288.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [8.0, 9.0, 12.0, 15.0]}
+{"prob_id": "prob_6226", "image_path": "images/img_1716.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.856", "choices": [3.4641016151377544, 6.928203230275509, 10.392304845413264, 13.856406460551018]}
+{"prob_id": "prob_6229", "image_path": "images/img_2899.png", "question": "Find h in the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [4.62, 5.66, 6.93, 8.0]}
+{"prob_id": "prob_6249", "image_path": "images/img_1402.png", "question": "Quadrilateral WXZY is a rectangle. Find the measure of \\angle 6 if m \\angle 1 = 30. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 45.0, 60.0, 90.0]}
+{"prob_id": "prob_6259", "image_path": "images/img_3744.png", "question": "Find the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "109.000", "choices": [54.5, 90.0, 109.0, 218.0]}
+{"prob_id": "prob_6266", "image_path": "images/img_1777.png", "question": "Find CD if AC = x-3, BE = 20, AB = 16, and CD = x+5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [32.0, 35.0, 36.0, 40.0]}
+{"prob_id": "prob_6279", "image_path": "images/img_2680.png", "question": "Find the measure of \\angle A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "41.810", "choices": [33.7, 41.8, 48.2, 56.3]}
+{"prob_id": "prob_6281", "image_path": "images/img_25.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.500", "choices": [37.5, 47.0, 52.5, 133.0]}
+{"prob_id": "prob_6293", "image_path": "images/img_1066.png", "question": "Tangent MP is drawn to \\odot O. Find x if MO = 20. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [5.0, 8.94427190999916, 12.0, 16.0]}
+{"prob_id": "prob_6297", "image_path": "images/img_2855.png", "question": "KL is tangent to \\odot M at K. Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.450", "choices": [6.0, 9.45, 18.9, 37.8]}
+{"prob_id": "prob_6303", "image_path": "images/img_1396.png", "question": "For the pair of similar figures, the area of the blue figure is 8 in^{2} and the green figure is 32 in^{2}, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [1.0, 2.0, 8.0, 16.0]}
+{"prob_id": "prob_6313", "image_path": "images/img_1391.png", "question": "QT bisects \\angle SQR. If m \\angle SQR = 6x+8 and m \\angle TQR = 4x-14, find m \\angle SQT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "58.000", "choices": [18.0, 32.0, 36.0, 58.0]}
+{"prob_id": "prob_6334", "image_path": "images/img_424.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.274", "choices": [9.4, 18.8, 28.3, 37.7]}
+{"prob_id": "prob_6343", "image_path": "images/img_3038.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [14.0, 24.24871130596428, 28.0, 42.0]}
+{"prob_id": "prob_6347", "image_path": "images/img_3934.png", "question": "Find the area of the trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "180.000", "choices": [45.0, 90.0, 180.0, 360.0]}
+{"prob_id": "prob_6356", "image_path": "images/img_566.png", "question": "Use parallelogram MNPR to find m \\angle MNP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "71.000", "choices": [33.0, 38.0, 71.0, 109.0]}
+{"prob_id": "prob_6393", "image_path": "images/img_848.png", "question": "Use parallelogram ABCD to find AD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [6.0, 12.0, 18.0, 30.0]}
+{"prob_id": "prob_6423", "image_path": "images/img_1122.png", "question": "Find x in the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.000", "choices": [37.0, 41.0, 78.0, 115.0]}
+{"prob_id": "prob_6427", "image_path": "images/img_2928.png", "question": "m \\angle 4 = 2y+32 and m \\angle 5 = 3y-3. Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [18.0, 35.0, 55.0, 72.0]}
+{"prob_id": "prob_6429", "image_path": "images/img_1626.png", "question": "If IJ / XJ = HJ / YJ, m \\angle WXJ = 130 and m \\angle WZG = 20, find m \\angle YIZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [40.0, 50.0, 65.0, 110.0]}
+{"prob_id": "prob_6432", "image_path": "images/img_1800.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.400", "choices": [0.8, 1.0, 1.4, 1.6]}
+{"prob_id": "prob_6434", "image_path": "images/img_347.png", "question": "Find the measure of \\angle 2 if AB \\perp BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "68.000", "choices": [64.0, 68.0, 72.0, 76.0]}
+{"prob_id": "prob_6440", "image_path": "images/img_1739.png", "question": "Find m \\angle H. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "97.000", "choices": [97.0, 102.0, 107.0, 122.0]}
+{"prob_id": "prob_6442", "image_path": "images/img_943.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [30.0, 35.0, 45.0, 85.0]}
+{"prob_id": "prob_6452", "image_path": "images/img_763.png", "question": "Use parallelogram ABCD to find m \\angle ACD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.000", "choices": [20.0, 29.0, 49.0, 59.0]}
+{"prob_id": "prob_6457", "image_path": "images/img_606.png", "question": "m \\angle 1 = 58, m \\angle 2 = 47, and m \\angle 3 = 26. Find the measure of \\angle 9. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "49.000", "choices": [39.0, 47.0, 49.0, 58.0]}
+{"prob_id": "prob_6468", "image_path": "images/img_418.png", "question": "Point D is the center of the circle. What is m \\angle ABC? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [30.0, 45.0, 60.0, 90.0]}
+{"prob_id": "prob_6473", "image_path": "images/img_2593.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [4.0, 6.0, 8.0, 10.0]}
+{"prob_id": "prob_6479", "image_path": "images/img_2009.png", "question": "Find x if AE = 3, AB = 2, BC = 6, and ED = 2x-3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [5.0, 6.0, 8.0, 9.0]}
+{"prob_id": "prob_6481", "image_path": "images/img_594.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.000", "choices": [22.0, 40.0, 44.0, 48.0]}
+{"prob_id": "prob_6515", "image_path": "images/img_154.png", "question": "Find x so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.000", "choices": [13.0, 26.0, 39.0, 52.0]}
+{"prob_id": "prob_6530", "image_path": "images/img_2031.png", "question": "P is the incenter of \\triangle AEC. Find m \\angle DEP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.500", "choices": [28.5, 30.0, 31.0, 33.0]}
+{"prob_id": "prob_6531", "image_path": "images/img_1063.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 7.0710678118654755, 8.660254037844386, 10.0]}
+{"prob_id": "prob_6556", "image_path": "images/img_114.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.414", "choices": [17.4, 22.1, 22.3, 45.9]}
+{"prob_id": "prob_6561", "image_path": "images/img_347.png", "question": "Find the measure of \\angle 3 if AB \\perp BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "76.000", "choices": [64.0, 68.0, 72.0, 76.0]}
+{"prob_id": "prob_6587", "image_path": "images/img_2823.png", "question": "If LK = 4, MP = 3, PQ = 6, KJ = 2, RS = 6, and LP = 2, find ML. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 3.0, 4.0, 6.0]}
+{"prob_id": "prob_6594", "image_path": "images/img_172.png", "question": "Equilateral pentagon PQRST is inscribed in \\odot U. Find m \\widehat QR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "72.000", "choices": [36.0, 72.0, 120.0, 144.0]}
+{"prob_id": "prob_6596", "image_path": "images/img_2382.png", "question": "Find m \\angle JKL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.000", "choices": [35.0, 37.0, 53.0, 73.0]}
+{"prob_id": "prob_6620", "image_path": "images/img_2011.png", "question": "Find WR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [6.0, 8.0, 10.0, 12.0]}
+{"prob_id": "prob_6640", "image_path": "images/img_2191.png", "question": "For trapezoid TRSV, M and N are midpoints of the legs. If TR = 32 and MN = 25, find VS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [18.0, 36.0, 50.0, 64.0]}
+{"prob_id": "prob_6666", "image_path": "images/img_2868.png", "question": "Find BD if BF bisects \\angle ABC and AC \\parallel ED, BA = 6, BC = 7.5, AC = 9, and DE = 9. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.500", "choices": [12.0, 13.5, 15.0, 18.0]}
+{"prob_id": "prob_6678", "image_path": "images/img_2651.png", "question": "The diameter of \\odot S is 30 units, the diameter of \\odot R is 20 units, and DS = 9 units. Find RC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 6.0, 9.0, 12.0]}
+{"prob_id": "prob_6733", "image_path": "images/img_706.png", "question": "Circle A has diameters DF and PG. If DF = 10, find DA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 10.0, 20.0, 25.0]}
+{"prob_id": "prob_6747", "image_path": "images/img_2868.png", "question": "Find CF if BF bisects \\angle ABC and AC \\parallel ED, BA = 6, BC = 7.5, AC = 9, and DE = 9. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 4.5, 5.0, 7.5]}
+{"prob_id": "prob_6780", "image_path": "images/img_1819.png", "question": "The diameters of \\odot A, \\odot B, and \\odot C are 10, 30 and 10 units, respectively. Find AC if AZ = CW and CW = 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [2.0, 10.0, 30.0, 34.0]}
+{"prob_id": "prob_6827", "image_path": "images/img_3882.png", "question": "Find AD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.500", "choices": [5.5, 6.0, 7.5, 9.0]}
+{"prob_id": "prob_6864", "image_path": "images/img_2638.png", "question": "If the area of the rhombus is 169 square millimeters, what is x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.000", "choices": [6.5, 13.0, 26.0, 52.0]}
+{"prob_id": "prob_6880", "image_path": "images/img_2314.png", "question": "Quadrilateral WXYZ is inscribed in \\odot V. Find m \\angle X. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [85.0, 95.0, 115.0, 120.0]}
+{"prob_id": "prob_6887", "image_path": "images/img_2067.png", "question": "In \\odot P, m \\angle MPL = 65 and NP \\perp PL. Find m \\widehat NJK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "155.000", "choices": [25.0, 75.0, 90.0, 155.0]}
+{"prob_id": "prob_6918", "image_path": "images/img_432.png", "question": "In \\odot F, FH = FL and FK = 17. Find JG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [15.0, 16.0, 17.0, 30.0]}
+{"prob_id": "prob_6923", "image_path": "images/img_3872.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [5.0, 6.0, 7.0, 8.0]}
+{"prob_id": "prob_6937", "image_path": "images/img_1585.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 4.0, 5.0, 6.0]}
+{"prob_id": "prob_6948", "image_path": "images/img_3393.png", "question": "Find m \\widehat LP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "150.000", "choices": [114.0, 144.0, 150.0, 156.0]}
+{"prob_id": "prob_6986", "image_path": "images/img_1745.png", "question": "In \\odot O, EC and AB are diameters, and m \\angle BOD = m \\angle DOE = m \\angle EOF = m \\angle FOA. Find m \\widehat AE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 90.0, 180.0, 360.0]}
+{"prob_id": "prob_6988", "image_path": "images/img_3214.png", "question": "Find the height of the parallelogram given its area with 2000 square units. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [30.0, 40.0, 50.0, 60.0]}
+{"prob_id": "prob_7014", "image_path": "images/img_576.png", "question": "Circles G, J, and K all intersect at L. If GH = 10, find FH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [5.0, 10.0, 20.0, 25.0]}
+{"prob_id": "prob_7024", "image_path": "images/img_835.png", "question": "For trapezoid ABDC, S and T are midpoints of the legs. If AB = x+4, CD = 3x+2, and ST = 9, find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [3.0, 5.0, 7.0, 9.0]}
+{"prob_id": "prob_7049", "image_path": "images/img_3322.png", "question": "Quadrilateral ABDC is a rectangle. If m \\angle 1 = 38, find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "52.000", "choices": [33.0, 38.0, 52.0, 87.0]}
+{"prob_id": "prob_7071", "image_path": "images/img_1943.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.321", "choices": [5.0, 10.0, 17.32050807568877, 20.0]}
+{"prob_id": "prob_7077", "image_path": "images/img_678.png", "question": "Find m \\widehat XZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "88.000", "choices": [56.0, 68.0, 88.0, 92.0]}
+{"prob_id": "prob_7105", "image_path": "images/img_1595.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.583", "choices": [3.4641016151377544, 4.123105625617661, 4.58257569495584, 5.385164807134504]}
+{"prob_id": "prob_7119", "image_path": "images/img_1853.png", "question": "In \\triangle PQR, ZQ = 3a-11, ZP = a+5, PY = 2c-1, YR = 4c-11, m \\angle PRZ = 4b-17, m \\angle ZRQ = 3b-4, m \\angle QYR = 7b+6, and m \\angle PXR = 2a+10. If RZ is an angle bisector, find m \\angle PRZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [20.0, 25.0, 30.0, 35.0]}
+{"prob_id": "prob_7128", "image_path": "images/img_2351.png", "question": "Find the side length DE in isosceles triangle DEF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [2.0, 8.0, 11.0, 20.0]}
+{"prob_id": "prob_7135", "image_path": "images/img_3776.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.167", "choices": [10.285714285714286, 14.0, 15.833333333333334, 16.166666666666668]}
+{"prob_id": "prob_7156", "image_path": "images/img_942.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [60.0, 80.0, 90.0, 120.0]}
+{"prob_id": "prob_7159", "image_path": "images/img_788.png", "question": "Quadrilateral ABCD is inscribed in \\odot Z such that m \\angle BZA = 104, m \\widehat CB = 94, and AB \\parallel DC. Find m \\angle ZAC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [9.0, 36.0, 94.0, 144.0]}
+{"prob_id": "prob_7165", "image_path": "images/img_1789.png", "question": "Find the perimeter of \\triangle RUW if \\triangle RUW \\sim \\triangle STV, ST = 24, VS = 12, VT = 18 and UW = 21. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "63.000", "choices": [63.0, 68.0, 70.0, 75.0]}
+{"prob_id": "prob_7166", "image_path": "images/img_2980.png", "question": "MC = 7, RM = 4, and AT = 16. Find MB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [6.0, 8.0, 10.0, 12.0]}
+{"prob_id": "prob_7188", "image_path": "images/img_945.png", "question": "GJ is a diameter of \\odot K. Find m \\widehat GLJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "180.000", "choices": [90.0, 120.0, 180.0, 360.0]}
+{"prob_id": "prob_7204", "image_path": "images/img_699.png", "question": "If AE = m-2, EC = m+4, AD = 4, and AB = 20, find m. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [3.0, 4.0, 5.0, 6.0]}
+{"prob_id": "prob_7218", "image_path": "images/img_3834.png", "question": "If c = 5, find a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.500", "choices": [2.5, 5.0, 7.5, 10.0]}
+{"prob_id": "prob_7237", "image_path": "images/img_835.png", "question": "For trapezoid ABDC, S and T are midpoints of the legs. If CD = 14, ST = 10, and AB = 2x, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 3.0, 10.0, 14.0]}
+{"prob_id": "prob_7242", "image_path": "images/img_474.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.265", "choices": [12.6, 25.1, 48.0, 50.27]}
+{"prob_id": "prob_7246", "image_path": "images/img_2224.png", "question": "A regular polygon is inscribed in a circle. Find the measure of the central angle \\angle KRL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_7248", "image_path": "images/img_101.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 8.0, 10.0, 12.0]}
+{"prob_id": "prob_7254", "image_path": "images/img_2502.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.641", "choices": [34.6, 36.0, 40.0, 48.0]}
+{"prob_id": "prob_7282", "image_path": "images/img_442.png", "question": "Find m \\angle Z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "110.000", "choices": [80.0, 108.0, 110.0, 112.0]}
+{"prob_id": "prob_7295", "image_path": "images/img_3174.png", "question": "Find the value of the variable y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [30.0, 50.0, 60.0, 80.0]}
+{"prob_id": "prob_7304", "image_path": "images/img_821.png", "question": "Find a, if FG = 18, GH = 42, and FK = 15. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "57.000", "choices": [15.0, 18.0, 42.0, 57.0]}
+{"prob_id": "prob_7306", "image_path": "images/img_3059.png", "question": "Find m \\angle H. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "31.000", "choices": [26.0, 31.0, 62.0, 88.0]}
+{"prob_id": "prob_7315", "image_path": "images/img_3038.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [14.0, 24.24871130596428, 28.0, 34.29285639896449]}
+{"prob_id": "prob_7323", "image_path": "images/img_974.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "95.247", "choices": [80.49844718999243, 95.24704719832526, 119.39849245279439, 129.79984591670362]}
+{"prob_id": "prob_7331", "image_path": "images/img_2267.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 8.0, 10.0, 12.0]}
+{"prob_id": "prob_7349", "image_path": "images/img_3539.png", "question": "Find the value of the variable x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "54.000", "choices": [36.0, 54.0, 60.0, 108.0]}
+{"prob_id": "prob_7363", "image_path": "images/img_2250.png", "question": "Find m \\angle RCM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.000", "choices": [27.0, 43.0, 47.0, 67.0]}
+{"prob_id": "prob_7365", "image_path": "images/img_3997.png", "question": "\\angle 6 and \\angle 8 are complementary, m \\angle 8 = 47. Find the measure of \\angle 7. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [43.0, 47.0, 86.0, 90.0]}
+{"prob_id": "prob_7379", "image_path": "images/img_201.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [25.0, 40.0, 65.0, 115.0]}
+{"prob_id": "prob_7402", "image_path": "images/img_1690.png", "question": "Find the area of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "54.000", "choices": [27.0, 36.0, 54.0, 108.0]}
+{"prob_id": "prob_7419", "image_path": "images/img_547.png", "question": "UJ = 9, VJ = 3, and ZT = 18. Find SJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [3.0, 6.0, 9.0, 12.0]}
+{"prob_id": "prob_7443", "image_path": "images/img_3900.png", "question": "BD bisects \\angle ABF. If m \\angle FBC = 2x+25 and m \\angle ABF = 10x-1, find m \\angle DBF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "64.500", "choices": [25.5, 50.0, 54.0, 64.5]}
+{"prob_id": "prob_7448", "image_path": "images/img_1356.png", "question": "Find x so that line m \\parallel line n. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [10.0, 20.0, 31.0, 40.0]}
+{"prob_id": "prob_7462", "image_path": "images/img_3603.png", "question": "Find a in the given parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [2.0, 8.0, 9.0, 10.0]}
+{"prob_id": "prob_7472", "image_path": "images/img_3740.png", "question": "Find the circumference of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.478", "choices": [18.6, 19.5, 37.7, 39.0]}
+{"prob_id": "prob_7473", "image_path": "images/img_1949.png", "question": "Find m \\angle B. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_7500", "image_path": "images/img_3501.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.889", "choices": [11.313708498984761, 13.856406460551018, 17.88854381999832, 21.166010488516726]}
+{"prob_id": "prob_7536", "image_path": "images/img_2841.png", "question": "Find the perimeter of \\triangle DEF, if \\triangle DEF \\sim \\triangle CBF, perimeter of \\triangle CBF = 27, DF = 3, and FC = 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.250", "choices": [20.25, 21.0, 27.0, 36.0]}
+{"prob_id": "prob_7549", "image_path": "images/img_2770.png", "question": "Find y so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 16.0, 20.0, 24.0]}
+{"prob_id": "prob_7553", "image_path": "images/img_974.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.697", "choices": [6.0, 7.348469228349534, 12.0, 14.696938456699067]}
+{"prob_id": "prob_7554", "image_path": "images/img_3610.png", "question": "Find \\sin N. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.923", "choices": [0.38, 0.42, 0.92, 2.4]}
+{"prob_id": "prob_7557", "image_path": "images/img_2740.png", "question": "Express the ratio of \\tan L. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.417", "choices": [0.38, 0.42, 0.92, 2.4]}
+{"prob_id": "prob_7561", "image_path": "images/img_1583.png", "question": "Find x so that line a \\parallel line b. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [2.5, 14.0, 15.0, 16.0]}
+{"prob_id": "prob_7586", "image_path": "images/img_1590.png", "question": "Find m \\angle S. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [28.0, 30.0, 32.0, 34.0]}
+{"prob_id": "prob_7601", "image_path": "images/img_3952.png", "question": "Find \\tan X. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.400", "choices": [0.4166666666666667, 0.9230769230769231, 1.4166666666666667, 2.4]}
+{"prob_id": "prob_7633", "image_path": "images/img_1602.png", "question": "Find the measure of \\angle T. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "21.801", "choices": [21.8, 23.6, 66.4, 68.2]}
+{"prob_id": "prob_7645", "image_path": "images/img_1903.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.657", "choices": [4.0, 5.656854249492381, 6.928203230275509, 8.0]}
+{"prob_id": "prob_7699", "image_path": "images/img_2560.png", "question": "m \\angle 4 = 42. Find m \\angle 7. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "138.000", "choices": [42.0, 48.0, 132.0, 138.0]}
+{"prob_id": "prob_7726", "image_path": "images/img_814.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.000", "choices": [22.0, 32.0, 40.0, 42.0]}
+{"prob_id": "prob_7731", "image_path": "images/img_2137.png", "question": "m \\widehat AC = 160 and m \\angle BEC = 38. What is m \\angle AEB? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "42.000", "choices": [42.0, 61.0, 80.0, 84.0]}
+{"prob_id": "prob_7741", "image_path": "images/img_46.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [12.0, 16.0, 51.0, 65.0]}
+{"prob_id": "prob_7742", "image_path": "images/img_562.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [3.0, 4.0, 5.0, 6.0]}
+{"prob_id": "prob_7746", "image_path": "images/img_628.png", "question": "Find TX if EX = 24 and DE = 7. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.000", "choices": [7.0, 24.0, 25.0, 32.0]}
+{"prob_id": "prob_7757", "image_path": "images/img_298.png", "question": "PQRS is a rhombus inscribed in a circle. Find m \\widehat SP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [30.0, 45.0, 60.0, 90.0]}
+{"prob_id": "prob_7776", "image_path": "images/img_3904.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.500", "choices": [22.5, 23.0, 23.5, 24.0]}
+{"prob_id": "prob_7807", "image_path": "images/img_2859.png", "question": "Find x so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 5.0, 12.0, 18.0]}
+{"prob_id": "prob_7826", "image_path": "images/img_584.png", "question": "\\triangle JKL \\sim \\triangle WYZ. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "21.000", "choices": [13.0, 21.0, 32.0, 44.0]}
+{"prob_id": "prob_7829", "image_path": "images/img_1131.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.500", "choices": [7.5, 10.0, 12.5, 15.0]}
+{"prob_id": "prob_7837", "image_path": "images/img_254.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.166", "choices": [8.082903768654761, 16.165807537309522, 24.24871130596428, 28.0]}
+{"prob_id": "prob_7845", "image_path": "images/img_3784.png", "question": "XY and XZ are midsegments of \\triangle RST. Find ST. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [7.0, 13.0, 14.0, 20.0]}
+{"prob_id": "prob_7852", "image_path": "images/img_3610.png", "question": "Solve for \\cos N. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.385", "choices": [0.38, 0.42, 0.92, 2.4]}
+{"prob_id": "prob_7881", "image_path": "images/img_1305.png", "question": "Quadrilateral WXYZ is a rectangle. If ZP = 4x-9 and PY = 2x+5, find ZX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [9.0, 10.0, 19.0, 38.0]}
+{"prob_id": "prob_7905", "image_path": "images/img_803.png", "question": "Find the length of \\widehat ZY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.854", "choices": [3.93, 6.0, 7.85, 15.71]}
+{"prob_id": "prob_7915", "image_path": "images/img_3258.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.000", "choices": [0.5, 1.0, 1.5, 2.0]}
+{"prob_id": "prob_7918", "image_path": "images/img_3943.png", "question": "Find the perimeter of \\triangle WZX, if \\triangle WZX \\sim \\triangle SRT, ST = 6, WX = 5, and the perimeter of \\triangle SRT = 15. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.500", "choices": [12.5, 13.0, 15.0, 18.0]}
+{"prob_id": "prob_7942", "image_path": "images/img_2313.png", "question": "The segment is tangent to the circle. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [16.0, 18.0, 30.0, 34.0]}
+{"prob_id": "prob_7995", "image_path": "images/img_452.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.777", "choices": [5.8, 6.5, 14.2, 44.3]}
+{"prob_id": "prob_8005", "image_path": "images/img_442.png", "question": "Find m \\angle Y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [80.0, 108.0, 110.0, 114.0]}
+{"prob_id": "prob_8008", "image_path": "images/img_3377.png", "question": "In \\triangle CDF, K is the centroid and DK = 16. Find CD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [9.0, 12.0, 18.0, 18.0]}
+{"prob_id": "prob_8022", "image_path": "images/img_3288.png", "question": "For the pair of similar figures, the area of the blue figure is 400 mm^{2} and the green figure is 64 mm^{2}, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [6.4, 16.0, 100.0, 250.0]}
+{"prob_id": "prob_8029", "image_path": "images/img_3610.png", "question": "Determine \\tan M. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.417", "choices": [0.38, 0.42, 0.92, 2.4]}
+{"prob_id": "prob_8087", "image_path": "images/img_1089.png", "question": "Find the area of the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "136.000", "choices": [68.0, 136.0, 272.0, 544.0]}
+{"prob_id": "prob_8131", "image_path": "images/img_1838.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.500", "choices": [3.5, 7.0, 10.5, 21.0]}
+{"prob_id": "prob_8136", "image_path": "images/img_412.png", "question": "\\triangle ABC \\sim \\triangle FDG. Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [8.0, 10.0, 12.0, 15.0]}
+{"prob_id": "prob_8152", "image_path": "images/img_1210.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "157.080", "choices": [104.7, 157.1, 235.6, 314.2]}
+{"prob_id": "prob_8160", "image_path": "images/img_981.png", "question": "Find m \\angle VXW. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [25.0, 65.0, 115.0, 180.0]}
+{"prob_id": "prob_8163", "image_path": "images/img_3589.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.091", "choices": [22.045407685048602, 44.090815370097204, 54.0, 62.35382907247958]}
+{"prob_id": "prob_8172", "image_path": "images/img_3675.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.746", "choices": [4.88, 5.96, 6.75, 8.42]}
+{"prob_id": "prob_8177", "image_path": "images/img_2900.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.798", "choices": [3.4641016151377544, 4.898979485566356, 6.928203230275509, 9.797958971132712]}
+{"prob_id": "prob_8207", "image_path": "images/img_1788.png", "question": "Square ABDC is inscribed in \\odot K. Find the measure of the central angle \\angle CFD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 60.0, 90.0, 180.0]}
+{"prob_id": "prob_8214", "image_path": "images/img_3201.png", "question": "Find the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [25.0, 55.0, 65.0, 75.0]}
+{"prob_id": "prob_8215", "image_path": "images/img_3874.png", "question": "Find the perimeter of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.731", "choices": [5.84, 6.65, 8.21, 8.73]}
+{"prob_id": "prob_8251", "image_path": "images/img_1584.png", "question": "The segment is tangent to the circle. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.485", "choices": [7.5, 8.5, 9.2, 13.0]}
+{"prob_id": "prob_8269", "image_path": "images/img_2250.png", "question": "Find m \\angle NCL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [60.0, 120.0, 240.0, 360.0]}
+{"prob_id": "prob_8270", "image_path": "images/img_3034.png", "question": "Use parallelogram WXYZ to find m \\angle XYZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "105.000", "choices": [30.0, 75.0, 105.0, 180.0]}
+{"prob_id": "prob_8277", "image_path": "images/img_3590.png", "question": "Q is the centroid and BE = 9. Find BQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [3.0, 6.0, 9.0, 12.0]}
+{"prob_id": "prob_8290", "image_path": "images/img_566.png", "question": "Use parallelogram MNPR to find m \\angle RNP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [38.0, 52.0, 52.0, 62.0]}
+{"prob_id": "prob_8294", "image_path": "images/img_3586.png", "question": "Find QM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [4.0, 8.0, 12.0, 16.0]}
+{"prob_id": "prob_8310", "image_path": "images/img_167.png", "question": "Use parallelogram to find b. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [7.0, 11.0, 21.0, 33.0]}
+{"prob_id": "prob_8311", "image_path": "images/img_3039.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [12.0, 15.0, 18.0, 21.0]}
+{"prob_id": "prob_8330", "image_path": "images/img_2056.png", "question": "Polygon ABCD \\sim polygon AEFG, m \\angle AGF = 108, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26. Find m \\angle ADC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "108.000", "choices": [14.0, 72.0, 108.0, 120.0]}
+{"prob_id": "prob_8360", "image_path": "images/img_3682.png", "question": "m \\angle 2 = 2x, m \\angle 3 = x. Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 45.0, 60.0, 90.0]}
+{"prob_id": "prob_8398", "image_path": "images/img_3795.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [7.0, 9.0, 12.0, 15.0]}
+{"prob_id": "prob_8422", "image_path": "images/img_703.png", "question": "Find m \\angle MPQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "101.000", "choices": [45.0, 56.0, 79.0, 101.0]}
+{"prob_id": "prob_8428", "image_path": "images/img_1193.png", "question": "Find the measure of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [23.0, 24.0, 28.0, 33.0]}
+{"prob_id": "prob_8438", "image_path": "images/img_3820.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "125.000", "choices": [55.0, 115.0, 125.0, 135.0]}
+{"prob_id": "prob_8439", "image_path": "images/img_606.png", "question": "m \\angle 1 = 58, m \\angle 2 = 47, and m \\angle 3 = 26. Find the measure of \\angle 5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "47.000", "choices": [43.0, 47.0, 58.0, 73.0]}
+{"prob_id": "prob_8448", "image_path": "images/img_1535.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "169.741", "choices": [56.6, 138.6, 169.7, 196.0]}
+{"prob_id": "prob_8486", "image_path": "images/img_2478.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "79.000", "choices": [21.0, 27.0, 52.0, 79.0]}
+{"prob_id": "prob_8503", "image_path": "images/img_1524.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.806", "choices": [6.0, 8.0, 10.0, 12.806248474865697]}
+{"prob_id": "prob_8507", "image_path": "images/img_3163.png", "question": "m \\angle 1 = 50 and m \\angle 3 = 60. Find the measure of \\angle 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [40.0, 50.0, 60.0, 70.0]}
+{"prob_id": "prob_8515", "image_path": "images/img_2996.png", "question": "The two polygons are similar. Find UT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.500", "choices": [12.0, 20.5, 22.5, 35.0]}
+{"prob_id": "prob_8530", "image_path": "images/img_3803.png", "question": "Find PT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.667", "choices": [6.0, 6.666666666666667, 7.0, 7.333333333333333]}
+{"prob_id": "prob_8543", "image_path": "images/img_335.png", "question": "Find the area of the trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2256.000", "choices": [191.5, 1128.0, 2256.0, 4512.0]}
+{"prob_id": "prob_8548", "image_path": "images/img_2928.png", "question": "m \\angle 3 = x-12 and m \\angle 6 = 72. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "84.000", "choices": [6.0, 18.0, 72.0, 84.0]}
+{"prob_id": "prob_8552", "image_path": "images/img_636.png", "question": "Find the value of the variable x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "125.000", "choices": [55.0, 115.0, 125.0, 135.0]}
+{"prob_id": "prob_8575", "image_path": "images/img_2469.png", "question": "Find m \\angle R. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.088", "choices": [29.1, 43.7, 54.8, 56.1]}
+{"prob_id": "prob_8577", "image_path": "images/img_1765.png", "question": "In \\odot M, FL = 24, HJ = 48, and m \\widehat HP = 65. Find m \\widehat PJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [37.5, 65.0, 85.0, 130.0]}
+{"prob_id": "prob_8593", "image_path": "images/img_1395.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [10.0, 20.0, 30.0, 40.0]}
+{"prob_id": "prob_8605", "image_path": "images/img_78.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [8.0, 13.856406460551018, 24.0, 27.712812921102035]}
+{"prob_id": "prob_8618", "image_path": "images/img_3104.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.750", "choices": [10.25, 12.75, 18.75, 25.5]}
+{"prob_id": "prob_8622", "image_path": "images/img_1284.png", "question": "In \\odot X, AB = CD = 30, and m \\widehat CZ = 40. Find ND. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [10.0, 15.0, 20.0, 30.0]}
+{"prob_id": "prob_8626", "image_path": "images/img_242.png", "question": "Find m \\angle WYZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.000", "choices": [4.0, 16.0, 23.0, 32.0]}
+{"prob_id": "prob_8631", "image_path": "images/img_2248.png", "question": "Given that the perimeter of \\triangle ABC = 25, find x. Assume that segments that appear tangent to circles are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 6.0, 7.0, 9.0]}
+{"prob_id": "prob_8650", "image_path": "images/img_3371.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "36.373", "choices": [21.0, 29.698484809834998, 36.373066958946424, 42.0]}
+{"prob_id": "prob_8662", "image_path": "images/img_2572.png", "question": "Find the area of the kite. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "336.000", "choices": [168.0, 336.0, 672.0, 1344.0]}
+{"prob_id": "prob_8665", "image_path": "images/img_1417.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.657", "choices": [5.656854249492381, 6.928203230275509, 8.0, 8.94427190999916]}
+{"prob_id": "prob_8683", "image_path": "images/img_292.png", "question": "Find x so that GJ \\parallel FK. GH = x+3.5, HJ = x-8.5, FH = 21, HK = 7. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.500", "choices": [12.0, 12.5, 14.5, 17.5]}
+{"prob_id": "prob_8724", "image_path": "images/img_2984.png", "question": "Find the length of \\widehat WN if \\triangle IWN is equilateral and WN = 5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.236", "choices": [1.8849555921538759, 5.235987755982989, 15.707963267948966, 31.41592653589793]}
+{"prob_id": "prob_8768", "image_path": "images/img_2798.png", "question": "in \\triangle XYZ, P is the centroid, KP = 3, and XJ = 8. Find YJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [3.0, 6.0, 8.0, 9.0]}
+{"prob_id": "prob_8781", "image_path": "images/img_611.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "31.069", "choices": [24.0, 31.1, 38.1, 52.3]}
+{"prob_id": "prob_8863", "image_path": "images/img_3465.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [10.0, 30.0, 90.0, 120.0]}
+{"prob_id": "prob_8868", "image_path": "images/img_664.png", "question": "JKLM is a rectangle. MLPR is a rhombus. m \\angle JMK = m \\angle RMP, m \\angle JMK = 55, and m \\angle MRP = 70. Find m \\angle KLP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "160.000", "choices": [20.0, 110.0, 140.0, 160.0]}
+{"prob_id": "prob_8885", "image_path": "images/img_1019.png", "question": "If CW = WF and ED = 30, what is DF? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [15.0, 30.0, 45.0, 60.0]}
+{"prob_id": "prob_8896", "image_path": "images/img_3171.png", "question": "Find the area of the shaded region. Assume that the polygon is regular. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1208.081", "choices": [1208.1, 1669.9, 3444.7, 4263.4]}
+{"prob_id": "prob_8900", "image_path": "images/img_2869.png", "question": "Find PN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [25.0, 30.0, 50.0, 60.0]}
+{"prob_id": "prob_8907", "image_path": "images/img_2363.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [10.0, 11.0, 12.0, 13.0]}
+{"prob_id": "prob_8929", "image_path": "images/img_2582.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.207", "choices": [37.2, 40.6, 49.4, 52.8]}
+{"prob_id": "prob_8939", "image_path": "images/img_3373.png", "question": "Find the length of AC in the isosceles triangle ABC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [1.5, 7.0, 11.0, 12.5]}
+{"prob_id": "prob_8943", "image_path": "images/img_566.png", "question": "Use parallelogram MNPR to find m \\angle RMN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "109.000", "choices": [33.0, 38.0, 71.0, 109.0]}
+{"prob_id": "prob_8952", "image_path": "images/img_2065.png", "question": "MN \\parallel BC. Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [6.0, 9.0, 12.0, 15.0]}
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diff --git a/test/geoqa/test.jsonl b/test/geoqa/test.jsonl
index 50c6154886bb0ffae78c6d9bbd5c25e898b64e75..3d52ccb5f2d6f7f0d349b65f89c621f31bd25e12 100644
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-{"prob_id": 0, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/0.png", "question": "如图,在△ABC中,已知∠A=80°,∠B=60°,DE∥BC,那么∠CED的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠A+∠B+∠C=180°(三角形内角和定理),∠A=80°,∠B=60°,∴∠C=180°-∠A-∠B=180°-80°-60°=40°,又∵DE//BC,∴∠CED+∠C=180°(两直线平行,同旁内角互补).∴∠CED=180°-40°=140°.故选D.", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["40°", "60°", "120°", "140°"], "choices": [40.0, 60.0, 120.0, 140.0], "label": 3}
-{"prob_id": 1, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1.png", "question": "如图,AB∥CD,直线EF交AB于点E,交CD于点F,EG平分∠BEF,交CD于点G,∠1=50°,则∠2等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵ABIICD,∴∠BEF+∠1=180°(两直线平行,同旁内角互补)∵∠1=50°,∴∠BEF=130°∵EG平分∠BEF,∴∠BEG=\\frac{1}{2}∠BEF=65°(角平分线的定义)5°(角平分线的定义)∴∠2=∠BEG=65°(两直线平行1内错角相等),故选C", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["50°", "60°", "65°", "90°"], "choices": [50.0, 60.0, 65.0, 90.0], "label": 2}
-{"prob_id": 101, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/101.png", "question": "如图,BD平分∠ABC,CD∥AB,若∠BCD=70°,则∠CDB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵CD//AB,∴∠BCD+CBA=180^{°},∴∠CBA=180°-70°=110°,∵BD平分∠ABC,∴∠ABD=\\frac{1}{2}∠CBA=55^{°},而AB//CD∴∠CDB=∠ABD=55^{°}.故选A.", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["55°", "50°", "45°", "30°"], "choices": [55.0, 50.0, 45.0, 30.0], "label": 0}
-{"prob_id": 103, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/103.png", "question": "如图,AB与⊙O相切于点B,AO的延长线交⊙O于点C,连接BC,若∠A=36°,则∠C等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB与⊙O相切于点B,∴∠ABO=90°,∵∠A=36°,∴∠BOA=54°∴由圆周角定理得:∠C=\\frac{1}{2}∠BOA=27^{°},故选D.", "dataset_name": "Geoqa", "ground_truth": "27.0", "org_choices": ["36°", "54°", "60°", "27°"], "choices": [36.0, 54.0, 60.0, 27.0], "label": 3}
-{"prob_id": 110, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/110.png", "question": "如图所示,直线a,b相交于点O,若∠1等于50°,则∠2等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵∠2与∠1是对顶角,∴∠2=∠1=50^{°}.故选A.", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["50°", "40°", "140°", "130°"], "choices": [50.0, 40.0, 140.0, 130.0], "label": 0}
-{"prob_id": 112, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/112.png", "question": "如图,AB//CD,EF分别为交AB,CD于点E,F,∠1=50°,则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:如答图,∵AB//C,∠1=50^{°}.∴∠3=∠1=50^{°}.∴∠2=180°-∠3=130°故选C.", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["50°", "120°", "130°", "150°"], "choices": [50.0, 120.0, 130.0, 150.0], "label": 2}
-{"prob_id": 120, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/120.png", "question": "如图,△ABC≌△ADE,若∠B=70°,∠C=30°,∠DAC=35°,则∠EAC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:∵∠B=70°,∠C=30°,∴∠BAC=180°-∠B-∠C=180^{°}-70^{°}-30^{°}=80^{°},∵△ABC≌△ADE,∴∠EAD=∠BAC=80°,∴∠EAC=∠EAD-∠DAC=80°-35°=45°,故选B.", "dataset_name": "Geoqa", "ground_truth": "45.0", "org_choices": ["40°", "45°", "35°", "25°"], "choices": [40.0, 45.0, 35.0, 25.0], "label": 1}
-{"prob_id": 121, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/121.png", "question": "如图,△ABC≌△DEF,点A与D,B与E分别是对应顶点,且测得BC=5cm,BF=7cm,则EC长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵△ABC≌△BAD∴EF=BC=5cm,∵BF=7cm,BC=5cm∴CF=EF-CF=3cm,故选C.", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["1cm", "2cm", "3cm", "4cm"], "choices": [1.0, 2.0, 3.0, 4.0], "label": 2}
-{"prob_id": 123, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/123.png", "question": "如图,在△ABC中,∠C=90°,AC=BC,AD平分∠CAB交BC于D,DE⊥AB于E,若AB=6cm,则△DBE的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AD平分∠CAB,AC⊥BC于点C,DE⊥AB于E,∴CD=DE.又∵AD=AD∴Rt△ACD≌Rt△AED,∴AC=AE.又∵AC=BC,∴△DBE的周长为DE+BD+EB=CD+BD+EB=BC+EB=AC+EB=AE+EB=AB=6故选A", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["6cm", "7cm", "8cm", "9cm"], "choices": [6.0, 7.0, 8.0, 9.0], "label": 0}
-{"prob_id": 150, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/150.png", "question": "如图,△ABC中,AB=AC,∠A=36°,AB的垂直平分线DE交AC于D,交AB于E,则∠BDC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵AB=AC,∠A=36°,∴∠ABC=∠C=\\frac{180^{°}-∠A}}{2}=\\frac{180^{°}-36^{°}}{2}=72^{°}∵DE垂直平分AB,∴∠A=∠ABD=36°,∴∠BDC=∠A+∠ABD=36^{°}+36^{°}=72^{°}.故选A.", "dataset_name": "Geoqa", "ground_truth": "72.0", "org_choices": ["72°", "36°", "60°", "82°"], "choices": [72.0, 36.0, 60.0, 82.0], "label": 0}
-{"prob_id": 159, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/159.png", "question": "如图,在△ABC中,∠C=36°,将△ABC绕点A逆时针旋转60°得到△AED,AD与BC交于点F,则∠AFC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:根据旋转图形可得∠FAC=60°,根据△AFC的内角和定理可得∠AFC=180°-36°-60°=84°.", "dataset_name": "Geoqa", "ground_truth": "84.0", "org_choices": ["84°", "80°", "60°", "90°"], "choices": [84.0, 80.0, 60.0, 90.0], "label": 0}
-{"prob_id": 165, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/165.png", "question": "如图,直线AB∥CD,Rt△DEF如图放置,∠EDF=90°,若∠1+∠F=70°,则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:根据∠1+∠F=70°以及三角形的外角的性质可得∠ABD=70°,根据AB//CD可得∠ABD+∠BDC=180°,则∠BDC=110°,根据∠EDF=90°可得∠2=110°-90°=20°.", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["20°", "25°", "30°", "40°"], "choices": [20.0, 25.0, 30.0, 40.0], "label": 0}
-{"prob_id": 167, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/167.png", "question": "如图,AB∥EF,CD⊥EF,∠BAC=50°,则∠ACD=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:如图,延长AC交EF于点G;∵AB//EF,∴∠DGC=∠BAC=50°;∵CD⊥EF,∴∠CDG=90°,∴∠ACD=90°+50°=140°,故选C.", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["120°", "130°", "140°", "150°"], "choices": [120.0, 130.0, 140.0, 150.0], "label": 2}
-{"prob_id": 186, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/186.png", "question": "如图,△ABC是⊙O的内接三角形,∠OAB=35°,则∠ACB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:根据OA=OB可得∠OBA=∠OAB=35°,则∠AOB=110°,根据圆的基本性质可得,∠ACB=\\frac{1}{2}∠AOB=55^{°}", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["35°", "55°", "60°", "70°"], "choices": [35.0, 55.0, 60.0, 70.0], "label": 1}
-{"prob_id": 188, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/188.png", "question": "将直尺和直角三角板按如图方式摆放(∠ACB为直角),已知∠1=30°,则∠2的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:先根据两角互余的性质求出∠3的度数,再由平行线的性质即可得出结论.∵∠1+∠3=90°,∠1=30°,∴∠3=60°.∵直尺的两边互相平行,∴∠2=∠3=60°.", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["30°", "45°", "60°", "65°"], "choices": [30.0, 45.0, 60.0, 65.0], "label": 2}
-{"prob_id": 194, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/194.png", "question": "如图,直线a与直线b被直线c所截,b⊥c,垂足为点A,∠1=70°．若使直线b与直线a平行,则可将直线b绕着点A顺时针旋转(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:∵b⊥c,∴∠2=90°.∵∠1=70°,a//b,∴直线b绕着点A顺时针旋转的度数=90°-70°=20°.故选D.", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["70°", "50°", "30°", "20°"], "choices": [70.0, 50.0, 30.0, 20.0], "label": 3}
-{"prob_id": 196, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/196.png", "question": "如图,在⊙O中,弦AC∥半径OB,∠BOC=50°,则∠OAB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图,∵∠BOC=50^{°},∴∠BAC=25^{°},∵AC//OB,∴∠OBA=∠BAC=25^{°},∵OA=OB∴∠OAB=∠OBA=25^{°}.故选A.", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["25°", "50°", "60°", "30°"], "choices": [25.0, 50.0, 60.0, 30.0], "label": 0}
-{"prob_id": 199, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/199.png", "question": "□ABCD中,对角线AC与BD交于点O,∠DAC=42°,∠CBD=23°,则∠COD是()．. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵AD//BC,∴∠BCA=∠DAC=42°,根据三角形的外角等于和它不相邻的内角和,∠COD=∠BCO+∠CBO=42°+23°=65°,故选", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["61°", "63°", "65°", "67°"], "choices": [61.0, 63.0, 65.0, 67.0], "label": 2}
-{"prob_id": 200, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/200.png", "question": "直线a、b、c、d的位置如图所示,如果∠1=58°,∠2=58°,∠3=70°,那么∠4等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:根据同位角相等,两直线平行这一定理可知a//b,再根据两直线平行,同旁内角互补可得∠3+∠5=180°,即∠5=180°-∠3=180°-70°=110°,因此可求得∠4=∠5=110°.故选C", "dataset_name": "Geoqa", "ground_truth": "110.0", "org_choices": ["58°", "70°", "110°", "116°"], "choices": [58.0, 70.0, 110.0, 116.0], "label": 2}
-{"prob_id": 202, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/202.png", "question": "如图所示,a∥b,∠1=158°,∠2=42°,∠4=50°．那么∠3=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:作BC//a,BE//b,∵a//b,∴a//b//BC//DE,∵∠1=158°,∠2=42°,∠4=50°∴∠ABC=180°-158°=22°∴∠CBD=∠BDE=42°-22°=20°,∠EDF=∠4=50°∴∠3=∠BDE+∠EDF=20°+50°=70°.故选C.", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["50°", "60°", "70°", "80°"], "choices": [50.0, 60.0, 70.0, 80.0], "label": 2}
-{"prob_id": 218, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/218.png", "question": "如图,AB是⊙O的直径,C、D是⊙O上的两点,分别连结AC、BC、CD、OD.若∠DOB=140°,则∠ACD=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵∠DOB=140°,∴∠AOD=40^{°},∴∠ACD=\\frac{1}{2}∠AOD=20^{°},故选A.", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["20°", "30°", "40°", ".70°A70°"], "choices": [20.0, 30.0, 40.0, 70.0], "label": 0}
-{"prob_id": 22, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/22.png", "question": "如图,已知∠1=∠2=∠3=55°,则∠4的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵∠1=∠2,∠5=∠1(对顶角相等),∴∠2=∠5,∴a//b(同位角相等,得两直线平行);∴∠3=∠6=55°(两直线平行,内错角相等),故∠4=180°-55°=125°(邻补角互补).故选D.", "dataset_name": "Geoqa", "ground_truth": "125.0", "org_choices": ["110°", "115°", "120°", "125°"], "choices": [110.0, 115.0, 120.0, 125.0], "label": 3}
-{"prob_id": 222, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/222.png", "question": "如图,在菱形ABCD中,M,N分别为AB、CD上,且AM=CN,MN与AC交于点O,连接BO.若∠DAC=28°,则∠OBC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵四边形ABCD为菱形,∴AB//CD,AB=BC,∴∠MAO=∠NCO,∠AMO=∠CNO,在△AMO和△CNO中,∴△AMO≌△CNO(ASA),∴AO=CO,∵AB=BC,∴BO⊥AC,∴∠BOC=90°,∵∠DAC=28°,BC//AD,∴∠BCA=∠DAC=28°,∴∠OBC=90°-28°=62°,故选C.", "dataset_name": "Geoqa", "ground_truth": "62.0", "org_choices": ["28°", "52°", "62°", "72°"], "choices": [28.0, 52.0, 62.0, 72.0], "label": 2}
-{"prob_id": 234, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/234.png", "question": "如图,PA,PB分别与⊙O相切于A,B两点,若∠C=65°,则∠P的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵PA、PB是⊙O的切线,∴OA⊥AP,OB⊥BP,∴∠OAP=∠OBP=90°,又∵∠AOB=2∠C=130°,则∠P=360°-(90°+90°+130°)=50°.故选C.", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["65°", "130°", "50°", "100°"], "choices": [65.0, 130.0, 50.0, 100.0], "label": 2}
-{"prob_id": 235, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/235.png", "question": "(4分)如图,直线a∥b,直线c分别与a,b相交,∠1=50°,则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:如图所示,∵a//b,∠1=50°,∴∠3=∠1=50°,∵∠2+∠3=180°,∴∠2=130°.故选B.", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["150°", "130°", "100°", "50°"], "choices": [150.0, 130.0, 100.0, 50.0], "label": 1}
-{"prob_id": 244, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/244.png", "question": "(3分)如图,EF∥BC,AC平分∠BAF,∠B=50°,则∠C的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵EF//BC,∴∠EAB=∠B=50°,∠C=∠CAF,∴∠BAF=180°-50°=130°,又∵AC平分∠BAF,∴∠CAF=130°÷2=65°,∴∠C=65°.故选D.", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["50°", "55°", "60°", "65°"], "choices": [50.0, 55.0, 60.0, 65.0], "label": 3}
-{"prob_id": 249, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/249.png", "question": "如图,为测量学校旗杆的高度,小东用长为3.2米的竹竿作测量工具,移动竹竿,使竹竿顶端与旗杆顶端的影子恰好落在地面的同一点,此时,竹竿与这一点相距8米,与旗杆相距22米,则旗杆的高度为()米.. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "若设旗杆高x米,则\\frac{3.2}{x}=\\frac{8}{8+22}∴x=12.故选C.", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["8.8", "10", "12", "14"], "choices": [8.8, 10.0, 12.0, 14.0], "label": 2}
-{"prob_id": 26, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/26.png", "question": "如图,在平地上种植树木时,要求株距(相邻两树间的水平距离)为4m．如果在坡度为0.75的山坡上种树,也要求株距为4m,那么相邻两树间的坡面距离为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "tan\\alpha=0.5=\\frac{铅直高度}{水平距离}=\\frac{AC}{AB}∵AB=4m,∴AC=0.75×4=3m由勾股定理知:面相邻两株数间的坡面距离BC=√{AB²+AC²}=√{4²+3²}=5m故选A.", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["5m", "6m", "7m", "8m"], "choices": [5.0, 6.0, 7.0, 8.0], "label": 0}
-{"prob_id": 269, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/269.png", "question": "如图,以线段AB为边分别作直角三角形ABC和等边三角形ABD,其中∠ACB=90°.连接CD,当CD的长度最大时,此时∠CAB的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图所示:∵AB长一定,∴只有C点距离AB距离最大,则CD的长度最大.∴只有C点在C′位置,即C′在半圆的中点时,此时当CD的长度最大故此时AC′=BC′,∴∠C′AB的大小是45°.故选B.", "dataset_name": "Geoqa", "ground_truth": "45.0", "org_choices": ["75°", "45°", "30°", "15°"], "choices": [75.0, 45.0, 30.0, 15.0], "label": 1}
-{"prob_id": 291, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/291.png", "question": "如图所示,D是△ABC的角平分线BD和CD的交点,若∠A=50°,则∠D=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵∠A=50°,∴∠ABC+∠ACB=180°-∠A=180°-50°=130°,∵D是△ABC的角平分线BD和CD的交点,∴∠DBC+∠DCB=\\frac{1}{2}(∠ABC+∠ACB)=\\frac{1}{2}×130^{°}=65^{°},在△BCD中,∠D=180°-(∠DBC+∠DCB)=180°-65°=115°.故选C.", "dataset_name": "Geoqa", "ground_truth": "115.0", "org_choices": ["120°", "130°", "115°", "110°"], "choices": [120.0, 130.0, 115.0, 110.0], "label": 2}
-{"prob_id": 3, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3.png", "question": "如图,已知OA=OB=OC且∠ACB=30°,则∠AOB的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵OA=OB=OC,∴A、B、C在以O为圆心OA为半径的圆上.作⊙O.∵∠ACB和∠AOB是同弧AB所对的圆周角和圆心角,且∠ACB=30°,∴根据同弧所对的圆周角是圆心角的一半的性质,得∠AOB=60°.故选C.", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["40°", "50°", "60°", "70°"], "choices": [40.0, 50.0, 60.0, 70.0], "label": 2}
-{"prob_id": 30, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/30.png", "question": "如图,直线a∥b,点B在直线b上,且AB⊥BC,∠2=65°,则∠1的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:直线a//b,可得∠3=∠2=65°,根据AB⊥BC,可得∠1=25°.", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["65°", "25°", "35°", "45°"], "choices": [65.0, 25.0, 35.0, 45.0], "label": 1}
-{"prob_id": 314, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/314.png", "question": "圆I是三角形ABC的内切圆,D,E,F为3个切点,若∠DEF=52°,则∠A的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:连接DI,FI,∵∠DEF=52^{°},∴∠DIF=104°,∵⊙I是△ABC的内切圆,D,E,F为三个切点,∴∠IDA=∠IFA=90°,∴∠A=360^{°}-90^{°}-90^{°}-104^{°}=76^{°}.故选C.", "dataset_name": "Geoqa", "ground_truth": "76.0", "org_choices": ["68°", "52°", "76°", "38°"], "choices": [68.0, 52.0, 76.0, 38.0], "label": 2}
-{"prob_id": 323, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/323.png", "question": "如图,直线AB∥CD,∠1=136°,∠E为直角,则∠C等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:∵∠1=136^{°},∴∠BAE=180^{°}-∠1=44^{°},过E作EF//AB,∴AB//CD,∴AB//EF//CD,∴∠BAE=∠AEF,∠CEF=∠C,∵∠BAE=44°,∠E为直角,∴∠AEF=44°,∴∠C=∠CEF=90^{°}-44^{°}=46^{°},故选C.", "dataset_name": "Geoqa", "ground_truth": "46.0", "org_choices": ["42°", "44°", "46°", "48°"], "choices": [42.0, 44.0, 46.0, 48.0], "label": 2}
-{"prob_id": 332, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/332.png", "question": "如图所示,直线AB、CD被直线EF所截,若AB∥CD,∠1=100°,则∠2的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵AB//CD,∠3=∠1=100°,∴∠2=180°-∠3=80°,故选C.", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["10°", "50°", "80°", "100°"], "choices": [10.0, 50.0, 80.0, 100.0], "label": 2}
-{"prob_id": 359, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/359.png", "question": "如图:AB∥DE,∠B=30°,∠C=110°,∠D的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:过点C作CF//AB,∵AB//DE,∴AB//DE//CF,∵∠B=30°,∴∠1=30°,∵∠C=110°,∴∠2=80°,∴∠D=180°∠2=180°-80°=100°.故选C.", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["115°", "120°", "100°", "80°"], "choices": [115.0, 120.0, 100.0, 80.0], "label": 2}
-{"prob_id": 361, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/361.png", "question": "如图,AB是⊙O的直径,点C在⊙O上,过点C作⊙O的切线交AB的延长线于点D,连接AC．若∠D=50°,则∠A的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:∵CD切⊙O于C,∴OC⊥CD,∴∠OCD=90°,∵∠D=50^{°},∴∠COD=180^{°}-90^{°}-50^{°}=40^{°},∵OA=OC,∴∠A=∠OCA,∵∠A+∠OCA=∠COD=40^{°},∴∠A=20°故选A.", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["20°", "25°", ".40°", "50°"], "choices": [20.0, 25.0, 0.4, 50.0], "label": 0}
-{"prob_id": 377, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/377.png", "question": "如图,AB∥CD,CP交AB于O,AO=PO,若∠C=50°,则∠A的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:∵AB//CD,CP交AB于O,∴∠POB=∠C,∵∠C=50°,∴∠POB=50°,∵AO=PO,∴∠A=∠P,∴∠A=25°故选A.", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["25°", "35°", "15°", "50°"], "choices": [25.0, 35.0, 15.0, 50.0], "label": 0}
-{"prob_id": 385, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/385.png", "question": "如图,在△ABC中,AB=AC,过点A作AD∥BC.若∠1=70°,则∠BAC的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:根据AD//BC可得出∠C=∠1=70°/再根据AB=AC即可得出∠B=∠C=70°,结合三角形的内角和为180°,即可算出C=180°-∠B-∠C=40°.故选A.", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "30°", ".70°", "50°"], "choices": [40.0, 30.0, 0.7, 50.0], "label": 0}
-{"prob_id": 399, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/399.png", "question": "将一张宽度相等的长方形纸条按如图所示的方式折叠一下,如果∠1=140°,那么∠2的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:根据平行线的性质可得∠3+∠4=∠1=140°,根据折叠图形的性质可得:∠3=∠4=70°,根据平行线的性质可得:∠2=180°-70°=110°.", "dataset_name": "Geoqa", "ground_truth": "110.0", "org_choices": ["100°", "110°", "120°", "140°"], "choices": [100.0, 110.0, 120.0, 140.0], "label": 1}
-{"prob_id": 402, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/402.png", "question": "如图,已知直线a、b被直线c所截,a∥b,∠1=50°,则∠2=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:先利用平行线的性质可得∠3=∠1,又由对顶角相等推出∠2=∠3,故∠2的度数可求.如图,∵a//b,∠1=50°,∴∠3=∠1=50°,∵∠2=∠3,∴∠2=∠1=50°", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["50°", "130°", "40°", "60°"], "choices": [50.0, 130.0, 40.0, 60.0], "label": 0}
-{"prob_id": 413, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/413.png", "question": "直线a、b、c、d的位置如图,如果∠1=100°,∠2=100°,∠3=125°,那么∠4等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠1=100°,∠2=100°,∴∠1=∠2,∴a//b,∴∠4=∠5,∵∠3+∠5=180°,∴∠5=180^{°}-∠3=180^{°}-125^{°}=55^{°},∴∠4=55°故选D.", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["80°", "65°", "60°", "55°"], "choices": [80.0, 65.0, 60.0, 55.0], "label": 3}
-{"prob_id": 417, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/417.png", "question": "如图是小刘做的一个风筝支架示意图,已知BC∥PQ,AB:AP=2:5,AQ=20cm,则CQ的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "[解析]试题解析:∵BC//PQ,∴△ABC\\sim△APQ,∴\\frac{AB}{AP}=\\frac{AC}{AQ},∵AB:AP=2:5,AQ=20cm,∴\\frac{Ac}{20}=\\frac{2}{5}解得:AC=8cm,∴CQ=AQ-AC=20-8=12(cm),故选B.", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["8cm", "12cm", "30cm", "50cm"], "choices": [8.0, 12.0, 30.0, 50.0], "label": 1}
-{"prob_id": 419, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/419.png", "question": "如图,△ODC是由△OAB绕点O顺时针旋转30°后得到的图形,若点D恰好落在AB上,且∠AOC的度数为100°,则∠DOB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意得,∠AOD=30°,∠BOC=30°,又∠AOC=100°,∴∠DOB=100°-30°-30°=40°.故选A.", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "30°", "38°", "15°"], "choices": [40.0, 30.0, 38.0, 15.0], "label": 0}
-{"prob_id": 422, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/422.png", "question": "如图,甲、乙两盏路灯相距30米,一天晚上,当小刚从路灯甲底部向路灯乙底部直行25米时,发现自己的身影顶部正好接触到路灯乙的底部,已知小刚的身高为1.5米,那么路灯甲的高为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:如图∵AB⊥OB,CD⊥OB,∴△ABO~△CDOr∴\\frac{CD}{AB}=\\frac{DO}{BO},\\frac{1.5}{AB}=\\frac{30-25}{30},解得AB=9,故选A.", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["9米", "8米", "7米", "6米"], "choices": [9.0, 8.0, 7.0, 6.0], "label": 0}
-{"prob_id": 430, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/430.png", "question": "如图,C是⊙O上一点,O是圆心,若∠C=35°,则∠AOB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:同弧所对的圆心角的度数等于圆周角度数的两倍,则∠AOB=2∠C=70°.", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["35°", "70°", "105°", "150°"], "choices": [35.0, 70.0, 105.0, 150.0], "label": 1}
-{"prob_id": 435, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/435.png", "question": "如图,若AB∥CD,∠A=70°,则∠1的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "[解析]试题解析:如图,∵AB//CD,∠A=70°∴∠2=∠A=70°∴∠1=180^{°}-∠2=180^{°}-70^{°}=110°故选D.", "dataset_name": "Geoqa", "ground_truth": "110.0", "org_choices": ["20°", "30°", "70°", "110°"], "choices": [20.0, 30.0, 70.0, 110.0], "label": 3}
-{"prob_id": 448, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/448.png", "question": "如图,直线AB∥CD,∠C=44°,∠E为直角,则∠1等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过E作EF//AB,∵AB//CD,∴AB//CD//EF,∴∠C=∠FEC,∠BAE=∠FEA,∵∠C=44°,∠AEC为直角,∴∠FEC=44°,∠BAE=∠AEF=90°-44°=46°∴∠1=180°-∠BAE=180°-46°=134°故选B.", "dataset_name": "Geoqa", "ground_truth": "134.0", "org_choices": ["132°", "134°", "136°", "138°"], "choices": [132.0, 134.0, 136.0, 138.0], "label": 1}
-{"prob_id": 449, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/449.png", "question": "如图,A、B、C为⊙O上的任意三点,若∠BOC=100°,则∠BAC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "取⊙O上的一点D,连接BD,CD,∵∠BOC=100°,△∠D=50°,∴∠BAC=180°50°=130°,故选D.", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["50°", "80°", "100°", "130°"], "choices": [50.0, 80.0, 100.0, 130.0], "label": 3}
-{"prob_id": 458, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/458.png", "question": "如图,在⊙O的内接五边形ABCDE中,∠CAD=35°,∠AED=115°,则∠B的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:∵四边形ACDE是圆内接四边形,∴∠AED+∠ACD=180^{°},∵∠AED=115°∴∠ACD=65°∵∠CAD=35°,∴∠ADC=80°,∵四边形ABCD是圆内接四边形,∴∠B+∠ADC=180°,∴∠B=100°,故选D.", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["50°", "75°", "80°", "100°"], "choices": [50.0, 75.0, 80.0, 100.0], "label": 3}
-{"prob_id": 462, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/462.png", "question": "如图,△ABC中,∠C=90°,AD是∠BAC的平分线,DE⊥AB于E,若DE=8cm,DB=10cm则BC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "已知△ABC中,∠C=90°,AD是∠BAC的平分线,DE⊥AB于E,根据角平分线的性质可得CD=DE=8cm,所以BC=CD+BD=18cm,故选C.", "dataset_name": "Geoqa", "ground_truth": "18.0", "org_choices": ["14cm", "16cm", "18cm", "20cm"], "choices": [14.0, 16.0, 18.0, 20.0], "label": 2}
-{"prob_id": 467, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/467.png", "question": "如图,直线AB,CD相交于点O,EO⊥AB,垂直为点O,∠BOD=50°,则∠COE=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:EO⊥AB,∴∠AOE=90^{°},∵∠AOC=∠BOD=50^{°},∴∠COE=∠AOC+∠AOE=50^{°}+90^{°}=140°故选B.", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["30°", "140°", "50°", "60°"], "choices": [30.0, 140.0, 50.0, 60.0], "label": 1}
-{"prob_id": 472, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/472.png", "question": "如图,点B,E,C,F在同一条直线上,△ABC≌△DEF,∠B=45°,∠F=65°,则∠COE的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵△ABC≌△DEF,∠B=45°∠F=65°∴∠DEF=∠B=45°,∠ACB=∠F=65°在△OEC中,∠COE=180°-∠DEF-∠ACB=180^{°}-45^{°}-65^{°}=70°故选C.", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["40°", "60°", "70°", "100°"], "choices": [40.0, 60.0, 70.0, 100.0], "label": 2}
-{"prob_id": 476, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/476.png", "question": "如图,把一块含有45°角的直角三角板的两个顶点放在直尺的对边上,如果∠1=27.5°,那么∠2等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB//CD,∴∠1=∠AEC,又∠1=27.5,∠FEC=45°,∴∠2=∠FEC-∠1=17.5°.故选D.", "dataset_name": "Geoqa", "ground_truth": "17.5", "org_choices": ["32.5°", "22.5°", "20.5°", "17.5°"], "choices": [32.5, 22.5, 20.5, 17.5], "label": 3}
-{"prob_id": 479, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/479.png", "question": "如图,直线a∥b,点B在直线b上,且AB⊥BC,∠1=55°,则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵a//b,∴BC与b所夹锐角等于∠1=55°,又AB⊥BC,∴∠2=180°-90°-55°=35°.故选B.", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["25°", "35°", "45°", "55°"], "choices": [25.0, 35.0, 45.0, 55.0], "label": 1}
-{"prob_id": 48, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/48.png", "question": "如图,直线a∥b,直线c与a,b相交,∠1=55°,则∠2=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图,a//b,,∠1=55^{°},∴∠3=∠1=55^{°}.∵∠2和∠3是对顶角,∴∠2=∠3=55°故选A.", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["55°", "35°", "125°", "65°"], "choices": [55.0, 35.0, 125.0, 65.0], "label": 0}
-{"prob_id": 484, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/484.png", "question": "把一尺与三角板如图放置,∠1=40°则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:如图,∵∠3=∠1+90^{°},而∠1=40°,∴∠3=130^{°},∵a//b,∴∠2=∠3=130^{°}.故选A.", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["130°", "140°", "120°", "125°"], "choices": [130.0, 140.0, 120.0, 125.0], "label": 0}
-{"prob_id": 489, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/489.png", "question": "如图,直线AB,CD相交于点O,射线OM平分∠AOC,ON⊥OM．若∠AOC=70°,则∠CON的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵ON⊥OM,∴∠MON=90°.OM平分∠AOC,∠AOC=70°∴∠MOC=\\frac{1}{2}∠AOC=35^{°},∴∠CON=90^{°}-35^{°}=55^{°}故选B.", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["65°", "55°", "45°", "35°"], "choices": [65.0, 55.0, 45.0, 35.0], "label": 1}
-{"prob_id": 50, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/50.png", "question": "如图,⊙O的直径CD过弦EF的中点G,∠DCF=20°,则∠EOD等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵⊙O的直径CD过弦EF的中点G,∠DCF=20°DF=DE,且弧的度数是40°.∴∠DOE=40°.故选C", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["10°", "20°", "40°", "80°"], "choices": [10.0, 20.0, 40.0, 80.0], "label": 2}
-{"prob_id": 51, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/51.png", "question": "如图,AB平行CD,如果∠B=20°,那么∠C为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB//CD,,∠B=20^{°}∴∠C=∠B=20^{°}故选B.", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["40°", "20°", "60°", "70°"], "choices": [40.0, 20.0, 60.0, 70.0], "label": 1}
-{"prob_id": 56, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/56.png", "question": "如图,AB∥CD,∠CED=90°,∠AEC=35°,则∠D的大小(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB//CD,∴∠D=∠BED.∵∠CED=90°,∠AEC=35°∴∠BED=180°-90°-35°=55°.故选B.", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["65°", "55°", "45°", "35°"], "choices": [65.0, 55.0, 45.0, 35.0], "label": 1}
-{"prob_id": 57, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/57.png", "question": "如图,AB∥CD,AD平分∠BAC,且∠C=80°,则∠D的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AD平分∠BAC,∴∠BAD=∠CAD.∵AB//CD,∴∠BAD=∠D.∴∠CAD=∠D.∵在△ACD中,∠C+∠D+∠CAD=180°,即80^{°}+∠D+∠D=180^{°}解得∠D=50°,故选A.", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["50°", "60°", "70°", "100°"], "choices": [50.0, 60.0, 70.0, 100.0], "label": 0}
-{"prob_id": 6, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/6.png", "question": "如图,AB∥CD,若∠2=135°,那么∠1的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "由AB1ICD,知∠1的对顶角与∠2互补,所以∠1=45°", "dataset_name": "Geoqa", "ground_truth": "45.0", "org_choices": ["30°", "45°", "60°", "75°"], "choices": [30.0, 45.0, 60.0, 75.0], "label": 1}
-{"prob_id": 81, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/81.png", "question": "如图,AB∥CD,点E在BC上,且CD=CE,∠D=74°,则∠B的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵CD=CE,∠D=74°∴∠C=32°又∵AB//CD故选B", "dataset_name": "Geoqa", "ground_truth": "32.0", "org_choices": ["74°", "32°", "22°", "16°"], "choices": [74.0, 32.0, 22.0, 16.0], "label": 1}
-{"prob_id": 86, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/86.png", "question": "如图,AB∥CD,点E在CA的延长线上.若∠BAE=40°,则∠ACD的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:如图,延长DC到F,则∵AB//CD,∠BAE=40°,∴∠ECF=∠BAE=40°∴∠ACD=180^{°}-∠ECF=140^{°}.故选B.", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["150°", "140°", "130°", "120°"], "choices": [150.0, 140.0, 130.0, 120.0], "label": 1}
-{"prob_id": 9, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9.png", "question": "如图,利用标杆BE测量树CD的高度,如果标杆BE长为2米,测得AB=3米,AC=9米,且点A、E、D在一条直线上,则树CD是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "本题考查的三角形的相似.由题意得三角形ABE~三角形ACD所以有\\frac{AB}{AC}=\\frac{BE}{CD}即\\frac{3}{9}=\\frac{2}{CD}解得CD=6故A正确.", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["6米", "7.5米", "8米", "8.5米"], "choices": [6.0, 7.5, 8.0, 8.5], "label": 0}
-{"prob_id": 95, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/95.png", "question": "在直径为200cm的圆柱形油槽内装入一些油以后,截面如图．若油面的宽AB=160cm,则油的最大深度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:连接OA,过点O作OE⊥AB,交AB于点M,由垂径定理求出AM的长,再根据勾股定理求出OM的长,进而可得出ME的长.", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40cm", "60cm", "80cm", "100cm"], "choices": [40.0, 60.0, 80.0, 100.0], "label": 0}
-{"prob_id": 1506, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1506.png", "question": "如图,∠1=∠2,∠3=30°,则∠4等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠1=∠2,∴allb,∴∠5=∠3=30°,∴∠4=180°-∠5,=150°,故选D", "dataset_name": "Geoqa", "ground_truth": "150.0", "org_choices": ["120°", "130°", "145°", "150°"], "choices": [120.0, 130.0, 145.0, 150.0], "label": 3}
-{"prob_id": 1518, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1518.png", "question": "如图,AB∥CD,∠B=20°,∠D=60°,则∠BED的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图:过点E做EF||AB,则CD||EF∴∠BEF=∠B=20°,∠DEF=∠D=60°∴∠BED=∠BEF+∠DEF=80°", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["40°", "80°", "90°", "l00°"], "choices": [40.0, 80.0, 90.0, 0.0], "label": 1}
-{"prob_id": 1524, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1524.png", "question": "如图,直线AB∥CD,AE平分∠CAB,∠ACD=40°,则∠AEC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵ABIICD,∴∠ACD+∠BAC=180°,∵∠ACD=40°,∴∠BAC=180°-40°=140°,∵AE平分∠CAB,∴∠BAE=\\frac{1}{2}∠BAC=\\frac{1}{2}×140^{°}=70^{°},∴∠AEC=∠BAE=70°,故选:B.", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["40°", "70°", "80°", "140°"], "choices": [40.0, 70.0, 80.0, 140.0], "label": 1}
-{"prob_id": 1525, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1525.png", "question": "轩轩和凯凯在同一个数学学习小组,在一次数学活动课上,他们各自用一张边长为12cm的正方形纸片制作了一副七巧板,并合作设计了如图所示的作品请你帮他们计算图中圈出来的三块图形的面积之和为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "根据七巧板的特点可知:圈出来的图形面积是正方形面积的四分之一,所以面积是12×12÷4=36故选:C", "dataset_name": "Geoqa", "ground_truth": "36.0", "org_choices": ["12cm", "24cm", "36cm", "48cm"], "choices": [12.0, 24.0, 36.0, 48.0], "label": 2}
-{"prob_id": 1528, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1528.png", "question": "如图,直线a∥b,∠2=35°,∠3=40°,则∠1的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵a||b,∴∠1=∠4,又∵∠2=35°,∠3=40°∴∠4=180°-35°-40°=105°,∴∠1=105°,故选:B.", "dataset_name": "Geoqa", "ground_truth": "105.0", "org_choices": ["75°", "105°", "140°", "145°"], "choices": [75.0, 105.0, 140.0, 145.0], "label": 1}
-{"prob_id": 1533, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1533.png", "question": "如图,BD是△ABC的角平分线,AE⊥BD,垂足为F,若∠ABC=35°,∠C=50°,则∠CDE的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵BD是△ABC的角平分线,AE⊥BD,∴∠ABD=∠EBD=\\frac{1}{2}∠ABC=\\frac{35^{°}}{2}\\quad∠AFB=∠EFB=90°,∴∠BAF=∠BEF=90°-17.5°∴AB=BE,∴AF=EF,∴AD=ED,∴∠DAF=∠DEF,∵∠BAC=180°-∠ABC-∠C=95°∴∠BED=∠BAD=95°∴∠CDE=95°-50°=45°,故选C.", "dataset_name": "Geoqa", "ground_truth": "45.0", "org_choices": ["35°", "40°", "45°", "50°"], "choices": [35.0, 40.0, 45.0, 50.0], "label": 2}
-{"prob_id": 1547, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1547.png", "question": "如图,直线AD∥BC,若∠1=42°,∠BAC=78°,则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠1=42^{°},∠BAC=78°,∴∠ABC=180°-∠1-∠BAC=60°,又∵AD||BC,∴∠2=∠ABC=60°,故选C.", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["42°", "50°", "60°", "68°"], "choices": [42.0, 50.0, 60.0, 68.0], "label": 2}
-{"prob_id": 1548, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1548.png", "question": "如图,□ABCD的周长为16cm,AC、BD相交于点O,OE⊥AC交AD于点E,则△DCE的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵平行四边形ABCD,∴AD=BC,AB=CD,OA=OC∵EO⊥AC∴AE=BC∵AB+BC+CD+AD=16cm∴AD+DC=8cm∴△DCE的周长是:CD+DE+CE-AE+DE+CD=AD+CD=8(cm)故选:B", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["10cm", "8cm", "6cm", "4cm"], "choices": [10.0, 8.0, 6.0, 4.0], "label": 1}
-{"prob_id": 1549, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1549.png", "question": "如图所示,△ABC是⊙O的内接三角形.若∠ABC=70°,则∠AOC的度数等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "因为∠ABC和∠AOC是同一条弧AC所对的圆周角和圆心角,所以∠AOC=2∠ABC×70°=140°", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["140°", "130°", "120°", "110°"], "choices": [140.0, 130.0, 120.0, 110.0], "label": 0}
-{"prob_id": 1559, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1559.png", "question": "如图,AB∥CD,射线AE交CD于点F,若∠1=115°,则∠2的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB||CD,∴∠1+∠AFD=180°,∵∠1=115°,∴∠AFD=65°,∵∠2和∠AFD是对顶角,∴∠2=∠AFD=65°故选B.", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["55°", "65°", "75°", "85°"], "choices": [55.0, 65.0, 75.0, 85.0], "label": 1}
-{"prob_id": 1561, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1561.png", "question": "如图,a//b,将一块三角板的直角顶点放在直线a上,∠1=42°,则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠1=42°∴∠3=90^{°}-42^{°}=48^{°},∵a||b,∴∠2=∠3,∴∠2=48°故选:B", "dataset_name": "Geoqa", "ground_truth": "48.0", "org_choices": ["46°", "48°", "56°", "72°"], "choices": [46.0, 48.0, 56.0, 72.0], "label": 1}
-{"prob_id": 1566, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1566.png", "question": "如图,a∥b,点B在直线b上,且AB⊥BC,∠1=36°,那么∠2=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "由题意可知:如下图所示∵AB⊥BC,∠1=36°,∴∠3=90°-∠1=54°∵a||b∴∠3=∠2=54°故选A", "dataset_name": "Geoqa", "ground_truth": "54.0", "org_choices": ["54°", "56°", "44°", "46°"], "choices": [54.0, 56.0, 44.0, 46.0], "label": 0}
-{"prob_id": 1579, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1579.png", "question": "如图,如果∠1=∠3,∠2=60°,那么∠4的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠1=∠3,∴a||b,∴∠5=∠2=60^{°},∴∠4=18O-60°=120°故选:C.", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["60°", "100°", "120°", "130°"], "choices": [60.0, 100.0, 120.0, 130.0], "label": 2}
-{"prob_id": 1593, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1593.png", "question": "如图,AB∥CD,AE平分∠CAB交CD于点E,若∠C=70°,则∠AED度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB||CD,∴∠BAC+∠C=180°,∵∠C=70°∴∠CAB=180°-70°=110°,又∵AE平分∠BAC,∴∠CAE=55°,∴∠AED=∠C+∠CAE=125°,故选B.", "dataset_name": "Geoqa", "ground_truth": "125.0", "org_choices": ["110°", "125°", "135°", "140°"], "choices": [110.0, 125.0, 135.0, 140.0], "label": 1}
-{"prob_id": 1594, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1594.png", "question": "如图,▱ABCD的周长为32cm,AC,BD相交于点O,OE⊥AC交AD于点E,则△DCE的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵平行四边形ABCD,∴AD=BC,AB=CD,OA=OC,∵EO⊥AC,∴AE=EC,∵AB+BC+CD+AD=32cm,∴AD+DC=16cm,∴△DCE的周长是:CD+DE+CE=AE+DE+CD=AD+CD=16cm,故选D.", "dataset_name": "Geoqa", "ground_truth": "16.0", "org_choices": ["8cm", "24cm", "10cm", "16cm"], "choices": [8.0, 24.0, 10.0, 16.0], "label": 3}
-{"prob_id": 1612, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1612.png", "question": "如图,一个底面圆周长为24m,高为5m的圆柱体,一只蚂蚁沿表面从点A到点B所经过的最短路线长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "将圆柱体的侧面展开,连接AB.如图所示:由于圆柱体的底面周长为24m,AD=24×\\frac{1}{2}=12m.又因为AC=5m,所以AB=√{12²+5²}=13m.即蚂蚁沿表面从点A到点B所经过的最短路线长为13m.故选C.", "dataset_name": "Geoqa", "ground_truth": "13.0", "org_choices": ["12m", "15m", "13m", "14m"], "choices": [12.0, 15.0, 13.0, 14.0], "label": 2}
-{"prob_id": 1626, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1626.png", "question": "如图,在△ABC中,∠BAC=90°,AD⊥BC于点D,AE平分∠DAC,∠B=50°,求∠DAE的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "在△ABC中,∵∠BAC=90°,∠B=50°,∴∠C=90°-∠B=40°∵AD⊥BC于点D,∴∠BAD=90°-∠B=40°;在△ADC中∵∠ADC=90°∠C=40°∴∠DAC=90°-∠C=50°,∵AE平分∠DAC,∴∠DAE=\\frac{1}{2}∠DAC=25^{°},故选:D", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["45°", "20°", "30°", "25°"], "choices": [45.0, 20.0, 30.0, 25.0], "label": 3}
-{"prob_id": 1632, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1632.png", "question": "如图,直线l∥m∥n,三角形ABC的顶点B,C分别在直线n和m上,边BC与直线n所夹的角为25°,且∠ACB=60°,则∠a的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图,∵I||m||n,∴∠a=∠1,∠2=25°∵∠ACB=∠a+∠2=60°∴∠a=60°-25°=35°故选C.", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["25°", "30°", "35°", "45°"], "choices": [25.0, 30.0, 35.0, 45.0], "label": 2}
-{"prob_id": 1638, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1638.png", "question": "如图,已知⊙O中,圆心角∠AOB=100°,则圆周角∠ACB等于().. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图:设点E是优弧AB上的一-点,连接EA,EB∵∠AOB=100^{°}∴∠E=\\frac{1}{2}∠AOB=50^{°}∴∠ACB=180^{°}-∠E=130^{°}", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["130°", "120°", "110°", "100°"], "choices": [130.0, 120.0, 110.0, 100.0], "label": 0}
-{"prob_id": 1656, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1656.png", "question": "如图,△ABC内接于半径为1的⊙O中,若∠BAC=60°,则BC的长度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作直径BD,连接CD,\n则∠BCD=90°,\n由圆周角定理得,∠D=∠BAC=60°,∴BC=BD×sin∠D=√{3},\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "1.7320508075688772", "org_choices": ["2", "2√{3}", "√{3}", "2√{2}"], "choices": [2.0, 3.464, 1.732, 2.828], "label": 2}
-{"prob_id": 1657, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1657.png", "question": "如图,圆O是△ABC的外接圆,∠BAC与∠ABC的平分线相交于点I,延长AI交圆O于点D,连结BD、DC．若圆O的半径为8,∠BAC=120°,则DI的长度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AI平分∠BAC,∴∠BAD=∠DAC,∴⁀{BD}=⁀{CD},∴BD=DC．∵BI平分∠ABC,∴∠ABI=∠CBI．∵∠BAD=∠DAC,∠DBC=∠DAC,∴∠BAD=∠DBC．\n又∵∠DBI=∠DBC+∠CBI,∠DIB=∠ABI+∠BAD,∴∠DBI=∠DIB,∴△BDI为等腰三角形,∴BD=ID,∴BD=DC=DI．∵∠BAC=120°,△ABC为钝角三角形,∴圆心O在△ABC外．\n连接OB、OD、OC．∵BD=CD,∴⁀{BD}=⁀{CD},∴∠DOC=∠BOD=2∠BAD=120°,∴∠DBC=∠DCB=60°,∴△BDC为正三角形．\n延长CO交BD于点E,则OE⊥BD,∴BE=\\frac{1}{2}BD,\n又∵OB=18,∴BD=2OB\\cos30°=2×8×\\frac{√{3}}{2}=√{3}8,∴DI=BD=8√{3},\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "13.856406460551018", "org_choices": ["4√{3}+2", "4√{3}+3", "8√{3}+1", "8√{3}"], "choices": [8.928, 9.928, 14.856, 13.856], "label": 3}
-{"prob_id": 1662, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1662.png", "question": "如图,⊙O是△ABC的外接圆,连接OB、OC,若⊙O的半径为2,∠BAC=60°,则BC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": ":延长BO交圆于D,连接CD．则∠BCD=90°,∠BDC=∠BAC=60°,∵⊙O的半径为2,∴BD=4,∴BC=2√{3},\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "3.4641016151377544", "org_choices": ["√{3}", "2√{3}", "4", "4√{3}"], "choices": [1.732, 3.464, 4.0, 6.928], "label": 1}
-{"prob_id": 1680, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1680.png", "question": "如图,AB和CD是⊙O的两条直径,弦DE∥AB,弧DE为50°的弧,那么∠BOC为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OE,∵弧DE为50°,∴∠EOD=50°,∴∠OED+∠ODE=130°∵OE=OD,∴∠OED=∠ODE=65°,∵DE∥AB,∴∠AOE=∠OED=65°,∴∠AOD=∠AOE+∠EOD=65°+50°=115°,∴∠BOC=∠AOD=115°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "115.0", "org_choices": ["115°", "100°", "80°", "50°"], "choices": [115.0, 100.0, 80.0, 50.0], "label": 0}
-{"prob_id": 1714, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1714.png", "question": "如图,点A、B、C在⊙O上,∠ABO=22°,∠ACO=42°,则∠BOC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过A作⊙O的直径,交⊙O于D；在△OAB中,OA=OB,则∠BOD=∠ABO+∠OAB=2×22°=44°,同理可得:∠COD=∠ACO+∠OAC=2×42°=84°,故∠BOC=∠BOD+∠COD=128°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "128.0", "org_choices": ["128°", "108°", "86°", "64°"], "choices": [128.0, 108.0, 86.0, 64.0], "label": 0}
-{"prob_id": 1716, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1716.png", "question": "如图,A,B,C是⊙O上三点,∠ACB=25°,则∠BAO的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB,∵∠ACB=25°,,∴∠AOB=2∠ACB=50°,,∵OA=OB,,∴∠OAB=∠OBA=\\frac{180^{°}-∠AOB}{2}=65°．,故选:D．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["50°", "55°", "60°", "65°"], "choices": [50.0, 55.0, 60.0, 65.0], "label": 3}
-{"prob_id": 1748, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1748.png", "question": "如图,已知⊙O中,∠AOB=50°,则圆周角∠ACB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠AOB=50°,∴∠ACB=\\frac{1}{2}∠AOB=25°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["50°", "25°", "100°", "30°"], "choices": [50.0, 25.0, 100.0, 30.0], "label": 1}
-{"prob_id": 1750, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1750.png", "question": "如图,AB为⊙O的直径,C、D是⊙O上的两点,∠BAC=30°,⁀{AD}=⁀{CD}．则∠DAC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB为⊙O的直径,∴∠ACB=90°,∴∠B=90°-∠BAC=90°-30°=60°,∴∠D=180°-∠B=120°,∵⁀{AD}=⁀{CD},∴AD=CD,∴∠DAC=∠DCA=\\frac{1}{2}(180°-120°)=30°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["70°", "45°", "30°", "25°"], "choices": [70.0, 45.0, 30.0, 25.0], "label": 2}
-{"prob_id": 1764, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1764.png", "question": "如图,AB是⊙O的直径,C、D为圆上两点,∠D=34°,则∠BOC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BC,∵∠D=34°,∴由圆周角定理得:∠B=∠D=34°,∵OC=OB,∴∠OCB=∠B=34°,∴∠BOC=180°-∠B-∠OCB=112°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "112.0", "org_choices": ["102°", "112°", "122°", "132°"], "choices": [102.0, 112.0, 122.0, 132.0], "label": 1}
-{"prob_id": 1781, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1781.png", "question": "如图,点A,B,C均在⊙O上,当∠OBC=40°时,∠A的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OB=OC,∴∠OCB=∠OBC=40°,∴∠BOC=180°-40°-40°=100°,∴∠A=\\frac{1}{2}∠BOC=50°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["50°", "55°", "60°", "65°"], "choices": [50.0, 55.0, 60.0, 65.0], "label": 0}
-{"prob_id": 1782, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1782.png", "question": "如图,⊙O的直径AB垂直于弦CD,垂足是点E,∠CAO=22.5°,OC=6,则CD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵CD⊥AB,∴CE=DE,∵∠BOC=2∠A=2×22.5°=45°,∴△OCE为等腰直角三角形,∴CE=\\frac{√{2}}{2}OC=\\frac{√{2}}{2}×6=3√{2},∴CD=2CE=6√{2}．故选:A．", "dataset_name": "Geoqa", "ground_truth": "8.48528137423857", "org_choices": ["6√{2}", "3√{2}", "6", "12"], "choices": [8.485, 4.243, 6.0, 12.0], "label": 0}
-{"prob_id": 1795, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1795.png", "question": "如图,⊙O中,弦BC与半径OA相交于点D,连接AB,OC．若∠A=60°,∠ADC=90°,则∠C的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ADC=∠A+∠B,∠A=60°,∠ADC=90°,∴∠B=30°,∴∠AOC=2∠B=60°,∵∠ADC=∠AOC+∠C,∴∠C=90°-60°=30°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["25°", "27.5°", "30°", "35°"], "choices": [25.0, 27.5, 30.0, 35.0], "label": 2}
-{"prob_id": 1805, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1805.png", "question": "如图,点A,B,P是⊙O上的三点,若∠AOB=40°,则∠APB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∠APB=\\frac{1}{2}∠AOB=\\frac{1}{2}×40°=20°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["80°", "140°", "20°", "50°"], "choices": [80.0, 140.0, 20.0, 50.0], "label": 2}
-{"prob_id": 1809, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1809.png", "question": "如图,AB是⊙O的弦,OC⊥AB,交⊙O于点C,连接OA,OB,BC,若∠ABC=25°,则∠AOB的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OC⊥AB,∴⁀{AC}=⁀{BC},∴∠AOC=∠BOC,∵∠AOC=2∠ABC=2×25°=50°,∴∠AOB=2∠AOC=100°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["80°", "90°", "100°", "120°"], "choices": [80.0, 90.0, 100.0, 120.0], "label": 2}
-{"prob_id": 1812, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1812.png", "question": "如图,已知圆周角∠A=50°,则∠OBC的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠A=50°,∴∠BOC=2∠A=100°．在△BOC中,OB=OC,∠BOC=100°,∴∠OBC=∠OCB=\\frac{1}{2}(180°-∠BOC)=40°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["50°", "40°", "130°", "80°"], "choices": [50.0, 40.0, 130.0, 80.0], "label": 1}
-{"prob_id": 1815, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1815.png", "question": "如图,AB为⊙O的直径,CD是⊙O的弦,∠ADC=26°,则∠CAB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由圆周角定理得,∠ABC=∠ADC=26°,∵AB为⊙O的直径,∴∠ACB=90°,∴∠CAB=90°-∠ABC=64°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "64.0", "org_choices": ["26°", "74°", "64°", "54°"], "choices": [26.0, 74.0, 64.0, 54.0], "label": 2}
-{"prob_id": 1822, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1822.png", "question": "如图,在⊙O中,AB是直径,CD是弦,AB⊥CD,垂足为点E,连接CO,AD,若∠BOC=30°,则∠BAD的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB⊥CD,∴⁀{BC}=⁀{BD},CE=DE,∴∠BAD=\\frac{1}{2}∠BOC=15°,故选:D．", "dataset_name": "Geoqa", "ground_truth": "15.0", "org_choices": ["30°", "25°", "20°", "15°"], "choices": [30.0, 25.0, 20.0, 15.0], "label": 3}
-{"prob_id": 1832, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1832.png", "question": "如图,AB是⊙O的直径,点C、D是圆上两点,且∠AOC=126°,则∠CDB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠AOC=126°,∴∠BOC=180°-∠AOC=54°,∵∠CDB=\\frac{1}{2}∠BOC=27°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "27.0", "org_choices": ["54°", "64°", "27°", "37°"], "choices": [54.0, 64.0, 27.0, 37.0], "label": 2}
-{"prob_id": 1848, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1848.png", "question": "如图,AB是⊙O的直径,点C、D在⊙O上,且点C是弧BD的中点,过点C作AD的垂线EF交直线AD于点E,若⊙O的半径为2.5,AC长为4,则CE的长度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BC,∵点C是弧BD的中点,∴∠EAC=∠CAB,又∵AB为直径,AE⊥EF,∴∠AEC=∠ACB=90°,∴△EAC∽△CAB,∴\\frac{AC}{AB}=\\frac{EC}{BC},∴EC=\\frac{AC\\cdotBC}{AB}=\\frac{4×√{5^{2}-4^{2}}}{5}=\\frac{12}{5}．故选:C．", "dataset_name": "Geoqa", "ground_truth": "2.4", "org_choices": ["3", "\\frac{20}{3}", "\\frac{12}{5}", "\\frac{16}{5}"], "choices": [3.0, 6.667, 2.4, 3.2], "label": 2}
-{"prob_id": 1849, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1849.png", "question": "如图,点A,B,C在⊙O上,已知∠ABC=130°,则∠AOC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在优弧AC上取点D,连接AD,CD,∵四边形ABCD是圆内接四边形,∠ABC=130°,∴∠D=180°-10°=50°．∵∠D与∠AOC是同弧所对的圆周角与圆心角,∴∠AOC=2∠D=100°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["100°", "110°", "120°", "130°"], "choices": [100.0, 110.0, 120.0, 130.0], "label": 0}
-{"prob_id": 1858, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1858.png", "question": "如图,已知⊙O的半径为5,弦AB、CD所对的圆心角分别是∠AOB,∠COD,且∠AOB与∠COD互补,弦CD=8,则弦AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:解:如图,延长AO交⊙O于点E,连接BE,则∠AOB+∠BOE=180°,又∵∠AOB+∠COD=180°,∴∠BOE=∠COD,∴BE=CD,∵AE为⊙O的直径,∴∠ABE=90°,∴AB=√{AE^{2}-BE^{2}}=√{10^{2}-8^{2}}=6,故选:A．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["6", "8", "5√{2}", "5√{3}"], "choices": [6.0, 8.0, 7.071, 8.66], "label": 0}
-{"prob_id": 1860, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1860.png", "question": "如图,AB是圆O的直径,CD是圆O的弦,AB、CD的延长线交于点E,已知AB=2DE,∠E=16°,则∠ABC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OD,∵AB是圆O的直径,∴AB=2OD,∵AB=2DE,∴OD=DE,∴∠EOD=∠E=16°∴∠C=\\frac{1}{2}∠BOD=8°,∴∠ABC=∠C+∠E=8°+16°=24°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "24.0", "org_choices": ["32°", "24°", "16°", "48°"], "choices": [32.0, 24.0, 16.0, 48.0], "label": 1}
-{"prob_id": 1903, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1903.png", "question": "本题考查了圆周角定理,关键是根据同弦所对圆心角与圆周角的关系解答．\n4．如图,AB是⊙O的直径,C是⊙O上一点(A、B除外),∠AOD=136°,则∠C的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解,∵∠AOD=136°,∴∠BOD=44°,∴∠C=22°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "22.0", "org_choices": ["44°", "22°", "46°", "36°"], "choices": [44.0, 22.0, 46.0, 36.0], "label": 1}
-{"prob_id": 1916, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1916.png", "question": "如图,AB是⊙O的直径,点C、D在⊙O上．若∠BOD=130°,则∠ACD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BOD=130°,∴∠AOD=50°,∴∠ACD=\\frac{1}{2}∠AOD=25°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["50°", "30°", "25°", "20°"], "choices": [50.0, 30.0, 25.0, 20.0], "label": 2}
-{"prob_id": 1929, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1929.png", "question": "绍兴是著名的桥乡．如图,圆拱桥的桥顶到水面的距离CD为8m,桥拱半径OC为5m,则水面宽AB为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OA,如图所示．∵CD⊥AB,∴AD=BD=\\frac{1}{2}AB．在Rt△ADO中,OA=OC=5m,OD=CD-OC=3m,∠ADO=90°,∴AD=√{0A^{2}-0D^{2}}=4m,∴AB=2AD=8m．故选:D．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["4m", "5m", "6m", "8m"], "choices": [4.0, 5.0, 6.0, 8.0], "label": 3}
-{"prob_id": 1933, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1933.png", "question": "如图,已知∠α=130°,则∠β=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠α=130°,∴∠1=130°-90°=40°,∴∠β=∠1=40°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["30°", "40°", "50°", "65°"], "choices": [30.0, 40.0, 50.0, 65.0], "label": 1}
-{"prob_id": 1937, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1937.png", "question": "如图,当圆形桥孔中的水面宽度AB为8米时,弧ACB恰为半圆．当水面上涨1米时,桥孔中的水面宽度A′B′为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设圆的圆心是O,作弦A′B′的弦心距OE,连接OA′．根据题意,得在直角三角形OA′E中,OA′=4,OE=1．根据勾股定理得A′E=√{15}m．再根据垂径定理得A′B′=2A′E=2√{15}m．故选:B．", "dataset_name": "Geoqa", "ground_truth": "7.745966692414834", "org_choices": ["√{15}米", "2√{15}米", "2√{17}米", "不能计算"], "choices": [3.873, 7.746, 8.246], "label": 1}
-{"prob_id": 1957, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1957.png", "question": "在直角三角形ABC中,∠CAB=90°,∠ABC=72°,AD是∠CAB的角平分线,交边BC于点D,过点C作△ACD中AD边上的高线CE,则∠ECD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠CAB=90°,AD是∠CAB的角平分线,∴∠CAD=\\frac{1}{2}×90°=45°,∵CE⊥AD,∴∠ACE=90°-45°=45°,又∵∠CAB=90°,∠ABC=72°,∴∠ACB=90°-72°=18°,∴∠ECD=∠ACE-∠ACB=45°-18°=27°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "27.0", "org_choices": ["63°", "45°", "27°", "18°"], "choices": [63.0, 45.0, 27.0, 18.0], "label": 2}
-{"prob_id": 1977, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1977.png", "question": "如图,AO是圆锥的高,圆锥的底面半径OB=0.7,AB的长为2.5,则AO的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由勾股定理得,AO=√{AB^{2}-0B^{2}}=2.4,故选:A．", "dataset_name": "Geoqa", "ground_truth": "2.4", "org_choices": ["2.4", "2.2", "1.8", "1.6"], "choices": [2.4, 2.2, 1.8, 1.6], "label": 0}
-{"prob_id": 1981, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1981.png", "question": "如图,在⊙O中,弦AC和BD相交于点E,⁀{AB}=⁀{BC}=⁀{CD},若∠BEC=110°,则∠BDC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵⁀{AB}=⁀{BC}=⁀{CD},∴∠BDC=∠ACB=∠DBC,∵∠BEC=110°,∴∠ACB=∠DBC=35°．∴∠BDC=35°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["35°", "45°", "55°", "70°"], "choices": [35.0, 45.0, 55.0, 70.0], "label": 0}
-{"prob_id": 1988, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1988.png", "question": "如图,半径为1cm,圆心角为90°的扇形OAB中,分别以OA,OB为直径作半圆,则图中阴影部分的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过点C作CD⊥OB,CE⊥OA,∵OB=OA,∠AOB=90°,∴△AOB是等腰直角三角形,∵OA是直径,∴∠ACO=90°,∴△AOC是等腰直角三角形,∵CE⊥OA,∴OE=AE,OC=AC,在Rt△OCE与Rt△ACE中,∵≥ft\\lbrace\\begin{array}{l}{OC=AC}\\\\{OE=AE}\\end{array}\\right.,∴Rt△OCE≌Rt△ACE,∵S扇形OEC=S扇形AEC,∴➝{0C}与弦OC围成的弓形的面积等于⌒{AC}与弦AC所围成的弓形面积,同理可得,➝{0C}与弦OC围成的弓形的面积等于⌒{BC}与弦BC所围成的弓形面积,∴S阴影=S△AOB=\\frac{1}{2}×1×1=\\frac{1}{2}cm²．故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.5", "org_choices": ["πcm²", "\\frac{2}{3}πcm²", "\\frac{1}{2}cm²", "\\frac{2}{3}cm²"], "choices": [3.142, 2.094, 0.5, 0.667], "label": 2}
-{"prob_id": 1991, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1991.png", "question": "用圆心角为120°,半径为6cm的扇形纸片卷成一个圆锥形无底纸帽(如图所示),则这个纸帽的底面周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:这个纸帽的底面周长=\\frac{120\\cdotπ\\cdot6}{180}=4π(cm)．故选:C．", "dataset_name": "Geoqa", "ground_truth": "12.566370614359172", "org_choices": ["2πcm", "3πcm", "4πcm", "5πcm"], "choices": [6.283, 9.425, 12.566, 15.708], "label": 2}
-{"prob_id": 2020, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2020.png", "question": "如图是一顶圆锥形烟囱小纸帽,它的母线长l是13cm,高h为12cm,则制作这顶纸帽所需纸张的面积是(接缝忽略不计)(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵圆锥的母线长l是13cm,高h为12cm,∴圆锥的底面半径为r=√{13^{2}-12^{2}}=5cm,∴这张扇形纸板的面积=\\frac{1}{2}×2π×5×13=65π(cm^{2})．故选:B．", "dataset_name": "Geoqa", "ground_truth": "204.20352248333657", "org_choices": ["60π", "65π", "78π", "156π"], "choices": [188.496, 204.204, 245.044, 490.088], "label": 1}
-{"prob_id": 2045, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2045.png", "question": "用圆心角为120°,半径为3cm的扇形纸片卷成一个圆锥形无底纸冒(如图所示),则这个纸冒的高是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设圆锥的底面半径长为xcm,根据题意得2πx=\\frac{120\\cdotπ\\cdot3}{180}解得x=1,所以这个纸冒的高=√{3^{2}-1^{2}}=2√{2}(cm)．故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.8284271247461903", "org_choices": ["3cm", "2√{2}cm", "3√{2}cm", "4√{2}cm"], "choices": [3.0, 2.828, 4.243, 5.657], "label": 1}
-{"prob_id": 2053, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2053.png", "question": "如图,一个圆锥的侧面展开图是半径为10的半圆,则它的底面半径是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设圆锥的底面半径为r,根据题意得\\frac{1}{2}•2π•r•10=\\frac{180\\cdotπ\\cdot10^{2}}{360},解得r=5,即圆锥的底面半径为5．故选:C．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["3", "4", "5", "6"], "choices": [3.0, 4.0, 5.0, 6.0], "label": 2}
-{"prob_id": 2069, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2069.png", "question": "如图,用一张半径为24cm的扇形纸板制作一顶圆锥形帽子(接缝忽略不计),如果圆锥形帽子的底面半径为10cm,那么这张扇形纸板的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:这张扇形纸板的面积=\\frac{1}{2}×2π×10×24=240π(cm^{2})．故选:A．", "dataset_name": "Geoqa", "ground_truth": "753.9822368615504", "org_choices": ["240πcm^{2}", "480πcm^{2}", "1200πcm^{2}", "2400πcm^{2}"], "choices": [753.982, 1507.964, 3769.911, 7539.822], "label": 0}
-{"prob_id": 2088, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2088.png", "question": "如图,圆锥的母线长为5cm,高线长为4cm,则圆锥的底面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:圆锥的底面圆的半径=√{5^{2}-4^{2}}=3,所以圆锥的底面积=π•3^{2}=9π(cm^{2})．故选:B．", "dataset_name": "Geoqa", "ground_truth": "28.274333882308138", "org_choices": ["3πcm^{2}", "9πcm^{2}", "16πcm^{2}", "25πcm^{2}"], "choices": [9.425, 28.274, 50.265, 78.54], "label": 1}
-{"prob_id": 2093, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2093.png", "question": "我国纸伞的制作工艺十分巧妙．如图,伞不管是张开还是收拢,伞柄AP始终平分同一平面内两条伞骨所成的角∠BAC,且AE=AF,DE=DF,从而保证伞圈能沿着伞柄滑动．有一种玩具伞张开时,BDC在同一直线上,若AB=50cm,AD=14cm,则制作一把这样的纸伞需要油纸的面积是(不记接缝)(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB=50cm,AD=14cm,∴BD=√{AB^{2}-AD^{2}}=√{50^{2}-14^{2}}=48cm,S侧=\\frac{1}{2}lR=\\frac{1}{2}•48π×2×50=2400π,故选:C．", "dataset_name": "Geoqa", "ground_truth": "7539.822368615503", "org_choices": ["48cm^{2}", "70πcm^{2}", "2400πcm^{2}", "2500πcm^{2}"], "choices": [48.0, 219.911, 7539.822, 7853.982], "label": 2}
-{"prob_id": 2099, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2099.png", "question": "如图用圆心角为120°,半径为6的扇形围成一个圆锥的侧面(接缝忽略不计),则这个圆锥的高是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设圆锥的底面圆的半径为r,根据题意得2πr=\\frac{120\\cdotπ\\cdot6}{180},解得r=2,所以圆锥的高=√{6^{2}-2^{2}}=4√{2}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "5.656854249492381", "org_choices": ["6", "8", "3√{3}", "4√{2}"], "choices": [6.0, 8.0, 5.196, 5.657], "label": 3}
-{"prob_id": 2110, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2110.png", "question": "如图,在Rt△ABC中,∠ACB=90°,AC=4,BC=3,将△ABC绕AC所在的直线旋转一周得到一个旋转体,则该旋转体的侧面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由勾股定理得AB=5,BC=3,则圆锥的底面周长=6π,旋转体的侧面积=\\frac{1}{2}×6π×5=15π,故选:B．", "dataset_name": "Geoqa", "ground_truth": "47.1238898038469", "org_choices": ["12π", "15π", "30π", "60π"], "choices": [37.699, 47.124, 94.248, 188.496], "label": 1}
-{"prob_id": 2142, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2142.png", "question": "如图,在纸上剪下一个圆形和一个扇形的纸片,使之恰好能围成一个圆锥模型．若圆的半径为1,扇形的圆心角等于90°,则扇形的半径是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:扇形的弧长等于底面圆的周长得出2π．设扇形的半径是r,则\\frac{90πr}{180}=2π,解得:r=4．故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["2", "4", "6", "8"], "choices": [2.0, 4.0, 6.0, 8.0], "label": 1}
-{"prob_id": 2161, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2161.png", "question": "如图一个扇形铁皮OAB,已知OA=30cm,∠AOB=120°,工人师傅将OA、OB合拢制成了一个圆锥形的烟囱帽(接缝忽略不计),则烟囱帽的底面圆的半径为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:扇形的弧长是:\\frac{120π×30}{180}=20πcm,设底面半径是r,则2πr=20π,解得:r=10．故选:C．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["5cm", "12cm", "10cm", "15cm"], "choices": [5.0, 12.0, 10.0, 15.0], "label": 2}
-{"prob_id": 2177, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2177.png", "question": "如图,已知圆锥的底面半径为6,母线长为10,则此圆锥的侧面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:底面周长是:2×6π=12π,则圆锥的侧面积是:\\frac{1}{2}×12π×10=60π．故选:A．", "dataset_name": "Geoqa", "ground_truth": "188.4955592153876", "org_choices": ["60π", "80π", "10π", "96π"], "choices": [188.496, 251.327, 31.416, 301.593], "label": 0}
-{"prob_id": 2201, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2201.png", "question": "露露从纸上剪下一个圆形和一个扇形的纸片(如图),用它们恰好能围成一个圆锥模型,若圆的半径为1．扇形的圆心角等于120°,则此扇形的半径为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:扇形的弧长是2π．设扇形的半径是r,则\\frac{120πr}{180}=2π,解得:r=3．故选:C．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["√{3}", "√{6}", "3", "6"], "choices": [1.732, 2.449, 3.0, 6.0], "label": 2}
-{"prob_id": 2203, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2203.png", "question": "如图,有一圆心角为120°、半径长为6cm的扇形,若将OA、OB重合后围成一圆锥侧面,那么圆锥底面的直径是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:扇形的弧长是:\\frac{120π×6}{180}=4π,即底面周长是4π．设底面半径是r,则2πr=4π,解得:2r=4cm．故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["2cm", "4cm", "3cm", "5cm"], "choices": [2.0, 4.0, 3.0, 5.0], "label": 1}
-{"prob_id": 2231, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2231.png", "question": "如图所示,圆锥形帐篷顶的母线长AB=10cm,底面半径长BO=5m,这个圆锥形帐篷顶的侧面积(不计接缝)是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意得,l=10cm,故可得S圆锥形帐篷顶的侧面积=πrl=50πcm^{2}．故选:C．", "dataset_name": "Geoqa", "ground_truth": "157.07963267948966", "org_choices": ["15πm^{2}", "30πm^{2}", "50πm^{2}", "75πm^{2}"], "choices": [47.124, 94.248, 157.08, 235.619], "label": 2}
-{"prob_id": 2237, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2237.png", "question": "如图,在⊙O中,弦AB的长为10,圆周角∠ACB=45°,则这个圆的直径AD为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BD,∵∠ACB=45°,∴∠ADB=45°,∵直径AD,∴∠ABD=90°,∵AB=10,∴AD=10√{2}．故选B．", "dataset_name": "Geoqa", "ground_truth": "14.142135623730951", "org_choices": ["5√{2}", "10√{2}", "15√{2}", "20√{2}"], "choices": [7.071, 14.142, 21.213, 28.284], "label": 1}
-{"prob_id": 2257, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2257.png", "question": "如图,△ABC中．∠C=90°,点D是边BC上一个动点(点D不与点C重合)．以CD为直径的圆交AD于点P．若AC=6．线段BP长度的最小值是2．则AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵CD为直径,∴∠CPD=90°,∵∠APC=90°,∴点P在以AC为直径的⊙O上,如图,连接OB交⊙O于P′,∵线段BP长度的最小值是2,∴BP′=2,∴OB=2+3=5,在Rt△OBC中,BC=√{5^{2}-3^{2}}=4,在Rt△ABC中,AB=√{4^{2}+6^{2}}=2√{13}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "7.211102550927978", "org_choices": ["8", "2√{10}", "4√{3}", "2√{13}"], "choices": [8.0, 6.325, 6.928, 7.211], "label": 3}
-{"prob_id": 2284, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2284.png", "question": "如图,小明为了测量一凉亭的高度AB(顶端A到水平地面BD的距离),在凉亭的旁边放置一个与凉亭台阶BC等高的台阶DE(DE=BC=0.6米,求A、B、C三点共线),把一面镜子水平放置在平台上的点G处,测得CG=12米,然后沿直线CG后退到点E处,这时恰好在镜子里看到凉亭的顶端A,测得GE=2米,小明身高EF=1.6米,则凉亭的高度AB约为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意∠AGC=∠FGE,∵∠ACG=∠FEG=90°,∴△ACG∽△FEG,∴AC:EF=CG:GE,∴\\frac{AC}{1.6}=\\frac{12}{2},∴AC=9.6米,∴AB=AC+BC=9.6+0.6=10.2米．故选:D．", "dataset_name": "Geoqa", "ground_truth": "10.2", "org_choices": ["9米", "9.6米", "10米", "10.2米"], "choices": [9.0, 9.6, 10.0, 10.2], "label": 3}
-{"prob_id": 2287, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2287.png", "question": "如图,为了估计荆河的宽度,在荆河的对岸选定一个目标点P,在近岸取点Q和S,使点P、Q、S在一条直线上,且直线PS与河垂直,在过点S且与PS垂直的直线a上选择适当的点T,PT与过点Q且与PS垂直的直线b的交点为R,如果QS=60m,ST=120m,QR=80m,则荆河的宽度PQ为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意可知:QR∥ST,∴△PQR∽△PST,∴\\frac{PQ}{PS}=\\frac{QR}{ST}设PQ=x,∴\\frac{x}{x+60}=\\frac{80}{120}解得:x=120故PQ=120m故选:B．", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["40m", "120m", "60m", "180m"], "choices": [40.0, 120.0, 60.0, 180.0], "label": 1}
-{"prob_id": 2303, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2303.png", "question": "如图是小莹设计用手电来测量某古城墙高度的示意图．在点P处放一水平的平面镜,光线从点A出发经平面镜反射后,刚好射到古城墙CD的顶端C处．已知AB⊥BD,CD⊥BD．且测得AB=1.4米,BP=2.1米,PD=12米．那么该古城墙CD的高度是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠APB=∠CPD,∠ABP=∠CDP,∴△ABP∽△CDP∴\\frac{AB}{CD}=\\frac{BP}{PD}即\\frac{1.4}{CD}=\\frac{2.1}{12}解得:CD=8米．故选:B．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["6米", "8米", "10米", "12米"], "choices": [6.0, 8.0, 10.0, 12.0], "label": 1}
-{"prob_id": 2312, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2312.png", "question": "如图,在⊙O中,点M是⁀{AB}的中点,连结MO并延长,交⊙O于点N,连结BN,若∠AOB=140°,则∠N的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵点M是⁀{AB}的中点,∴⁀{AM}=⁀{BM},∵∠AOB=140°,∴∠BOM=\\frac{1}{2}∠AOB=70°,∴∠N=\\frac{1}{2}∠BOM=35°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["70°", "40°", "35°", "20°"], "choices": [70.0, 40.0, 35.0, 20.0], "label": 2}
-{"prob_id": 2317, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2317.png", "question": "如图,某数学学习兴趣小组为了测量树AB的度数,他们测得此树在阳光下的影子BC的长为9m,在相同时刻,他们还测得小亮在阳光下的影长为1.5m,已知小亮的身高为1.8m,则树AB的高为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵同一时刻物高与影长成正比例．∴1.8:1.5=树AB的高:9,∴树AB的高是10.8米．故选:A．", "dataset_name": "Geoqa", "ground_truth": "10.8", "org_choices": ["10.8m", "9m", "7.5m", "0.3m"], "choices": [10.8, 9.0, 7.5, 0.3], "label": 0}
-{"prob_id": 2319, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2319.png", "question": "如图所示为农村一古老的捣碎器,已知支撑柱AB的高为0.3米,踏板DE长为1米,支撑点A到踏脚D的距离为0.6米,原来捣头点E着地,现在踏脚D着地,则捣头点E上升了(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图:∵AB∥EF,∴△DAB∽△DEF,∴AD:DE=AB:EF,∴0.6:1=0.3:EF,∴EF=0.5(米)．∴捣头点E上升了0.5米．故选:A．", "dataset_name": "Geoqa", "ground_truth": "0.5", "org_choices": ["0.5米", "0.6米", "0.3米", "0.9米"], "choices": [0.5, 0.6, 0.3, 0.9], "label": 0}
-{"prob_id": 2356, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2356.png", "question": "如图,光源P在横杆AB的正上方,AB在灯光下的影子为CD,AB∥CD,AB=2m,CD=5m,点P到CD的距离是3m,则AB与CD的距离是()m．. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设点P到AB的距离为xm,∵AB∥CD,∴△PAB∽△PCD,∴\\frac{x}{3}=\\frac{AB}{CD}=\\frac{2}{5},解得x=\\frac{6}{5}m．3-\\frac{6}{5}=\\frac{9}{5}m,故选:C．", "dataset_name": "Geoqa", "ground_truth": "1.8", "org_choices": ["\\frac{6}{5}", "\\frac{7}{6}", "\\frac{9}{5}", "\\frac{15}{2}"], "choices": [1.2, 1.167, 1.8, 7.5], "label": 2}
-{"prob_id": 2358, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2358.png", "question": "如图,小强自制了一个小孔成像装置,其中纸筒的长度为15cm,他准备了一支长为20cm的蜡烛,想要得到高度为4cm的像,蜡烛与纸筒的距离应该为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,AB=20cm,OF=15cm,CD=4cm,∵AB∥CD,EF⊥AB∴EF⊥CD,∴△OAB∽△ODC,∴\\frac{CD}{AB}=\\frac{0F}{OE},即\\frac{4}{20}=\\frac{15}{OE},解得OE=75cm．故选:D．", "dataset_name": "Geoqa", "ground_truth": "75.0", "org_choices": ["60cm", "65cm", "70cm", "75cm"], "choices": [60.0, 65.0, 70.0, 75.0], "label": 3}
-{"prob_id": 2375, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2375.png", "question": "如图,在一场羽毛球比赛中,站在场内M处的运动员林丹把求从N点击到了对方内的B点,已知网高OA=1.52m,OB=4m,OM=5m,则林丹起跳后击球点离地面的距离NM=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:根据题意得:AO⊥BM,NM⊥BM,∴AO∥NM,∴△ABO∽△NBM,∴\\frac{0A}{NM}=\\frac{OB}{BM},∵OA=1.52米,OB=4米,OM=5米,∴BM=OB+OM=4+5=9(米),∴\\frac{1.52}{NM}=\\frac{4}{9},解得:NM=3.42(米),∴林丹起跳后击球点N离地面的距离NM为3.42米．故选:A．", "dataset_name": "Geoqa", "ground_truth": "3.42", "org_choices": ["3.42m", "1.9m", "3m", "3.24m"], "choices": [3.42, 1.9, 3.0, 3.24], "label": 0}
-{"prob_id": 2377, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2377.png", "question": "小明在测量楼高时,先测出楼房落在地面上的影长BA为15米(如图),然后在A处树立一根高2米的标杆,测得标杆的影长AC为3米,则楼高为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵\\frac{标杆的高}{标杆的影长}=\\frac{楼高}{楼影长}即\\frac{2}{3}=\\frac{楼高}{15},∴楼高=10米．故选:A．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["10米", "12米", "15米", "22.5米"], "choices": [10.0, 12.0, 15.0, 22.5], "label": 0}
-{"prob_id": 2383, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2383.png", "question": "如图所示:两根竖直的电线杆AB长为6,CD长为3,AD交于BC于点E点,则E到地面的距离EF的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵两根电线杆AB、CD都竖直,EF垂直于地面,∴△ABD∽△EFD,△BCD∽△BEF,∴\\frac{DF}{BD}=\\frac{EF}{AB},\\frac{BF}{BD}=\\frac{EF}{CD},∴\\frac{DF}{BD}+\\frac{BF}{BD}=\\frac{EF}{CD}+\\frac{EF}{AB},即\\frac{EF}{6}+\\frac{EF}{3}=1,解得EF=2．故选:A．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["2", "2.2", "2.4", "2.5"], "choices": [2.0, 2.2, 2.4, 2.5], "label": 0}
-{"prob_id": 2420, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2420.png", "question": "如图,要在一块△ABC的纸片上截取正方形DEFG模型．其中,G、F在BC边上,D、E分别在AB、AC边上,AH⊥BC交DE于M,若BC=12cm,AH=8cm,则正方形DEFG的边长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:假设正方形边长为x厘米,\n在△ABC中可得:\\frac{DE}{BC}=\\frac{AM}{AH},∵BC=12cm,BC边上的高为8cm,∴AH=8cm,DE=xcm,AM=(8-x)cm代入上式得:\\frac{x}{12}=\\frac{8-x}{8},\n解得:x=4.8cm．∴正方形的边长是4.8cm．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "4.8", "org_choices": ["\\frac{24}{5}cm", "4cm", "\\frac{24}{7}cm", "5cm"], "choices": [4.8, 4.0, 3.429, 5.0], "label": 0}
-{"prob_id": 2431, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2431.png", "question": "2009年l0月27日,上海队小将吴迪在全运会赛场上脱颖而出,以2:0的比分战胜了男子单打头号种子选手曾少眩,勇夺全运会网球男子单打冠军．下图是吴迪在决赛中打的一个球,已知网高0.8米,击球点到网的水平距离为4米,打球时使球恰好能打过网,且落点恰好在离网6米的位置上,则球拍击球的高度h为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图:∵AB∥CD∴△ABE∽△CDE,∴\\frac{CE}{AE}=\\frac{CD}{AB},∴\\frac{6}{10}=\\frac{0.8}{AB},∴h=AB=\\frac{4}{3}(米)．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "1.3333333333333333", "org_choices": ["\\frac{8}{5}米", "\\frac{4}{3}米", "1米", "\\frac{8}{15}米"], "choices": [1.6, 1.333, 1.0, 0.533], "label": 1}
-{"prob_id": 2432, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2432.png", "question": "如图,点A、B、C在⊙O上,∠ABO=40°,∠ACO=30°,则∠BOC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过A作⊙O的直径,交⊙O于D；在△OAB中,OA=OB,即∠OBA=∠OAB,则∠BOD=∠ABO+∠OAB=2×40°=80°,同理可得:∠COD=∠ACO+∠OAC=2×30°=60°,故∠BOC=∠BOD+∠COD=140°,故选:D．", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["60°", "70°", "120°", "140°"], "choices": [60.0, 70.0, 120.0, 140.0], "label": 3}
-{"prob_id": 2434, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2434.png", "question": "如图,AB是斜靠在墙上的梯子,梯脚距墙2米,梯子上的D点距墙1.8米,BD长0.6米,则梯子的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE⊥AC,BC⊥AC,∴DE∥BC,∴△ADE∽△ABC,∴\\frac{AB}{AD}=\\frac{BC}{DE},∴AB=6．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["5.60米", "6.00米", "6.10米", "6.20米"], "choices": [5.6, 6.0, 6.1, 6.2], "label": 1}
-{"prob_id": 2436, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2436.png", "question": "某校数学兴趣小组为测量学校旗杆AC的高度,在点F处竖立一根长为1.5米的标杆DF,如图所示,量出DF的影子EF的长度为1米,再量出旗杆AC的影子BC的长度为6米,那么旗杆AC的高度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵\\frac{标杆的高}{标杆的影长}=\\frac{旗杆的高}{旗杆的影长}\n即\\frac{1.5}{1}=\\frac{AC}{6},∴AC=6×1.5=9米．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["6米", "7米", "8.5米", "9米"], "choices": [6.0, 7.0, 8.5, 9.0], "label": 3}
-{"prob_id": 2438, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2438.png", "question": "如图,小东用长3.2m的竹竿做测量工具测量学校旗杆的高度,移动竹竿,使竹竿、旗杆顶端的影子恰好落在地面的同一点．此时,竹竿与这一点相距8m,与旗杆相距22m,则旗杆的高为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:因为BE∥CD,所以△AEB∽△ADC,\n于是\\frac{AE}{AD}=\\frac{BE}{CD},即\\frac{8}{22+8}=\\frac{3.2}{CD},\n解得:CD=12．\n旗杆的高为12m．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["12m", "10m", "8m", "7m"], "choices": [12.0, 10.0, 8.0, 7.0], "label": 0}
-{"prob_id": 2445, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2445.png", "question": "如图,CD是平面镜子,光线从A点射出,经CD上一点E反射后照射到B点,若入射角为α,AC⊥CD,BD⊥CD,垂足分别为C、D,且AC=3,BD=6,CD=10,则线段ED的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,∵CD是平面镜,α为入射角,∠1为反射角∴α=∠1．∵α+∠AEC=90°,∠1+∠BED=90°∴∠AEC=BED,∵AC⊥CD,BD⊥CD∴∠ACE=∠BDE=90°∴Rt△ACE∽Rt△BDE,∴\\frac{AC}{BD}=\\frac{CE}{ED},∵AC=3,BD=6,CD=10∴\\frac{3}{6}=\\frac{10-ED}{ED},\n解得ED=\\frac{20}{3}．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "6.666666666666667", "org_choices": ["\\frac{20}{3}", "\\frac{10}{3}", "7", "\\frac{14}{3}"], "choices": [6.667, 3.333, 7.0, 4.667], "label": 0}
-{"prob_id": 2446, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2446.png", "question": "如图,小明设计两个直角,来测量河宽BC,他量得AB=2米,BD=\\frac{7}{3}米,CE=9米,则河宽BC为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BD∥CE∴△ABD∽△ACE∴,∵AB=2,BD=\\frac{7}{3},CE=9∴AC=\\frac{AB\\cdotCE}{BD}=\\frac{2×9}{\\frac{7}{3}}=\\frac{54}{7},∴BC=AC-AB=\\frac{54}{7}-2=\\frac{40}{7}米．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "5.714285714285714", "org_choices": ["\\frac{7}{2}米", "\\frac{17}{2}米", "\\frac{40}{7}米", "11米"], "choices": [3.5, 8.5, 5.714, 11.0], "label": 2}
-{"prob_id": 2451, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2451.png", "question": "如图,一同学在湖边看到一棵树,他目测出自己与树的距离为20m,树的顶端在水中的倒影距自己5m远,该同学的身高为1.7m,则树高为()m．. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由相似三角形的性质,设树高x米,\n则\\frac{5}{20-5}=\\frac{1.7}{x},∴x=5.1m．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "5.1", "org_choices": ["3.4", "5.1", "6.8", "8.5"], "choices": [3.4, 5.1, 6.8, 8.5], "label": 1}
-{"prob_id": 2466, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2466.png", "question": "如图,AB是斜靠在墙壁上的固定爬梯,梯脚B到墙脚C的距离1.6m,梯上一点D到墙面的距离1.4m,BD长0.5m,则梯子的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:因为梯子每一条踏板均和地面平行,所以构成一组相似三角形,\n即△ABC∽△ADE,则\\frac{DE}{BC}=\\frac{AD}{AB},\n设梯子长为x米,则\\frac{x-0.5}{x}=\\frac{1.4}{1.6},\n解得,x=4(m)．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["3.5m", "4m", "4.5m", "5m"], "choices": [3.5, 4.0, 4.5, 5.0], "label": 1}
-{"prob_id": 2472, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2472.png", "question": "如图,阳光从教室的窗户射入室内,窗户框AB在地面上的影长DE=1.8m,窗户下檐到地面的距离BC=1m,EC=1.2m,那么窗户的高AB为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BE∥AD,∴△BCE∽△ACD,∴\\frac{CB}{AC}=\\frac{CE}{CD}即\\frac{BC}{AB+BC}=\\frac{EC}{DE+EC}\n且BC=1,DE=1.8,EC=1.2∴\\frac{1}{AB+1}=\\frac{1.2}{1.8+1.2}∴1.2AB=1.8,∴AB=1.5m．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "1.5", "org_choices": ["1.5m", "1.6m", "1.86m", "2.16m"], "choices": [1.5, 1.6, 1.86, 2.16], "label": 0}
-{"prob_id": 2484, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2484.png", "question": "如图,AB是斜靠在墙壁上的长梯,梯脚B距墙1.6米,梯上点D距墙1.4米,BD长0.55米,则梯子长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:因为梯子每一条踏板均和地面平行,所以构成一组相似三角形,\n即△ABC∽△ADE,则\\frac{DE}{BC}=\\frac{AD}{AB}\n设梯子长为x米,则\\frac{x-0.55}{x}=\\frac{1.4}{1.6},\n解得,x=4.40．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "4.4", "org_choices": ["3.85米", "4.00米", "4.40米", "4.50米"], "choices": [3.85, 4.0, 4.4, 4.5], "label": 2}
-{"prob_id": 2496, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2496.png", "question": "如图,身高1.6米的学生小李想测量学校的旗杆的高度,当他站在C处时,他头顶端的影子正好与旗杆顶端的影子重合,并测得AC=2米,BC=8米,则旗杆的高度是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设旗杆高度为h,\n由题意得\\frac{1.6}{h}=\\frac{2}{2+8},h=8米．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["6.4米", "7米", "8米", "9米"], "choices": [6.4, 7.0, 8.0, 9.0], "label": 2}
-{"prob_id": 2500, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2500.png", "question": "如图,四边形ABCD和A′B′C′D′是以点O为位似中心的位似图形,若OA′:A′A=2:1,四边形A′B′C′D′的面积为12cm^{2},则四边形ABCD的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD和A′B′C′D′是以点O为位似中心的位似图形,OA′:A′A=2:1,∴OA′:OA=2:3,∴四边形ABCD与四边形A′B′C′D′的面积比为:9:4,∵四边形A′B′C′D′的面积为12cm^{2},∴四边形ABCD的面积为:27cm^{2}．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "27.0", "org_choices": ["24cm^{2}", "27cm^{2}", "36cm^{2}", "54cm^{2}"], "choices": [24.0, 27.0, 36.0, 54.0], "label": 1}
-{"prob_id": 2542, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2542.png", "question": "如图,△ABC中,∠C=90°,若AC=4,BC=3,则\\cosB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由勾股定理,得\nAB=√{AC^{2}+BC^{2}}=5,\n\\cosB=\\frac{BC}{AB}=\\frac{3}{5},\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "0.6", "org_choices": ["\\frac{3}{5}", "\\frac{3}{4}", "\\frac{4}{5}", "\\frac{4}{3}"], "choices": [0.6, 0.75, 0.8, 1.333], "label": 0}
-{"prob_id": 2545, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2545.png", "question": "如图,在Rt△ABC中,∠C=90°,AC=4,BC=3,则sinB的值等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在Rt△ABC中,由勾股定理,得\nAB=√{AC^{2}+BC^{2}}=5．\nsinB=\\frac{AC}{AB}=\\frac{4}{5},\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.8", "org_choices": ["\\frac{4}{3}", "\\frac{3}{4}", "\\frac{4}{5}", "\\frac{3}{5}"], "choices": [1.333, 0.75, 0.8, 0.6], "label": 2}
-{"prob_id": 2546, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2546.png", "question": "如图,在Rt△ABC中,∠C=90°,AC=3,BC=4,则\\cosA的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在Rt△ABC中,∠C=90°,AC=3,BC=4,\n由勾股定理,得\nAB=√{AC^{2}+BC^{2}}=5．\n\\cosA=\\frac{AC}{AB}=\\frac{3}{5},\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "0.6", "org_choices": ["\\frac{3}{5}", "\\frac{5}{3}", "\\frac{4}{5}", "\\frac{3}{4}"], "choices": [0.6, 1.667, 0.8, 0.75], "label": 0}
-{"prob_id": 2554, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2554.png", "question": "如图,已知Rt△ABC中,∠C=90°,AB=10,AC=8,则tanB的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在Rt△ABC中,由勾股定理,得\nBC=√{AB^{2}-AC^{2}}=√{10^{2}-8^{2}}=6,\n由正切函数的意义,得\ntanB=\\frac{AC}{BC}=\\frac{8}{6}=\\frac{4}{3},\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "1.3333333333333333", "org_choices": ["\\frac{3}{5}", "\\frac{3}{4}", "\\frac{4}{5}", "\\frac{4}{3}"], "choices": [0.6, 0.75, 0.8, 1.333], "label": 3}
-{"prob_id": 2572, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2572.png", "question": "如图,位似图形由三角尺与其灯光照射下的中心投影组成,若灯泡到三角尺一顶点的距离与灯泡到三角尺投影的对应顶点距离比为2:5,且三角尺的一边长为8cm,则投影三角形的对应边长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵位似图形由三角尺与其灯光照射下的中心投影组成,相似比为2:5,三角尺的一边长为8cm,∴投影三角形的对应边长为:8÷\\frac{24}{5}=20cm．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["8cm", "20cm", "3.2cm", "10cm"], "choices": [8.0, 20.0, 3.2, 10.0], "label": 1}
-{"prob_id": 2592, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2592.png", "question": "如图,已知圆周角∠BAC=40°,那么圆心角∠BOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BOC=2∠BAC,∠BAC=40°,∴∠BOC=80°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["40°", "60°", "80°", "100°"], "choices": [40.0, 60.0, 80.0, 100.0], "label": 2}
-{"prob_id": 2601, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2601.png", "question": "如图,在Rt△ABC中,∠C=90°,AC=4,AB=5,则\\cosA的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在Rt△ABC中,\\cosA=\\frac{AC}{AB}=\\frac{4}{5},\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.8", "org_choices": ["\\frac{3}{5}", "\\frac{4}{5}", "\\frac{3}{4}", "\\frac{4}{3}"], "choices": [0.6, 0.8, 0.75, 1.333], "label": 1}
-{"prob_id": 2632, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2632.png", "question": "如图,在△ABC中,∠C=Rt∠,AB=5,AC=4,则sinA的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由勾股定理得,BC=√{AB^{2}-AC^{2}}=√{5^{2}-4^{2}}=3,\n所以,sinA=\\frac{BC}{AB}=\\frac{3}{5}．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.6", "org_choices": ["\\frac{3}{4}", "\\frac{4}{5}", "\\frac{3}{5}", "\\frac{5}{3}"], "choices": [0.75, 0.8, 0.6, 1.667], "label": 2}
-{"prob_id": 2657, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2657.png", "question": "在Rt△ABC中,∠C=90°,AB=2,BC=1,则sinB的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:根据勾股定理可得:AC=√{AB^{2}-BC^{2}}=√{3},∴sinB=\\frac{AC}{AB}=\\frac{√{3}}{2}．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.8660254037844386", "org_choices": ["\\frac{1}{2}", "\\frac{√{2}}{2}", "\\frac{√{3}}{2}", "2"], "choices": [0.5, 0.707, 0.866, 2.0], "label": 2}
-{"prob_id": 2662, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2662.png", "question": "如图,在Rt△ABC中,已知∠A=90°,AC=3,AB=4,则sinB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由勾股定理得,BC=√{AC^{2}+AB^{2}}=√{3^{2}+4^{2}}=5,\n所以,sinB=\\frac{AC}{BC}=\\frac{3}{5}．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.6", "org_choices": ["\\frac{3}{4}", "\\frac{3}{5}", "\\frac{4}{5}", "\\frac{5}{4}"], "choices": [0.75, 0.6, 0.8, 1.25], "label": 1}
-{"prob_id": 2664, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2664.png", "question": "在Rt△ACB中,∠C=90°,BC=5,AC=12,则sinA=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:AB=√{AC^{2}+BC^{2}}=13,\n则sinA=\\frac{BC}{AB}=\\frac{5}{13}．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.38461538461538464", "org_choices": ["\\frac{5}{12}", "\\frac{12}{5}", "\\frac{5}{13}", "\\frac{12}{13}"], "choices": [0.417, 2.4, 0.385, 0.923], "label": 2}
-{"prob_id": 2707, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2707.png", "question": "如图,在直角坐标系中,P是第一象限内的点,其坐标是(4,m),且OP与x轴正半轴的夹角α的余弦值是\\frac{3}{5},则tan∠α的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图所示:过点P作PA⊥x轴于点A,∵P是第一象限内的点,其坐标是(4,m),∴AO=4,∵OP与x轴正半轴的夹角α的余弦值是\\frac{3}{5},∴OP=\\frac{20}{3},∴PA=√{0P^{2}-A0^{2}}=\\frac{16}{3},∴tan∠α的值是:\\frac{16}{\\frac{3}{4}}=image_018080.png\\frac{4}{3}．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "1.3333333333333333", "org_choices": ["\\frac{4}{5}", "\\frac{5}{4}", "\\frac{3}{4}", "\\frac{4}{3}"], "choices": [0.8, 1.25, 0.75, 1.333], "label": 3}
-{"prob_id": 2730, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2730.png", "question": "如图,已知Rt△ABC中,∠C=90°,AC=6,BC=8,则tanA的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在Rt△ABC中,∠C=90°,AC=6,BC=8,∴tanA=\\frac{BC}{AC}=\\frac{8}{6}=\\frac{4}{3}．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "1.3333333333333333", "org_choices": ["\\frac{3}{5}", "\\frac{4}{5}", "\\frac{3}{4}", "\\frac{4}{3}"], "choices": [0.6, 0.8, 0.75, 1.333], "label": 3}
-{"prob_id": 2738, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2738.png", "question": "如图:在Rt△ABC中,∠C=90°,AC=8,AB=10,则sinB的值等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:sinB=\\frac{AC}{AB}=\\frac{4}{5}．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.8", "org_choices": ["\\frac{3}{5}", "\\frac{4}{5}", "\\frac{3}{4}", "\\frac{4}{3}"], "choices": [0.6, 0.8, 0.75, 1.333], "label": 1}
-{"prob_id": 2747, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2747.png", "question": "如图,在Rt△ABC中,∠C=90°,AC=1,BC=2,则\\cosB的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在Rt△ABC中,∠C=90°,AC=1,BC=2,由勾股定理,得\nAB=√{AC^{2}+BC^{2}}=√{5}．\n由锐角的余弦,得\\cosB=\\frac{BC}{AB}=\\frac{2}{√{5}}=\\frac{2√{5}}{5},\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.8944271909999159", "org_choices": ["\\frac{√{5}}{5}", "\\frac{2√{5}}{5}", "\\frac{1}{2}", "2"], "choices": [0.447, 0.894, 0.5, 2.0], "label": 1}
-{"prob_id": 2750, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2750.png", "question": "如图,在直角坐标系中,点A的坐标是(2,3),则tanα的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,过点A作AB⊥x轴于B,∵A(2,3),∴OB=2,AB=3,∴tanα=\\frac{AB}{OB}=\\frac{3}{2}．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "1.5", "org_choices": ["\\frac{2}{3}", "\\frac{3}{2}", "\\frac{2√{13}}{13}", "\\frac{3√{13}}{13}"], "choices": [0.667, 1.5, 0.555, 0.832], "label": 1}
-{"prob_id": 2760, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2760.png", "question": "如图,已知Rt△ABC中,∠C=90°,AC=4,tanA=\\frac{1}{2},则BC的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵tanA=\\frac{1}{2}=\\frac{BC}{AC},AC=4,∴BC=2,\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["2", "8", "2√{5}", "4√{5}"], "choices": [2.0, 8.0, 4.472, 8.944], "label": 0}
-{"prob_id": 2785, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2785.png", "question": "如图,ABC中,AB=AC=4cm,BC=6cm,则\\cosB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作AD⊥BC于点D．∵AB=AC,∴BD=\\frac{1}{2}BC=3cm,∴\\cosB=\\frac{BD}{AB}=\\frac{3}{4}．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "0.75", "org_choices": ["\\frac{3}{4}", "\\frac{4}{3}", "\\frac{3}{5}", "\\frac{4}{5}"], "choices": [0.75, 1.333, 0.6, 0.8], "label": 0}
-{"prob_id": 2801, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2801.png", "question": "如图,在Rt△ABC中,∠C=90°,AC=4,AB=5,则sinB的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在△ABC中,∠C=90°,AC=4,AB=5,∴sin∠B=\\frac{AC}{AB}=\\frac{4}{5},\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "0.8", "org_choices": ["\\frac{2}{3}", "\\frac{3}{5}", "\\frac{3}{4}", "\\frac{4}{5}"], "choices": [0.667, 0.6, 0.75, 0.8], "label": 3}
-{"prob_id": 2803, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2803.png", "question": "如图,四个边长为1的小正方形拼成一个大正方形,A、B、O是小正方形顶点,⊙O的半径为1,P是⊙O上的点,且位于右上方的小正方形内,则sin∠APB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接AB,BC．∵AC是直径．∴∠ABC=90°,则△ABC是等腰直角三角形．∴∠C=45°∴sin∠APB=sinC=sin45°=\\frac{√{2}}{2}．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.7071067811865476", "org_choices": ["\\frac{√{3}}{2}", "\\frac{√{2}}{2}", "\\frac{1}{2}", "1"], "choices": [0.866, 0.707, 0.5, 1.0], "label": 1}
-{"prob_id": 2820, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2820.png", "question": "如图,Rt△ABC的斜边AB=10cm,\\cosA=\\frac{3}{5},则BC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵\\cosA=\\frac{CA}{BA}=\\frac{3}{5},∵AB=10,∴AC=6．∴BC=8,\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["5cm", "6cm", "3cm", "8cm"], "choices": [5.0, 6.0, 3.0, 8.0], "label": 3}
-{"prob_id": 2836, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2836.png", "question": "如图,在四边形ABCD中,E、F分別是AB、AD的中点,若EF=2,BC=5,CD=3,则tanC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BD．∵E、F分別是AB、AD的中点．∴BD=2EF=4∵BC=5,CD=3∴△BCD是直角三角形．∴tanC=\\frac{BD}{CD}=\\frac{4}{3}\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "1.3333333333333333", "org_choices": ["\\frac{3}{4}", "\\frac{4}{3}", "\\frac{3}{5}", "\\frac{4}{5}"], "choices": [0.75, 1.333, 0.6, 0.8], "label": 1}
-{"prob_id": 2867, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2867.png", "question": "在Rt△ABC中,∠ACB=90°,CD⊥AB于点D,若AC=3,BC=4,则tanα等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ACB=90°,∴∠ACD+∠DCB=90°,∵CD⊥AB于点D,∴∠AB+∠DCB=90°,∴∠ACD=∠B,∴tanα=tanB=\\frac{AC}{CB}=\\frac{3}{4},\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.75", "org_choices": ["\\frac{4}{5}", "\\frac{3}{5}", "\\frac{3}{4}", "\\frac{4}{3}"], "choices": [0.8, 0.6, 0.75, 1.333], "label": 2}
-{"prob_id": 2882, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2882.png", "question": "如图,在Rt△ABC中,∠C=90°,sinA=\\frac{1}{3},则\\cosB的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠C=90°,∴∠A+∠B=90°,∴\\cosB=sinA,\n而sinA=\\frac{1}{3},∴\\cosB=\\frac{1}{3}．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "0.3333333333333333", "org_choices": ["\\frac{1}{3}", "\\frac{2}{3}", "\\frac{√{2}}{3}", "\\frac{2√{2}}{3}"], "choices": [0.333, 0.667, 0.471, 0.943], "label": 0}
-{"prob_id": 2883, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2883.png", "question": "我们知道,如果两个锐角的和等于一直角,那么这两个角互为余角,简称互余．如图,∠A与∠B互余,且有:sinA=\\frac{∠A的对边}{斜边}=\\frac{a}{c},\\cosB=\\frac{∠B的邻边}{斜边}=\\frac{a}{c},因此知sinA=\\cosB,注意到在△ABC中,∠A+∠B=90°,即∠B=90°-∠A,∠A=90°-∠B,于是有:sin(90°-A)=\\cosA,\\cos(90°-A)=sinA．试完成下列选择题:如果α是锐角,且\\cosα=\\frac{4}{5},那么sin(90°-α)的值等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵\\cosα=\\frac{4}{5},∴sin(90°-α)=\\cosα=\\frac{4}{5}．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.8", "org_choices": ["\\frac{9}{25}", "\\frac{4}{5}", "\\frac{3}{5}", "\\frac{16}{25}"], "choices": [0.36, 0.8, 0.6, 0.64], "label": 1}
-{"prob_id": 2970, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2970.png", "question": "如图,已知AB、AD是⊙O的弦,∠BOD=50°,则∠BAD的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BOD=50°,∴∠BAD=25°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["50°", "40°", "25°", "35°"], "choices": [50.0, 40.0, 25.0, 35.0], "label": 2}
-{"prob_id": 2999, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/2999.png", "question": "如图,在△ABC中,∠ABC和∠ACB的外角平分线交于点O,且∠BOC=40°,则∠A=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∠BOC=40°∴∠OBC+∠OCB=140°∴∠ABC+∠ACB=180°×2-140°×2=80°∴∠A=180°-(∠ABC+∠ACB)=180°-80°=100°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["10°", "70°", "100°", "160°"], "choices": [10.0, 70.0, 100.0, 160.0], "label": 2}
-{"prob_id": 3001, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3001.png", "question": "如图,已知CD为圆O的直径,过点D的弦DE平行于半径OA,若角D=50°,则角C的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA∥DE,∴∠AOD=∠D=50°,∴∠C=\\frac{1}{2}∠AOD=25°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["50°", "25°", "30°", "40°"], "choices": [50.0, 25.0, 30.0, 40.0], "label": 1}
-{"prob_id": 3022, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3022.png", "question": "如图,点B在⊙O上,弦AC∥OB,∠BOC=50°,则∠OAB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BOC=2∠BAC,∠BOC=50°,∴∠BAC=25°,∵AC∥OB,∴∠BAC=∠B=25°,∵OA=OB,∴∠OBA=∠BAO=25°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["25°", "50°", "60°", "30°"], "choices": [25.0, 50.0, 60.0, 30.0], "label": 0}
-{"prob_id": 3039, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3039.png", "question": "如图,点A、B、C是⊙O上的三点,若∠A=40°,则∠BOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∠BOC=2∠A=2×40°=80°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["100°", "80°", "60°", "40°"], "choices": [100.0, 80.0, 60.0, 40.0], "label": 1}
-{"prob_id": 3055, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3055.png", "question": "在⊙O中,AB是直径,CD是弦,∠ABD=28°,则∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接AD．∵AB是直径,∴∠ADB=90°,∵∠ABD=28°,∴∠DAB=90°-28°=62°,∴∠C=∠DAB=62°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "62.0", "org_choices": ["28°", "56°", "62°", "72°"], "choices": [28.0, 56.0, 62.0, 72.0], "label": 2}
-{"prob_id": 3059, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3059.png", "question": "如图,点A、B、C是⊙O上的三点,若∠BOC=80°,则∠A的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BOC与∠A是同弧所对的圆心角与圆周角,∠BOC=80°,∴∠A=\\frac{1}{2}∠BOC=40°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "60°", "80°", "100°"], "choices": [40.0, 60.0, 80.0, 100.0], "label": 0}
-{"prob_id": 3071, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3071.png", "question": "已知如图,AB是⊙O的直径,CD是⊙O的弦,∠CDB=40°,则∠CBA的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接AC,∵AB是⊙O的直径,∴∠ACB=90°,∵∠A=∠CDB=40°,∴∠CBA=90°-∠A=50°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["60°", "50°", "40°", "30°"], "choices": [60.0, 50.0, 40.0, 30.0], "label": 1}
-{"prob_id": 3116, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3116.png", "question": "如图,已知O是四边形ABCD内一点,OA=OB=OC,∠ABC=∠ADC=65°,则∠DAO+∠DCO=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA=OB=OC,∴∠ABO=∠BAO,∠OBC=∠OCB,∵∠ABC=65°=∠ABO+∠OBC,∴∠BAO+∠BCO=65°,∵∠ADC=65°,∴∠DAO+∠DCO=360°-(∠ADC+∠BAO+∠BCO+∠ABC)=360°-(65°+65°+65°)=165°,\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "165.0", "org_choices": ["90°", "110°", "120°", "165°"], "choices": [90.0, 110.0, 120.0, 165.0], "label": 3}
-{"prob_id": 3153, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3153.png", "question": "如图,AB是⊙O直径,∠D=33°,则∠AOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BOC=2∠BDC=66°,\n又∵∠AOC=180°-∠BOC,∴∠AOC=114°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "114.0", "org_choices": ["99°", "108°", "114°", "127°"], "choices": [99.0, 108.0, 114.0, 127.0], "label": 2}
-{"prob_id": 3164, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3164.png", "question": "如图,在⊙O中,OA⊥BC,∠AOB=48°,D为⊙O上一点,则∠ADC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA⊥BC,∴⁀{AC}=⁀{AB},∴∠ADC=\\frac{1}{2}∠AOB=\\frac{1}{2}×48°=24°．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "24.0", "org_choices": ["24°", "42°", "48°", "12°"], "choices": [24.0, 42.0, 48.0, 12.0], "label": 0}
-{"prob_id": 3171, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3171.png", "question": "如图,A、B、C三点都在⊙O上,∠ABO=50°,则∠ACB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA=OB∴∠OAB=∠OBA=50°∴∠AOB=80°∴∠ACB=40°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["50°", "40°", "30°", "25°"], "choices": [50.0, 40.0, 30.0, 25.0], "label": 1}
-{"prob_id": 3176, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3176.png", "question": "如图,点AC是⊙O的直径,若∠OBC=40°,则∠AOB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OC=OB,∴∠OBC=∠C,∵弧AB所对的圆周角是∠C,所对的圆心角是∠AOB,∴∠AOB=2∠OCB=80°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["40°", "50°", "80°", "100°"], "choices": [40.0, 50.0, 80.0, 100.0], "label": 2}
-{"prob_id": 3180, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3180.png", "question": "如图,在⊙A中,已知弦BC=8,DE=6,∠BAC+∠EAD=180°,则⊙A的半径长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作直径CF,连结BF,如图,∵∠BAC+∠EAD=180°,\n而∠BAC+∠BAF=180°,∴∠DAE=∠BAF,∴⁀{DE}=⁀{BF},∴DE=BF=6,∵CF是直径,∴∠CBF=90°,∴CF=√{BC^{2}+BF^{2}}=√{8^{2}+6^{2}}=10．∴⊙A的半径为5．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["10", "6", "5", "8"], "choices": [10.0, 6.0, 5.0, 8.0], "label": 2}
-{"prob_id": 3191, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3191.png", "question": "将量角器按如图所示的方式放在一个残缺的玻璃碎片上,使点A在半圆上,点B、C的读数分别为105°、155°,则∠BAC的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设半圆的圆心为O,连接OB,OC,\n由题意得:∠COB=50°,∵∠BAC与∠COB都对⁀{BC},∴∠BAC=\\frac{1}{2}∠COB=25°,\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["55°", "50°", "27.5°", "25°"], "choices": [55.0, 50.0, 27.5, 25.0], "label": 3}
-{"prob_id": 3198, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3198.png", "question": "如图,点A、B、是⊙O上三点且AB=AC,连接BO、CO,若∠ABC=65°,则∠BOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意可得:AB=AC,∵∠ABC=65°,∴∠ACB=65°,∴∠A=50°,∴∠BOC=100°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["50°", "65°", "100°", "130°"], "choices": [50.0, 65.0, 100.0, 130.0], "label": 2}
-{"prob_id": 3208, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3208.png", "question": "如图,已知圆心角∠AOB的度数为110°,则圆周角∠ACB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设点E是优弧AB上的一点,连接EA,EB∵∠AOB=110°∴∠E=\\frac{1}{2}∠AOB=55°∴∠ACB=180°-∠E=125°．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "125.0", "org_choices": ["110°", "70°", "55°", "125°"], "choices": [110.0, 70.0, 55.0, 125.0], "label": 3}
-{"prob_id": 3225, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3225.png", "question": "如图,某隧道的截面是一个半径为3.4m的半圆形,一辆宽3.2m的卡车恰好能通过该隧道,连车带货一起最高为多少米(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过O作OE⊥AB于E,则∠OEB=90°,AB=DC=3.2m,由垂径定理得:AE=BE=\\frac{1}{2}×3.2m=1.6m,在Rt△BEO中,∠BEO=90°,BE=1.6m,OB=3.4m,由勾股定理得:OE=√{3.4^{2}-1.6^{2}}=3(m),即连车带货一起最高为3m,故选:A．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["3m", "3.4m", "4m", "2.8m"], "choices": [3.0, 3.4, 4.0, 2.8], "label": 0}
-{"prob_id": 3232, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3232.png", "question": "如图,AB和CD是⊙O的两条直径,弦DE∥AB,若弧DE为40°的弧,则∠BOC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OE,∵弧DE为40°的弧,∴∠DOE=40°．∵OD=OE,∴∠ODE=\\frac{180^{°}-40^{°}}{2}=70°．∵弦DE∥AB,∴∠AOC=∠ODE=70°,∴∠BOC=180°-∠AOC=180°-70°=110°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "110.0", "org_choices": ["110°", "80°", "40°", "70°"], "choices": [110.0, 80.0, 40.0, 70.0], "label": 0}
-{"prob_id": 3234, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3234.png", "question": "如图,在⊙O中,若点C是⁀{AB}的中点,∠A=50°,则∠BOC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠A=50°,OA=OB,∴∠OBA=∠OAB=50°,∴∠AOB=180°-50°-50°=80°,∵点C是⁀{AB}的中点,∴∠BOC=\\frac{1}{2}∠AOB=40°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "45°", "50°", "60°"], "choices": [40.0, 45.0, 50.0, 60.0], "label": 0}
-{"prob_id": 3255, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3255.png", "question": "若AB∥CD,∠C=60°,则∠A+∠E等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB∥CD,∴∠C=∠EFB=60°,∵∠EFB是△AEF的一个外角,∴∠EFB=∠A+∠E=60°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["20°", "30°", "40°", "60°"], "choices": [20.0, 30.0, 40.0, 60.0], "label": 3}
-{"prob_id": 3275, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3275.png", "question": "已知:如图,在⊙O中,OA⊥BC,∠AOB=70°,则∠ADC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA⊥BC,∠AOB=70°,∴⁀{AB}=⁀{AC},∴∠ADC=\\frac{1}{2}∠AOB=35°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["30°", "35°", "45°", "70°"], "choices": [30.0, 35.0, 45.0, 70.0], "label": 1}
-{"prob_id": 3280, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3280.png", "question": "如图,CD是⊙O的弦,O是圆心,把⊙O的劣弧沿着CD对折,A是对折后劣弧上的一点,∠CAD=110°,则∠B的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,翻折△ACD,点A落在A'处,∴∠A'=∠A=110°,∵四边形A'CBD是⊙O的内接四边形,∴∠A'+∠B=180°,∴∠B=70°,\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["110°", "70°", "60°", "55°"], "choices": [110.0, 70.0, 60.0, 55.0], "label": 1}
-{"prob_id": 3287, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3287.png", "question": "如图,AB是⊙O直径,点C为⊙O上一点,∠C=20°,则∠BOC度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA=OC,∴∠A=∠C=20°,\n由圆周角定理得,∠BOC=2∠A=40°\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["20°", "30°", "40°", "60°"], "choices": [20.0, 30.0, 40.0, 60.0], "label": 2}
-{"prob_id": 3292, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3292.png", "question": "如图,⊙O是△ABC的外接圆,若∠AOB=130°,则∠ACB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,在优弧AB上取一点D,连接AD,BD,\n则∠ADB=\\frac{1}{2}AOB=65°,∴∠ACB=180°-∠ADB=115°．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "115.0", "org_choices": ["115°", "120°", "125°", "130°"], "choices": [115.0, 120.0, 125.0, 130.0], "label": 0}
-{"prob_id": 3306, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3306.png", "question": "如图,在⊙O中,弦AB与CD交于点E,BE=DE,∠B=40°,则∠A的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BE=DE,∠B=40°,∴∠D=∠B=40°,∴∠A=∠D=40°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["20°", "30°", "40°", "80°"], "choices": [20.0, 30.0, 40.0, 80.0], "label": 2}
-{"prob_id": 3308, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3308.png", "question": "如图,点A、B、C、D在⊙O上,DE⊥OA,DF⊥OB,垂足分别为E,F,若∠EDF=50°,则∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE⊥OA,DF⊥OB,∴∠OED=∠OFD=90°,∴∠AOB=360°-90°-90°-50°=130°,\n由圆周角定理得,∠C=\\frac{1}{2}∠AOB=65°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["40°", "50°", "65°", "130°"], "choices": [40.0, 50.0, 65.0, 130.0], "label": 2}
-{"prob_id": 3316, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3316.png", "question": "如图,CD为⊙O的直径,弦AB交CD于点M,M是AB的中点,点P在⁀{AD}上,PC与AB交于点N,∠PNA=60°,则∠PDC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵CD为⊙O的直径,∴∠P=90°．∵M是AB的中点,∴CM⊥AB．∵∠PNA=60°,∴∠C=90°-60°=30°,∴∠PDC=90°-∠C=90°-30°=60°．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["40°", "50°", "60°", "70°"], "choices": [40.0, 50.0, 60.0, 70.0], "label": 2}
-{"prob_id": 3317, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3317.png", "question": "如图,AB是⊙O的直径,弦CD⊥AB于E,连结OC、AD,且∠A=35°,则∠AOC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OD,∵∠A=35°,∴∠BOD=70°．∵AB是⊙0的直径,弦CD⊥AB于E,∴∠BOC=∠BOD=70°,∴∠AOC=180°-70°=110°．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "110.0", "org_choices": ["70°", "105°", "110°", "140°"], "choices": [70.0, 105.0, 110.0, 140.0], "label": 2}
-{"prob_id": 3321, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3321.png", "question": "如图,在△ABC中,AB=AC,以BC为直径画半圆交AB于E,交AC于D,⁀{CD}的度数为40°,则∠A的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BC为圆的直径,∴∠BDC=90°,∵⁀{CD}的度数为40°,∴∠DBC=20°,∴∠C=70°,∵AB=AC,∴∠ABC=∠C=70°,∴∠A=40°,\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "70°", "50°", "20°"], "choices": [40.0, 70.0, 50.0, 20.0], "label": 0}
-{"prob_id": 3324, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3324.png", "question": "如图,点A,B,C,P在⊙O上,CD⊥OA,CE⊥OB,垂足分别为D,E,∠DCE=36°,则∠P的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵CD⊥OA,CE⊥OB,垂足分别为D,E,∠DCE=36°,∴∠DOE=180°-36°=144°,∴∠P=\\frac{1}{2}∠DOE=72°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "72.0", "org_choices": ["144°", "72°", "60°", "36°"], "choices": [144.0, 72.0, 60.0, 36.0], "label": 1}
-{"prob_id": 3328, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3328.png", "question": "如图,点A、B、C、P在⊙O上,CD⊥OA,CE⊥OB,垂足分别为D,E,∠DCE=40°,则∠P的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵CD⊥OA,CE⊥OB,垂足分别为D,E,∠DCE=40°,∴∠DOE=180°-40°=140°,∴∠P=\\frac{1}{2}∠DOE=70°．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["70°", "60°", "40°", "35°"], "choices": [70.0, 60.0, 40.0, 35.0], "label": 0}
-{"prob_id": 3333, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3333.png", "question": "如图,A、B、C三点在圆上,在△ABC中,∠ABC=70°,∠ACB=30°,D是弧BAC的中点,连结DB,DC,则∠DBC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在△ABC中,∠ABC=70°,∠ACB=30°,∴∠A=180°-∠ABC-∠ACB=80°,∴∠D=∠A=80°,∵D是弧BAC的中点,∴⁀{BD}=⁀{CD},∴∠DBC=∠DCB,∴∠DBC=\\frac{1}{2}(180°-∠D)=50°,\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["70°", "50°", "45°", "30°"], "choices": [70.0, 50.0, 45.0, 30.0], "label": 1}
-{"prob_id": 3345, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3345.png", "question": "如图,AB,CD是⊙O的两条弦,连接AD,BC,若∠BCD=50°,则∠BAD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BCD=70°,∴∠BAD=∠BCD=70°．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["70°", "60°", "50°", "40°"], "choices": [70.0, 60.0, 50.0, 40.0], "label": 2}
-{"prob_id": 3357, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3357.png", "question": "如图,△ABC内接于⊙O,若∠OAB=26°,则∠C的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB,\n在△OAB中,∵OA=OB,∴∠OAB=∠OBA,\n又∵∠OAB=26°,∴∠OBA=26°；∴∠AOB=180°-2×26°=128°；∴∠C=\\frac{1}{2}∠AOB=64°．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "64.0", "org_choices": ["26°", "52°", "60°", "64°"], "choices": [26.0, 52.0, 60.0, 64.0], "label": 3}
-{"prob_id": 3358, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3358.png", "question": "如图,⊙O是△ABC的外接圆,∠A=70°,则∠BOC的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵⊙O是△ABC的外接圆,∠A=70°,∴∠BOC=2∠A=140°．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["30°", "35°", "70°", "140°"], "choices": [30.0, 35.0, 70.0, 140.0], "label": 3}
-{"prob_id": 3382, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3382.png", "question": "如图,在⊙O中,弦AC∥半径OB,∠BOC=50°,则∠OBA的度数(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BOC=2∠BAC,∠BOC=50°,∴∠BAC=25°,∵AC∥OB,∴∠BAC=∠B=25°,∵OA=OB,∴∠OBA=∠BAO=25°,\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["25°", "50°", "60°", "30°"], "choices": [25.0, 50.0, 60.0, 30.0], "label": 0}
-{"prob_id": 3384, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3384.png", "question": "如图,若∠ABC=30°,则∠AOC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠AOC=2∠ABC,∴∠AOC=2×30°=60°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["30°", "45°", "60°", "70°"], "choices": [30.0, 45.0, 60.0, 70.0], "label": 2}
-{"prob_id": 3385, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3385.png", "question": "如图,在⊙O中,CD是直径,点A,点B在⊙O上,连接OA、OB、AC、AB,若∠AOB=40°,CD∥AB,则∠BAC的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA=OB,∴∠OAB=∠OBA=\\frac{180^{°}-∠AOB}{2}=\\frac{180^{°}-40^{°}}{2}=70°,\n又∵CD∥AB,∴∠COB=∠OBA=70°,∴∠BAC=\\frac{1}{2}∠COB=35°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["30°", "35°", "40°", "70°"], "choices": [30.0, 35.0, 40.0, 70.0], "label": 1}
-{"prob_id": 3389, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3389.png", "question": "如图,是一个圆形展厅,为了监控整个展厅,在其圆形边缘上安装了甲、乙两台监视器,若甲监视器的监控角度为65°,则乙监控器的监控角度至少为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∠D=180°-∠B=180°-65°=115°．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "115.0", "org_choices": ["25°", "65°", "115°", "130°"], "choices": [25.0, 65.0, 115.0, 130.0], "label": 2}
-{"prob_id": 3394, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3394.png", "question": "如图,⊙O是△ABC的外接圆,连接OA、OB,∠AOB=50°,则∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵⊙O是△ABC的外接圆,∠AOB=50°,∴∠ACB\\frac{1}{2}∠AOB=\\frac{1}{2}×50°=25°．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["25°", "40°", "50°", "80°"], "choices": [25.0, 40.0, 50.0, 80.0], "label": 0}
-{"prob_id": 3397, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3397.png", "question": "已知:如图,AB是圆O的直径,CD为弦,连AD、AC,∠CAB=55°,则∠D=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB为⊙O的直径,∴∠ACB=90°,∵∠CAB=55°,∴∠B=90°-∠CAB=35°,∴∠ADC=∠B=35°．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["55°", "50°", "35°", "45°"], "choices": [55.0, 50.0, 35.0, 45.0], "label": 2}
-{"prob_id": 3440, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3440.png", "question": "如图,点A,B,C在⊙O上,若∠C=35°,则∠AOB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由圆周角定理可得:∠AOB=2∠ACB=70°．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["17.5°", "35°", "60°", "70°"], "choices": [17.5, 35.0, 60.0, 70.0], "label": 3}
-{"prob_id": 3442, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3442.png", "question": "如图,AB是⊙O的直径,∠ADC的度数是35°,则∠BOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠D=35°,∴∠AOC=2∠D=35°×2=70°,∵∠AOC+∠BOC=180°,∴∠BOC=180°-70°=110°,\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "110.0", "org_choices": ["120°", "110°", "100°", "70°"], "choices": [120.0, 110.0, 100.0, 70.0], "label": 1}
-{"prob_id": 3448, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3448.png", "question": "如图,四边形ABCD内接于⊙O,AB为⊙O的直径,点C为⁀{BD}的中点,若∠DAB=50°,则∠ABC的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC,∵点C为⁀{BD}的中点,∴∠BOC=∠DAB=50°,∵OC=OB,∴∠ABC=∠OCB=65°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["55°", "60°", "65°", "70°"], "choices": [55.0, 60.0, 65.0, 70.0], "label": 2}
-{"prob_id": 3481, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3481.png", "question": "如图,四边形ABCD是⊙O的内接四边形,AB为⊙O的直径,连结BD．若∠BCD=120°,则∠ABD的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是⊙O的内接四边形,∴∠BAD+∠BCD=180°,∵∠BCD=120°,∴∠BAD=60°,∵AB为⊙O的直径,∴∠ADB=90°,∴∠ABD=90°-60°=30°,\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["60°", "50°", "40°", "30°"], "choices": [60.0, 50.0, 40.0, 30.0], "label": 3}
-{"prob_id": 3519, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3519.png", "question": "如图,点A、B、C、D在圆O上,点E在AD的延长线上,若∠ABC=60°,则∠CDE的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD为圆O的内接四边形,∴∠ABC+∠ADC=180°,∵∠CDE+∠ADC=180°,∠B=60°,∴∠CDE=∠B=60°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["30°", "45°", "60°", "70°"], "choices": [30.0, 45.0, 60.0, 70.0], "label": 2}
-{"prob_id": 3520, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3520.png", "question": "如图,四边形ABCD内接于半圆O,已知∠ADC=140°,则∠AOC的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是圆内接四边形,∴∠ADC+∠B=180°,又∠ADC=140°,∴∠B=40°,∴∠AOC=2∠B=80°,\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["40°", "60°", "70°", "80°"], "choices": [40.0, 60.0, 70.0, 80.0], "label": 3}
-{"prob_id": 3524, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3524.png", "question": "如图,四边形ABCD内接于圆O,若∠BOD=138°,则它的一个外角∠DCE的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由圆周角定理得,∠A=\\frac{1}{2}∠BOD=69°,∴∠DCE=,∠A=69°,\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "69.0", "org_choices": ["138°", "69°", "52°", "42°"], "choices": [138.0, 69.0, 52.0, 42.0], "label": 1}
-{"prob_id": 3528, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3528.png", "question": "如图,四边形ABCD内接于⊙O,E为BC延长线上一点,∠A=50°,则∠DCE的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB,OD,∵∠DOB与∠A都对⁀{BD},∠DOB(大于平角的角)与∠BCD都对⁀{DAB},∴∠DOB=2∠A,∠DOB(大于平角的角)=2∠BCD,∵∠DOB+∠DOB(大于平角的角)=360°,∴∠A+∠BCD=180°,∵∠DCE+∠BCD=180°,∴∠DCE=∠A=50°,\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["40°", "50°", "60°", "130°"], "choices": [40.0, 50.0, 60.0, 130.0], "label": 1}
-{"prob_id": 3533, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3533.png", "question": "如图,四边形ABCD内接于⊙O,F是⁀{CD}上一点,且⁀{DF}=⁀{BC},连接CF并延长交AD的延长线于点E,连接AC．若∠ABC=105°,∠BAC=25°,则∠E的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD内接于⊙O,∠ABC=105°,∴∠ADC=180°-∠ABC=180°-105°=75°．∵⁀{DF}=⁀{BC},∠BAC=25°,∴∠DCE=∠BAC=25°,∴∠E=∠ADC-∠DCE=75°-25°=50°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["45°", "50°", "55°", "60°"], "choices": [45.0, 50.0, 55.0, 60.0], "label": 1}
-{"prob_id": 3535, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3535.png", "question": "如图,四边形ABCD是⊙O的内接四边形,若∠C=140°,则∠BOD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是⊙O的内接四边形,∴∠A+∠C=180°,∴∠A=40°,\n由圆周角定理得,∠BOD=2∠A=80°,\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["70°", "80°", "90°", "100°"], "choices": [70.0, 80.0, 90.0, 100.0], "label": 1}
-{"prob_id": 3536, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3536.png", "question": "如图,在⊙O中,AB∥CD,∠BCD=100°,E为⁀{DC}上的任意一点,A、B、C、D是⊙O上的四个点,则∠AEC的角度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB∥CD,∠BCD=100°,∴∠ABC=180°-∠BCD=80°,∵四边形AECB是圆内接四边形,∴∠AEC+∠ABC=180°,∴∠AEC=100°,\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["110°", "70°", "80°", "100°"], "choices": [110.0, 70.0, 80.0, 100.0], "label": 3}
-{"prob_id": 3539, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3539.png", "question": "如图．已知A、B、C三点在⊙O上,点C在劣弧AB上,且∠AOB=130°,则∠ACB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在优弧⁀{AB}上取一点D,连接AD、BD,∠D=\\frac{1}{2}∠AOB=65°,∵四边形ADBC是⊙O的内接四边形,∴∠D+∠ACB=180°,∴∠ACB=115°,\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "115.0", "org_choices": ["130°", "125°", "120°", "115°"], "choices": [130.0, 125.0, 120.0, 115.0], "label": 3}
-{"prob_id": 3545, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3545.png", "question": "如图,四边形ABCD内接于⊙O,若∠ABC=40°,则∠ADC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD内接于⊙O,∴∠ABC+∠ADC=180°,\n又∵∠ABC=40°,∴∠ADC=140°．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["90°", "100°", "120°", "140°"], "choices": [90.0, 100.0, 120.0, 140.0], "label": 3}
-{"prob_id": 3558, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3558.png", "question": "如图,四边形ABCD的一个外角∠DCE=70°,则∠BAD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD内接于⊙O,∴∠BAD=∠DCE=70°,\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["70°", "110°", "140°", "120°"], "choices": [70.0, 110.0, 140.0, 120.0], "label": 0}
-{"prob_id": 3569, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3569.png", "question": "如图,四边形ABCD内接于⊙O,∠BOD=70°,则∠BCD的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠A与∠BOD是同弧所对的圆周角与圆心角,∠BOD=70°,∴∠A=\\frac{1}{2}∠BOD=35°．∵四边形ABCD是圆内接四边形,∴∠BCD=180°-∠A=180°-35°=145°．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "145.0", "org_choices": ["70°", "100°", "145°", "150°"], "choices": [70.0, 100.0, 145.0, 150.0], "label": 2}
-{"prob_id": 3573, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3573.png", "question": "如图,四边形ABCD内接于⊙O,如果它的一个外角∠DCE=64°,那么∠BOD=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": ":∵四边形ABCD内接于⊙O,∴∠BAD+∠BCD=180°,∵∠BCD+∠DCE=180°,∴∠BAD=∠DCE=64°,∴∠BOD=2∠BAD=128°．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "128.0", "org_choices": ["128°", "100°", "64°", "32°"], "choices": [128.0, 100.0, 64.0, 32.0], "label": 0}
-{"prob_id": 3575, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3575.png", "question": "如图,四边形ABCD是圆内接四边形,E是AD延长线上一点,若∠CBA=120°,则∠EDC的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是圆内接四边形,∠CBA=120°,∴∠ADC=180°-120°=60°．∵∠ADC+∠EDC=180°,∴∠EDC=180°-60°=120°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["60°", "120°", "150°", "130°"], "choices": [60.0, 120.0, 150.0, 130.0], "label": 1}
-{"prob_id": 3586, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3586.png", "question": "如图,圆内接四边形ABCD中,圆心角∠1=100°,则圆周角∠ABC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵圆心角∠1=100°,∴∠ADC=\\frac{1}{2}∠1=50°,∵四边形ABCD是圆内接四边形,∴∠ABC=180°-∠ADC=180°-50°=130°．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["100°", "120°", "130°", "150°"], "choices": [100.0, 120.0, 130.0, 150.0], "label": 2}
-{"prob_id": 3593, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3593.png", "question": "如图,在圆的内接四边形ABCD中,∠ABC=120°,则四边形ABCD的外角∠ADE的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是圆内接四边形,∴∠ADC+∠B=180°,∵∠ADC+∠ADE=180°,∴∠ADE=∠B．∵∠B=120°,∴∠ADE=120°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["130°", "120°", "110°", "100°"], "choices": [130.0, 120.0, 110.0, 100.0], "label": 1}
-{"prob_id": 3622, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3622.png", "question": "如图,ABCD是⊙O的内接四边形,且∠ABC=115°,那么∠AOC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵ABCD是⊙O的内接四边形,且∠ABC=115°,∴∠ADC=180°-∠ABC=180°-115°=65°,∴∠AOC=2∠ADC=2×65°=130°．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["115°", "120°", "130°", "135°"], "choices": [115.0, 120.0, 130.0, 135.0], "label": 2}
-{"prob_id": 3624, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3624.png", "question": "如图,已知圆周角∠BAD=50°,那么圆周角∠BCD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD内接⊙O,∴∠BAD+∠BCD=180°,∴∠BCD=180°-∠A=180°-50°=130°．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["130°", "100°", "50°", "40°"], "choices": [130.0, 100.0, 50.0, 40.0], "label": 0}
-{"prob_id": 3626, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3626.png", "question": "如图,⊙O是四边形ABCD的外接圆,若∠O=110°,则∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由圆周角定理得,∠A=\\frac{1}{2}∠O=55°,∵⊙O是四边形ABCD的外接圆,∴∠A+∠C=180°,∴∠C=125°,\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "125.0", "org_choices": ["125°", "120°", "105°", "90°"], "choices": [125.0, 120.0, 105.0, 90.0], "label": 0}
-{"prob_id": 3633, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3633.png", "question": "如图,四边形ABCD内接于⊙O,若∠C=36°,则∠A的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD内接于⊙O,∴∠A+∠C=180°,\n而∠C=36°,∴∠A=180°-36°=144°．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "144.0", "org_choices": ["36°", "56°", "72°", "144°"], "choices": [36.0, 56.0, 72.0, 144.0], "label": 3}
-{"prob_id": 3635, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3635.png", "question": "如图,⊙O上有A,B,C,D四点,其中∠A=80°,那么∠C的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是圆内接四边形,∠A=80°,∴∠C=180°-80°=100°．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["40°", "60°", "80°", "100°"], "choices": [40.0, 60.0, 80.0, 100.0], "label": 3}
-{"prob_id": 3661, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3661.png", "question": "如图,△ABC是⊙O的内接三角形,若∠ACB=30°,AB=6,则⊙O的半径是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接OA,OB,∵∠ACB=30°,∴∠AOB=2∠ACB=60°,∵OA=OB,∴△AOB是等边三角形,∴OA=AB=6,\n即⊙O的半径是6,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["3", "2√{3}", "6", "4√{3}"], "choices": [3.0, 3.464, 6.0, 6.928], "label": 2}
-{"prob_id": 3665, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3665.png", "question": "如图,线段AB是⊙O的直径,弦CD丄AB,∠CAB=20°,则∠BOD等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵线段AB是⊙O的直径,弦CD丄AB,∴⁀{BC}=⁀{BD},∴∠BOD=2∠CAB=2×20°=40°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["20°", "40°", "80°", "70°"], "choices": [20.0, 40.0, 80.0, 70.0], "label": 1}
-{"prob_id": 3671, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3671.png", "question": "如图,△ABC是⊙O的内接三角形,AB为⊙O的直径,点D为⊙O上一点,若∠ACD=40°,则∠BAD的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BD,∵AB为圆O的直径,∴∠ADB=90°,∵∠ACD=∠ABD=40°,∴∠BAD=90°-40°=50°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["35°", "50°", "40°", "60°"], "choices": [35.0, 50.0, 40.0, 60.0], "label": 1}
-{"prob_id": 3685, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3685.png", "question": "如图,△ABC内接于⊙O,∠C=20°,则∠OAB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由圆周角定理得,∠AOB=2∠C=40°,∵OA=OB,∴∠OAB=∠OBA=\\frac{1}{2}×(180°-40°)=70°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["50°", "60°", "70°", "72°"], "choices": [50.0, 60.0, 70.0, 72.0], "label": 2}
-{"prob_id": 3699, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3699.png", "question": "如图,△ABC内接于⊙O,连接OA,OB,若∠C=35°,则∠OBA的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠C=35°,∴∠AOB=70°,∵OA=OB,∴∠OAB=∠OBA=55°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["60°", "55°", "50°", "45°"], "choices": [60.0, 55.0, 50.0, 45.0], "label": 1}
-{"prob_id": 3700, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3700.png", "question": "如图,已知△ABC内接于⊙O,∠BAC=50°,则∠BOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由圆周角定理得,∠BOC=2∠BAC=100°,\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["90°", "100°", "110°", "120°"], "choices": [90.0, 100.0, 110.0, 120.0], "label": 1}
-{"prob_id": 3705, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3705.png", "question": "如图,△ABC中,AB=AC,∠BAC=70°,⊙O是△ABC的外接圆,点D在劣弧⁀{AC}上,则∠D的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB=AC,∠BAC=70°,∴∠B=∠ACB=55°,∵四边形ABCD是⊙O的内接四边形,∴∠D=180°-∠A=125°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "125.0", "org_choices": ["55°", "110°", "125°", "140°"], "choices": [55.0, 110.0, 125.0, 140.0], "label": 2}
-{"prob_id": 3708, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3708.png", "question": "如图,△ABC内接于⊙O,∠AOB=80°,则∠ACB的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵△ABC内接于⊙O,∠AOB=80°,∴∠ACB=\\frac{1}{2}∠AOB=40°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["20°", "40°", "80°", "90°"], "choices": [20.0, 40.0, 80.0, 90.0], "label": 1}
-{"prob_id": 3746, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3746.png", "question": "如图,△ABC是⊙O的内接三角形,∠C=30°,⊙O的半径为5,若点P是⊙O上的一点,在△ABP中,PB=AB,则PA的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OA、OB、OP,∵∠C=30°,∴∠APB=∠C=30°,∵PB=AB,∴∠PAB=∠APB=30°∴∠ABP=120°,∵PB=AB,∴OB⊥AP,AD=PD,∴∠OBP=∠OBA=60°,∵OB=OA,∴△AOB是等边三角形,∴AB=OA=5,\n则Rt△PBD中,PD=\\cos30°•PB=\\frac{√{3}}{2}×5=\\frac{5√{3}}{2},∴AP=2PD=5√{3},\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "8.660254037844387", "org_choices": ["5", "\\frac{5√{3}}{2}", "5√{2}", "5√{3}"], "choices": [5.0, 4.33, 7.071, 8.66], "label": 3}
-{"prob_id": 3749, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3749.png", "question": "如图,△ABC内接于⊙O,OC⊥OB,OD⊥AB于D交AC于E点,已知⊙O的半径为1,则AE²+CE²的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BE,∵OD⊥AB,∴AD=DB,∴EA=EB,∠EAO=∠EBO=∠ACO,∵∠ECB+∠EBC=∠ECO+45°+∠EBC=∠OBE+45°+∠EBC=90°,∴∠BEC=90°,\n在直角△BEC中,BE²+CE²=BC²,∵BC²=2OA²=2,∴BE²+CE²=2,即AE²+CE²=2．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["1", "2", "3", "4"], "choices": [1.0, 2.0, 3.0, 4.0], "label": 1}
-{"prob_id": 3771, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3771.png", "question": "如图,已知⊙O为△ABC的外接圆,且AB为⊙O的直径,若OC=5,AC=6,则BC长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB为⊙O的直径,∴∠ACB=90°．∵OC=5,AC=6,∴AB=2OC=10,∴BC=√{AB^{2}-AC^{2}}=√{10^{2}-6^{2}}=8．故选:C．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["10", "9", "8", "无法确定"], "choices": [10.0, 9.0, 8.0], "label": 3}
-{"prob_id": 3777, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3777.png", "question": "如图,∠XOY=45°,一把直角三角尺ABC的两个顶点A、B分别在OX,OY上移动,其中AB=10,那么点O到顶点A的距离的最大值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵\\frac{AB}{sin45^{°}}=\\frac{AO}{sin∠ABO},∴当∠ABO=90°时,点O到顶点A的距离的最大．则OA=√{2}AB=10√{2}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "14.142135623730951", "org_choices": ["8", "10", "8√{2}", "10√{2}"], "choices": [8.0, 10.0, 11.314, 14.142], "label": 3}
-{"prob_id": 3789, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3789.png", "question": "如图,△ABC中,∠BAC=70°,∠ABC=45°,点O是△ABC的外接圆的圆心,则∠AOB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BAC=70°,∠ABC=45°,∴∠C=180°-70°-45°=65°,∴∠AOB=2∠C=130°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["65°", "90°", "130°", "140°"], "choices": [65.0, 90.0, 130.0, 140.0], "label": 2}
-{"prob_id": 3796, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3796.png", "question": "如图,⊙O是△ABD的外接圆,若∠A=135°,则∠BDO的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在优弧BD上任意找一点E,连接BE、DE,根据圆内接四边形的性质,得∠E=45°,根据圆周角定理,得∠BOD=2∠E=90°,∴∠BDO=45°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "45.0", "org_choices": ["30°", "67.5°", "45°", "135°"], "choices": [30.0, 67.5, 45.0, 135.0], "label": 2}
-{"prob_id": 3805, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3805.png", "question": "如图,△ABC内接于⊙O,若∠AOB=110°,则∠ACB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ACB与∠AOB是同弧所对的圆周角与圆心角,∠AOB=110°,∴∠ACB=\\frac{1}{2}∠AOB=55°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["70°", "60°", "55°", "50°"], "choices": [70.0, 60.0, 55.0, 50.0], "label": 2}
-{"prob_id": 3837, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3837.png", "question": "如图,已知⊙O的直径AB与弦AC的夹角为30°,过C点的切线PC与AB延长线交于点P,⊙O的半径为2,则PC为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PC为切线,∴OC⊥PC,∵OA=OC,∴∠OCA=∠A=30°,∴∠POC=∠A+∠OCA=60°,∴∠P=30°,在Rt△OCP中,PC=√{3}OC=2√{3}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "3.4641016151377544", "org_choices": ["4", "4√{3}", "6", "2√{3}"], "choices": [4.0, 6.928, 6.0, 3.464], "label": 3}
-{"prob_id": 3839, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3839.png", "question": "如图,AB切⊙O于点B,AO交⊙O于点C,点D在⊙O上,若∠A=40°,则∠BDC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB,∵AB切⊙O于点B,∴OB⊥AB,∴∠OBA=90°,∵∠A=40°,∴∠BOA=90°-40°=50°,由圆周角定理得,∠BDC=\\frac{1}{2}∠BOA=25°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["50°", "30°", "25°", "20°"], "choices": [50.0, 30.0, 25.0, 20.0], "label": 2}
-{"prob_id": 3877, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3877.png", "question": "如图,AB是⊙O的直径,点D在AB的延长线上,过点D作⊙O的切线,切点为C,若∠A=25°,则∠D=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC．∵OC=OA,∴∠OCA=∠A=25°,∴∠DOC=∠A+∠OCA=50°,∵CD是⊙O的切线,∴OC⊥CD,∴∠OCD=90°,∴∠D=90°-∠DOC=40°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["25°", "40°", "50°", "65°"], "choices": [25.0, 40.0, 50.0, 65.0], "label": 1}
-{"prob_id": 3883, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3883.png", "question": "如图,在半径为2的⊙O中,C为直径AB延长线上一点,CD与圆相切于点D,连接AD,已知∠DAC=30°,则线段CD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵CD与圆相切于点D,∴OD⊥CD,∵∠DOC=2∠DAC=2×30°=60°,∴∠C=30°,∴CD=√{3}OD=2√{3}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "3.4641016151377544", "org_choices": ["1", "√{3}", "2", "2√{3}"], "choices": [1.0, 1.732, 2.0, 3.464], "label": 3}
-{"prob_id": 3896, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3896.png", "question": "⊙O是半径为1的圆,点O到直线L的距离为3,过直线L上的任一点P作⊙O的切线,切点为Q；若以PQ为边作正方形PQRS,则正方形PQRS的面积最小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连结OQ、OP,作OH⊥l于H,如图,则OH=3,∵PQ为⊙O的切线,∴OQ⊥PQ,在Rt△POQ中,PQ=√{0P^{2}-0Q^{2}}=√{0P^{2}-1},当OP最小时,PQ最小,正方形PQRS的面积最小,而当OP=OH=3时,OP最小,所以PQ的最小值为√{3^{2}-1}=2√{2},所以正方形PQRS的面积最小值为8．故选:B．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["7", "8", "9", "10"], "choices": [7.0, 8.0, 9.0, 10.0], "label": 1}
-{"prob_id": 3916, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3916.png", "question": "如图,AB是⊙O的直径,C是⊙O上的点,过点C作⊙O的切线交AB的延长线于点E,OD⊥AC于点D,若∠E=30°,CE=6,则OD的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC,∵CE为⊙O的切线,∴OC⊥EC,∴∠ECO=90°,∵∠E=30°,CE=6,∴OC=\\frac{6}{√{3}}=2√{3},∠EOC=60°,∵OA=OC,∴OA=2√{3},由圆周角定理得,∠EOC=2∠A,∴∠A=30°,∵OD⊥AC,∴∠ADO=90°,∴OD=\\frac{1}{2}OA=√{3},故选:B．", "dataset_name": "Geoqa", "ground_truth": "1.7320508075688772", "org_choices": ["1", "√{3}", "2", "2√{3}"], "choices": [1.0, 1.732, 2.0, 3.464], "label": 1}
-{"prob_id": 3920, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3920.png", "question": "如图,直线AB与⊙O相切于点A,⊙O的半径为1,若∠OBA=30°,则OB长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵直线AB与⊙O相切于点A,连接OA则∠OAB=90°．∵OA=1,∴OB=\\frac{0A}{sinB}=\\frac{1}{\\frac{1}{2}}=2．故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["1", "2", "√{3}", "2√{3}"], "choices": [1.0, 2.0, 1.732, 3.464], "label": 1}
-{"prob_id": 3921, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3921.png", "question": "如图,已知BA是⊙O的切线,切点为A,连接OB交⊙O于点C,若∠B=45°,AB长为2,则BC的长度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": ":连接OA,∵BA是⊙O的切线,切点为A,∴∠OAB=90°,∵∠B=45°,∴△OAB是等腰直角三角形,∵AB长为2,∴AO=2,则BO=2√{2},故BC=2√{2}-2,故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.8284271247461901", "org_choices": ["2√{2}-1", "√{2}", "2√{2}-2", "2-√{2}"], "choices": [1.828, 1.414, 0.828, 0.586], "label": 2}
-{"prob_id": 3941, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3941.png", "question": "如图,AB是⊙O的直径,点P是⊙O外一点,PO交⊙O于点C,连接BC、PA．若∠P=36°,PA与⊙O相切,则∠B等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA是⊙O的切线,∴∠PAO=90°,∴∠AOP=90°-∠P=54°,∵OB=OC,∴∠AOP=2∠B,∴∠B=\\frac{1}{2}∠AOP=27°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "27.0", "org_choices": ["20°", "27°", "36°", "42°"], "choices": [20.0, 27.0, 36.0, 42.0], "label": 1}
-{"prob_id": 3949, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3949.png", "question": "如图,AB、AC、BD是⊙O的切线,切点分别为P、C、D,若AB=5,AC=3,则BD的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AC、AP为⊙O的切线,∴AC=AP,∵BP、BD为⊙O的切线,∴BP=BD,∴BD=PB=AB-AP=5-3=2．故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["1.5", "2", "2.5", "3"], "choices": [1.5, 2.0, 2.5, 3.0], "label": 1}
-{"prob_id": 3967, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3967.png", "question": "如图所示,AB是⊙O的直径,PA切⊙O于点A,线段PO交⊙O于点C,连结BC,若∠P=36°,则∠B等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA切⊙O于点A,∴∠OAP=90°,∵∠P=36°,∴∠AOP=54°,∴∠B=27°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "27.0", "org_choices": ["27°", "32°", "36°", "54°"], "choices": [27.0, 32.0, 36.0, 54.0], "label": 0}
-{"prob_id": 3981, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/3981.png", "question": "如图,PA和PB是⊙O的切线,点A和B的切点,AC是⊙O的直径,已知∠P=50°,则∠ACB的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB,如图,∵PA、PB是⊙O的切线,∴OA⊥PA,OB⊥PB,∴∠OAP=∠OBP=90°,∴∠AOB=360°-90°-90°-50°=130°,∵OB=OC,∴∠OCB=∠OBC,而∠AOB=∠OCB+∠OBC,∴∠OCB=\\frac{1}{2}×130°=65°,即∠ACB=65°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["65°", "60°", "55°", "50°"], "choices": [65.0, 60.0, 55.0, 50.0], "label": 0}
-{"prob_id": 4005, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4005.png", "question": "如图,点A、B、C在⊙O上,过点A作⊙O的切线交OC的延长线于点P,∠B=30°,OP=3,则AP的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OA,∵∠B=30°,∴∠AOC=2∠B=60°,∵过点A作⊙O的切线交OC的延长线于点P,∴∠OAP=90°,∵OP=3,∴AP=OPsin60°=3×\\frac{√{3}}{2}=\\frac{3√{3}}{2},故选:D．", "dataset_name": "Geoqa", "ground_truth": "2.598076211353316", "org_choices": ["3", "\\frac{3}{2}", "\\frac{2}{3}√{3}", "\\frac{3}{2}√{3}"], "choices": [3.0, 1.5, 1.155, 2.598], "label": 3}
-{"prob_id": 4009, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4009.png", "question": "如图,在⊙O中,AD,CD是弦,连接OC并延长,交过点A的切线于点B,若∠ADC=25°,则∠ABO的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接OA,∵∠ADC=25°,∴∠AOC=2∠ADC=50°,∵AB切⊙O于A,∴∠OAB=90°,∴∠ABO=90°-∠AOC=40°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["50°", "40°", "30°", "20°"], "choices": [50.0, 40.0, 30.0, 20.0], "label": 1}
-{"prob_id": 4026, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4026.png", "question": "如图,直线PA、PB是⊙O的两条切线,A、B分别为切点,若∠APB=120°,⊙O的半径为10,则弦AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连OA,OB,∵直线PA,PB是⊙O的两条切线,∴OA⊥PA,OB⊥PB,∴∠OAP=∠OBP=90°∵∠APB=120°,∠OAP+∠OBP+∠APB+∠AOB=360°,∴∠AOB=60°,∵OA=OB,∴△AOB为等边三角形,∴AB=OA=10,故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["5", "10", "10√{3}", "5√{3}"], "choices": [5.0, 10.0, 17.321, 8.66], "label": 1}
-{"prob_id": 4027, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4027.png", "question": "如图,AC是⊙O的切线,切点为C,BC是⊙O的直径,AB交⊙O于点D,连接OD,若∠BAC=50°,则∠COD的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AC是⊙O的切线,∴BC⊥AC,∴∠C=90°,∵∠BAC=50°,∴∠B=90°-∠BAC=40°,∴∠COD=2∠B=80°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["100°", "80°", "50°", "40°"], "choices": [100.0, 80.0, 50.0, 40.0], "label": 1}
-{"prob_id": 4039, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4039.png", "question": "如图,AB是⊙O的直径,BP是⊙O的切线,AP与⊙O交于点G,点D为⁀{BC}上一点,若∠P=40°,则∠ADC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BC．∵PB是切线,∴AB⊥PB,∴∠ABP=90°,∵AB是直径,∴∠ACB=90°,∴∠ABC+∠BAC=90°,∠P+∠BAC=90°,∴∠ABC=∠P=40°,∴∠ADC=∠ABC=40°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["20°", "25°", "40°", "50°"], "choices": [20.0, 25.0, 40.0, 50.0], "label": 2}
-{"prob_id": 4053, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4053.png", "question": "如图,AB是⊙O的直径,PA切⊙O于点A,OP交⊙O于点C,连接BC．若∠P=20°,则∠B的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接AC,根据切线的性质定理得AB⊥AP,∴∠AOP=70°,∵OA=OC,∴∠OAC=∠OCA=55°；∵AB是直径,∴∠ACB=90°,∴∠B=35°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["20°", "25°", "30°", "35°"], "choices": [20.0, 25.0, 30.0, 35.0], "label": 3}
-{"prob_id": 4074, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4074.png", "question": "如图,PA、PB分别与⊙O相切于点A、B,⊙O的切线EF分别交PA、PB于点E、F,切点C在弧AB上,若PA长为2,则△PEF的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA、PB分别与⊙O相切于点A、B,⊙O的切线EF分别交PA、PB于点E、F,切点C在弧AB上,∴AE=CE,FB=CF,PA=PB=2,∴△PEF的周长=PE+EF+PF=PA+PB=4．故选:C．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["8", "6", "4", "2"], "choices": [8.0, 6.0, 4.0, 2.0], "label": 2}
-{"prob_id": 4079, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4079.png", "question": "把直尺、三角尺和圆形螺母按如图所示放置于桌面上,∠CAB=60°,若量出AD=6cm,则圆形螺母的外直径是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设圆形螺母的圆心为O,与AB切于E,连接OD,OE,OA,如图所示:∵AD,AB分别为圆O的切线,∴AO为∠DAB的平分线,OD⊥AC,OD⊥AC,又∠CAB=60°,∴∠OAE=∠OAD=\\frac{1}{2}∠DAB=60°,在Rt△AOD中,∠OAD=60°,AD=6cm,∴tan∠OAD=tan60°=\\frac{OD}{AD},即\\frac{OD}{6}=√{3},∴OD=6√{3}cm,则圆形螺母的直径为12√{3}cm．故选:D．", "dataset_name": "Geoqa", "ground_truth": "20.784609690826528", "org_choices": ["12cm", "24cm", "6√{3}cm", "12√{3}cm"], "choices": [12.0, 24.0, 10.392, 20.785], "label": 3}
-{"prob_id": 4090, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4090.png", "question": "AB是⊙O的直径,PA切⊙O于点A,PO交⊙O于点C；连接BC,若∠P=40°,则∠B等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA切⊙O于点A,∴∠PAB=90°,∵∠P=40°,∴∠POA=90°-40°=50°,∵OC=OB,∴∠B=∠BCO=25°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["20°", "25°", "30°", "40°"], "choices": [20.0, 25.0, 30.0, 40.0], "label": 1}
-{"prob_id": 4107, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4107.png", "question": "如图,AB是圆O的直径,DB,DC分别切圆O于点B,C,若∠ACE=25°,则∠D的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BC,∵DB、DE分别切⊙O于点B、C,∴∠ACE=∠ABC,BD=DC,∵∠ACE=25°,∴∠ABC=25°,∵AB是⊙O的直径,∴∠ACB=90°,∴∠DBC=∠DCB=90°-25°=65°,∴∠D=50°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["50°", "55°", "60°", "65°"], "choices": [50.0, 55.0, 60.0, 65.0], "label": 0}
-{"prob_id": 4111, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4111.png", "question": "如图,AB为⊙O的切线,A为切点,BO的延长线交⊙O于点C,∠OAC=35°,则∠B的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB为⊙O的切线,∴OA⊥AB,∴∠BAO=90°,∵OA=OC,∴∠C=∠OAC=35°,∴∠B=180°-∠C-∠BAC=180°-35°-35°-90°=20°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["15°", "20°", "25°", "35°"], "choices": [15.0, 20.0, 25.0, 35.0], "label": 1}
-{"prob_id": 4115, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4115.png", "question": "如图,在△ABC中,∠B=20°,点O是BC边上一点,以O为圆心,OB为半径作圆,交AB边于点D,连结CD,若CD恰好与⊙O相切,则∠DCB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OD,∵DC为⊙O的切线,∴∠ODC=90°,∵OB=OD,∴∠B=∠ODB=20°,∴∠DCB=180°-90°-20°-20°=50°,故选:D．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["30°", "40°", "45°", "50°"], "choices": [30.0, 40.0, 45.0, 50.0], "label": 3}
-{"prob_id": 4128, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4128.png", "question": "如图,PA、PB是⊙O的切线,点A和B是切点,AC是⊙O的直径,已知∠P=50°,则∠ACB的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB,如图,∵PA、PB是⊙O的切线,∴OA⊥PA,OB⊥PB,∴∠OAP=∠OBP=90°,∴∠AOB=360°-90°-90°-50°=130°,∵OB=OC,∴∠OCB=∠OBC,而∠AOB=∠OCB+∠OBC,∴∠OCB=\\frac{1}{2}×130°=65°,即∠ACB=65°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["60°", "65°", "70°", "75°"], "choices": [60.0, 65.0, 70.0, 75.0], "label": 1}
-{"prob_id": 4137, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4137.png", "question": "如图,PA、PB分别切⊙O于A、B两点,点C在优弧⁀{ACB}上,∠P=80°,则∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA是圆的切线．∴∠OAP=90°,同理∠OBP=90°,根据四边形内角和定理可得:∠AOB=360°-∠OAP-∠OBP-∠P=360°-90°-90°-80°=100°,∴∠C=\\frac{1}{2}∠AOB=50°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["50°", "60°", "70°", "80°"], "choices": [50.0, 60.0, 70.0, 80.0], "label": 0}
-{"prob_id": 4141, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4141.png", "question": "如图,⊙O是Rt△ABC的外接圆,∠ACB=90°,∠A=25°,过点C作⊙O的切线,交AB的延长线于点D,则∠D的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC,则∠COD=2∠A=50°,∵CD为⊙O的切线,∴OC⊥CD,∴∠OCD=90°,∴∠D=90°∠COD=40°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["25°", "30°", "40°", "55°"], "choices": [25.0, 30.0, 40.0, 55.0], "label": 2}
-{"prob_id": 4145, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4145.png", "question": "如图,AB是⊙O的直径,点C在AB的延长线上,CD与⊙O相切,切点为D,如果∠A=35°,那么∠C=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接OD,∵CD是⊙O的切线,∴OD⊥CD,即∠ODC=90°,∵AB为直径,∴∠COD=2∠A=70°,∴∠C=90°-70°=20°,故选:D．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["55°", "35°", "30°", "20°"], "choices": [55.0, 35.0, 30.0, 20.0], "label": 3}
-{"prob_id": 4149, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4149.png", "question": "如图,点P是⊙O的直径AB延长线上的一点,过点P作⊙O的切线PC,切点为C,若AO=OB=PB=1,则PC的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC．∵PC是切线,∴OC⊥PC．在直角△OPC中,OC=OB=1,OP=OB+PB=2．∴PC=√{0P^{2}-0C^{2}}=√{3}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "1.7320508075688772", "org_choices": ["1", "√{3}", "2", "√{5}"], "choices": [1.0, 1.732, 2.0, 2.236], "label": 1}
-{"prob_id": 4165, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4165.png", "question": "如图,△ABC中,AB=5,BC=3,AC=4,以点C为圆心的圆与AB相切,则⊙C的半径为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在△ABC中,∵AB=5,BC=3,AC=4,∴AC²+BC²=3²+4²=5²=AB²,∴∠C=90°,如图:设切点为D,连接CD,∵AB是⊙C的切线,∴CD⊥AB,∵S_{△ABC}=\\frac{1}{2}AC•BC=\\frac{1}{2}AB•CD,∴AC•BC=AB•CD,即CD=\\frac{AC\\cdotBC}{AB}=\\frac{3×4}{5}=2.4,∴⊙C的半径为2.4,故选:C．", "dataset_name": "Geoqa", "ground_truth": "2.4", "org_choices": ["2.6", "2.5", "2.4", "2.3"], "choices": [2.6, 2.5, 2.4, 2.3], "label": 2}
-{"prob_id": 4170, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4170.png", "question": "如图,点A,B,C是⊙O上的三点,直线CD与⊙O相切于点C,若∠DCB=40°,则∠CAB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵直线CD与⊙O相切于点C,∴∠OCD=90°,∵∠DCB=40°,∴∠OCB=50°,∵CO=BO,∴∠OBC=50°,∴∠COB=80°,∴∠CAB=\\frac{1}{2}×80°=40°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "50°", "80°", "100°"], "choices": [40.0, 50.0, 80.0, 100.0], "label": 0}
-{"prob_id": 4184, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4184.png", "question": "如图,直线AB与⊙O相切于点A,⊙O的半径为2,若∠OBA=30°,则AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB为切线,∴∠OAB=90°,∵∠OBA=30°,OA=2,∴AB=\\frac{0A}{tan30^{°}}=\\frac{2}{\\frac{√{3}}{3}}=2√{3},故选:C．", "dataset_name": "Geoqa", "ground_truth": "3.4641016151377544", "org_choices": ["4√{3}", "4", "2√{3}", "2"], "choices": [6.928, 4.0, 3.464, 2.0], "label": 2}
-{"prob_id": 4188, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4188.png", "question": "如图,AB是⊙O的直径,AC切⊙O于A,BC交⊙O于点D,若∠C=70°,则∠AOD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AC是圆O的切线,AB是圆O的直径,∴AB⊥AC．∴∠CAB=90°．又∵∠C=70°,∴∠CBA=20°．∴∠DOA=40°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["70°", "35°", "20°", "40°"], "choices": [70.0, 35.0, 20.0, 40.0], "label": 3}
-{"prob_id": 4193, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4193.png", "question": "如图,PA、PB分别切⊙O于点A、B,点E是⊙O上一点,且∠AEB=60°,则∠P=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OA,BO；∵∠AOB=2∠E=120°,∴∠OAP=∠OBP=90°,∴∠P=180°-∠AOB=60°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["90°", "60°", "45°", "30°"], "choices": [90.0, 60.0, 45.0, 30.0], "label": 1}
-{"prob_id": 4201, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4201.png", "question": "如图,PA、PB是⊙O的切线,AC是⊙O直径,∠c=55°,则∠APB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB,∵PA、PB是⊙O的切线,AC是⊙O直径,∴∠OAP=∠OBP=∠ABC=90°,∵∠C=55°,OC=OB,∴∠OBC=55°,∴∠AOB=110°,则在四边形AOBP中,∠APB=70°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["55°", "60°", "65°", "70°"], "choices": [55.0, 60.0, 65.0, 70.0], "label": 3}
-{"prob_id": 4224, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4224.png", "question": "如图,PA,PB分别与⊙O相切于A,B两点,∠P=70°,则∠C为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OA、OB,∵直线PA、PB分别与⊙O相切于点A、B,∴OA⊥PA,OB⊥PB,∵∠P=70°,∴∠AOB=110°,∵C是⊙O上一点,∴∠ACB=55°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["55°", "70°", "110°", "140°"], "choices": [55.0, 70.0, 110.0, 140.0], "label": 0}
-{"prob_id": 4234, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4234.png", "question": "如图,线段AB是⊙O的直径,点C、D为⊙O上的点,过点C作⊙O的切线交AB的延长线于点E,若∠E=50°,则∠CDB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC,∵CE是⊙O的切线,∴∠OCE=90°,∵∠E=50°,∴∠COE=90°-50°=40°,∴∠CDB=\\frac{1}{2}∠COE=20°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["20°", "25°", "30°", "40°"], "choices": [20.0, 25.0, 30.0, 40.0], "label": 0}
-{"prob_id": 4239, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4239.png", "question": "直线AB与⊙O相切于点A,如图,若∠OBA=60°,AB=1,则⊙O的半径为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵直线AB与⊙O相切于点A,∴OA⊥AB,∵∠OBA=60°,∴∠BOA=30°,∵AB=1,∴OB=2,∴OA=√{0B^{2}-AB^{2}}=√{2^{2}-1^{2}}=√{3},∴⊙O的半径为√{3}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "1.7320508075688772", "org_choices": ["√{5}", "√{3}", "1", "2"], "choices": [2.236, 1.732, 1.0, 2.0], "label": 1}
-{"prob_id": 4248, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4248.png", "question": "如图,Rt△ABC中,AC=4,AB=5,∠C=90°,经过点C且与边AB相切的圆与△ABC的边CB,CA分别相交于点E、F,线段EF长度的最小值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:取EF的中点O,作OG⊥AB于G,CH⊥AB于H,连结OC,如图,在Rt△ABC中,∵AC=4,AB=5,∠C=90°,∴BC=√{5^{2}-4^{2}}=3,∵\\frac{1}{2}CH•AB=\\frac{1}{2}BC•AC,∴CH=\\frac{3×4}{5}=2.4,∵∠ECF=90°,∴EF为经过点C且与边AB相切的圆的直径,点O为圆心,∵AB为⊙O的切线,∴OG为⊙O的半径,∴EF=OC+OG,当OC、OG共线时,OC+OG的值最小,最小值为CH的长,∴EF的最小值为2.4．故选:A．", "dataset_name": "Geoqa", "ground_truth": "2.4", "org_choices": ["2.4", "2", "2.5", "2√{2}"], "choices": [2.4, 2.0, 2.5, 2.828], "label": 0}
-{"prob_id": 4255, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4255.png", "question": "如图,两个同心圆的半径分别为3cm和5cm,大圆的一条弦AB与小圆相切,则弦AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC和OB,∵弦AB与小圆相切,∴OC⊥AB,在Rt△OBC中,BC=√{OB^{2}-OC^{2}}=√{5^{2}-3^{2}}=4cm,∴AB=2BC=8cm．故选:D．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["3cm", "4cm", "6cm", "8cm"], "choices": [3.0, 4.0, 6.0, 8.0], "label": 3}
-{"prob_id": 4261, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4261.png", "question": "如图,⊙O是△ABC的外接圆,AD是⊙O的直径,EA是⊙O的切线．若∠EAC=120°,则∠ABC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵EA是⊙O的切线,AD是⊙O的直径,∴∠EAD=90°,∵∠EAC=120°,∴∠DAC=∠EAC-∠EAD=30°,∵AD是⊙O的直径,∴∠ACD=90°,∴∠ADC=180°-∠ACD-∠DAC=60°,∴∠ABC=∠ADC=60°(圆周角定理),故选:C．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["80°", "70°", "60°", "50°"], "choices": [80.0, 70.0, 60.0, 50.0], "label": 2}
-{"prob_id": 4264, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4264.png", "question": "如图,⊙O的半径为2,点O到直线l的距离为3,点P是直线l上的一个动点．若PB切⊙O于点B,则PB的最小值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连结OB,作OP′⊥l于P′如图,OP′=3,∵PB切⊙O于点B,∴OB⊥PB,∴∠PBO=90°,∴PB=√{OP^{2}-OB^{2}}=√{OP^{2}-2^{2}},当点P运动到点P′的位置时,OP最小时,则PB最小,此时OP=3,∴PB的最小值为√{3^{2}-2^{2}}=√{5}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.23606797749979", "org_choices": ["√{13}", "√{5}", "3", "2"], "choices": [3.606, 2.236, 3.0, 2.0], "label": 1}
-{"prob_id": 4268, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4268.png", "question": "如图,PA、PB、CD是⊙O的切线,A、B、E是切点,CD分别交线段PA、PB于C、D两点,若∠APB=40°,则∠COD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意得,连接OA、OC、OE、OD、OB,所得图形如下:由切线性质得,OA⊥PA,OB⊥PB,OE⊥CD,DB=DE,AC=CE,∵AO=OE=OB,∴△AOC≌△EOC(SAS),△EOD≌△BOD(SAS),∴∠AOC=∠EOC,∠EOD=∠BOD,∴∠COD=\\frac{1}{2}∠AOB,∵∠APB=40°,∴∠AOB=140°,∴∠COD=70°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["50°", "60°", "70°", "75°"], "choices": [50.0, 60.0, 70.0, 75.0], "label": 2}
-{"prob_id": 4282, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4282.png", "question": "如图,AB是⊙O直径,点C在⊙O上,AE是⊙O的切线,A为切点,连接BC并延长交AE于点D．若∠AOC=80°,则∠ADB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB是⊙O直径,AE是⊙O的切线,∴∠BAD=90°,∵∠B=\\frac{1}{2}∠AOC=40°,∴∠ADB=90°-∠B=50°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["40°", "50°", "60°", "20°"], "choices": [40.0, 50.0, 60.0, 20.0], "label": 1}
-{"prob_id": 4283, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4283.png", "question": "如图,AC是⊙O的切线,切点为C,BC是⊙O的直径,AB交⊙O于点D,连接OD．若∠BAC=55°,则∠COD的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AC是⊙O的切线,∴BC⊥AC,∴∠C=90°,∵∠BAC=55°,∴∠B=90°-∠BAC=35°,∴∠COD=2∠B=70°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["70°", "60°", "55°", "35°"], "choices": [70.0, 60.0, 55.0, 35.0], "label": 0}
-{"prob_id": 4284, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4284.png", "question": "如图,在△ABC中,AB=3,AC=2．当∠B最大时,BC的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:以A为圆心,AC为半径作⊙O,当BC为⊙O的切线时,即BC⊥AC时,∠B最大,此时BC=√{AB^{2}-AC^{2}}=√{3^{2}-2^{2}}=√{5}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.23606797749979", "org_choices": ["1", "√{5}", "√{13}", "5"], "choices": [1.0, 2.236, 3.606, 5.0], "label": 1}
-{"prob_id": 4295, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4295.png", "question": "如图,AB是半圆的直径,点O是圆心,点C是AB延长线的一点,CD与半圆相切于点D．若AB=6,CD=4,则sin∠C的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OD,∵AB是半圆的直径,AB=6,∴OD=3,∵CD与半圆相切于点D,∴∠CDO=90°,∵CD=4,∴OC=√{CD^{2}+OD^{2}}=5,∴sin∠C=\\frac{OD}{OC}=\\frac{3}{5},故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.6", "org_choices": ["\\frac{3}{4}", "\\frac{3}{5}", "\\frac{4}{5}", "\\frac{2}{3}"], "choices": [0.75, 0.6, 0.8, 0.667], "label": 1}
-{"prob_id": 4305, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4305.png", "question": "如图,在Rt△ABC中,∠C=90°,∠A=30°,BC=2,⊙C的半径为1,点P是斜边AB上的点,过点P作⊙C的一条切线PQ(点Q是切点),则线段PQ的最小值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接CP、CQ；如图所示:∵PQ是⊙C的切线,∴CQ⊥PQ,∠CQP=90°,根据勾股定理得:PQ²=CP²-CQ²,∴当PC⊥AB时,线段PQ最短,∵在Rt△ACB中,∠A=30°,BC=2,∴AB=2BC=4,AC=2√{3},∴CP\\frac{AC\\cdotBC}{AB}=\\frac{2√{3}}{2}=√{3},∴PQ√{CP^{2}-CQ^{2}}=√{3-1}=√{2},∴PQ的最小值是√{2},故选:C．", "dataset_name": "Geoqa", "ground_truth": "1.4142135623730951", "org_choices": ["2", "√{3}", "√{2}", "2-\\frac{√{3}}{3}"], "choices": [2.0, 1.732, 1.414, 1.423], "label": 2}
-{"prob_id": 4317, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4317.png", "question": "如图,AB、AC是⊙O的两条弦,过点B的切线与OC的延长线交于点D,若∠D=36°,则∠CAB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB,∵BD是⊙O的切线,∴OB⊥BD,∴∠OBD=90°,∵∠D=36°,∴∠DOB=∠OBD-∠D=90°-36°=54°,∵∠DOB与∠CAB对着同一条弧,∴∠CAB=\\frac{1}{2}∠DOB=\\frac{1}{2}×54^{°}=27^{°}．故选:C．", "dataset_name": "Geoqa", "ground_truth": "27.0", "org_choices": ["54°", "44°", "27°", "22°"], "choices": [54.0, 44.0, 27.0, 22.0], "label": 2}
-{"prob_id": 4334, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4334.png", "question": "如图,两个同心圆的直径分别为6cm和10cm,大圆的一条弦AB与小圆相切,则弦AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作OC⊥AB于C,连结OA,如图,∵弦AB与小圆相切,∴OC=3cm,在Rt△OAC中,∵OA=5,OC=3,∴AC=√{OA^{2}-OC^{2}}=4,∵OC⊥AB,∴AC=BC,∴AB=2AC=8cm．故选:C．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["4cm", "6cm", "8cm", "10cm"], "choices": [4.0, 6.0, 8.0, 10.0], "label": 2}
-{"prob_id": 4364, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4364.png", "question": "如图,AP、BP分别切⊙O于点A、B,∠P=60°,点C在优弧AB上,则∠C度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AP、BP分别切⊙O于点A、B,∴∠OAP=∠OBP=90°,∴∠AOB=360°-60°-90°-90°=120°,∴∠C=\\frac{1}{2}∠AOB=60°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["30°", "60°", "40°", "72°"], "choices": [30.0, 60.0, 40.0, 72.0], "label": 1}
-{"prob_id": 4369, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4369.png", "question": "如图,P是⊙O的直径AB延长线上一点,PC切⊙O于C,∠P=50°,∠A为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OP,∵CP为圆O的切线,∴OC⊥CP,在Rt△OPC中,∠P=50°,∴∠POC=40°,∵OA=OC,∴∠A=∠OCA,∵∠POC为△AOC的外角,∴∠A=\\frac{1}{2}∠POC=20°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["40°", "35°", "25°", "20°"], "choices": [40.0, 35.0, 25.0, 20.0], "label": 3}
-{"prob_id": 4390, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4390.png", "question": "如图,PA、PB是⊙O的切线,切点为A、B,若∠OAB=30°,则∠P的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠OAB=30°,∴∠AOB=180°-2×30°=120°,又∵PA、PB是⊙O的切线,∴∠OAP=∠OBP=90°,∴∠P=360°-90°-90°-120°=60°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["60°", "90°", "120°", "无法确定"], "choices": [60.0, 90.0, 120.0], "label": 0}
-{"prob_id": 4400, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4400.png", "question": "如图,PA,PB是⊙O是切线,A,B为切点,AC是O的直径,若∠BAC=25°,则∠P为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA,PB是⊙O是切线,∴∠OAP=∠OBP=90°,∵OA=OB,∠BAC=25°,∴∠AOB=180°-2∠BAC=130°,又∵∠OAP+∠OBP+∠AOB+∠P=360°,∴∠P=360°-∠OAP-∠OBP-∠AOB=360°-90°-90°-130°=50°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["25°", "50°", "30°", "65°"], "choices": [25.0, 50.0, 30.0, 65.0], "label": 1}
-{"prob_id": 4403, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4403.png", "question": "如图,直线BC与⊙O相切于点A,AD是⊙O的弦,连接OD,若∠DAC=50°,则∠ODA的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵直线BC与⊙O相切于点A,∴OA⊥BC,∴∠OAC=90°,∵∠DAC=50°,∴∠OAD=40°,∵OD=OA,∴∠ODA=∠OAD=40°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["30°", "40°", "50°", "60°"], "choices": [30.0, 40.0, 50.0, 60.0], "label": 1}
-{"prob_id": 4404, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4404.png", "question": "如图所示,某宾馆大厅要铺圆环形的地毯,工人师傅只测量了与小圆相切的大圆的弦AB的长,就计算出了圆环的面积．若测量得AB的长为8米,则圆环的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过O作OC⊥AB于C,连OA,如图,∴AC=BC,而AB=8米,∴AC=4米,∵AB与小圆相切,∴OC为小圆的半径,∴圆环的面积=π•OA²-π•OC²=π(OA²-OC²)=π•AC²=16π(平方米)．故选:D．", "dataset_name": "Geoqa", "ground_truth": "50.26548245743669", "org_choices": ["16平方米", "8π平方米", "64平方米", "16π平方米"], "choices": [16.0, 25.133, 64.0, 50.265], "label": 3}
-{"prob_id": 4406, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4406.png", "question": "如图,AB是⊙O的直径,CD切于点D,AB的延长线交CD于点C,若∠ACD=40°,则∠A=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接OD．∵AB是⊙O的直径,CD切于点D,∴∠CDO=90°．又∵∠ACD=40°,∴∠COD=50°．∴∠A=\\frac{1}{2}∠COD=25°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["45°", "40°", "30°", "25°"], "choices": [45.0, 40.0, 30.0, 25.0], "label": 3}
-{"prob_id": 4414, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4414.png", "question": "如图,AB是⊙O的直径,点D在AB的延长线上,DC切⊙O于点C,若∠A=26°,则∠D等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如右图所示,连接BC,∵AB是直径,∴∠BCA=90°,又∵∠A=26°,∴∠CBA=90°-26°=64°,∵DC是切线,∴∠BCD=∠A=26°,∴∠D=∠CBA-∠BCD=64°-26°=38°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "38.0", "org_choices": ["38°", "50°", "60°", "570°"], "choices": [38.0, 50.0, 60.0, 570.0], "label": 0}
-{"prob_id": 4424, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4424.png", "question": "如图,△ABC中,AB=AC,∠BA0=45°,△ABC内接于⊙O,D为⊙O上一点,过点D作⊙O的切线交BC的延长线于E,若DE⊥BC,AD=2√{2},则DE的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过点A作AH⊥BC于点H,连接OC,OD,∵AB=AC,∴AH=CH,∴AH过点O,∵DE是⊙O的切线,∴OD⊥DE,∵DE⊥BC,∴∠OHE=∠E=∠EDO=90°,∴四边形ODEH是矩形,∴∠AOD=90°,∵AD=2√{2},∴OA=OD=2,∵∠BAC=45°,∴∠COH=45°,∵OC=2,∴OH=CH=√{2},∴DE=OH=√{2}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "1.4142135623730951", "org_choices": ["2", "1", "\\frac{3}{2}", "√{2}"], "choices": [2.0, 1.0, 1.5, 1.414], "label": 3}
-{"prob_id": 4426, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4426.png", "question": "如图,AB是⊙O的切线,B为切点,AO与⊙O交于点C,若∠BAO=40°,则∠OCB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB是⊙O的切线,B为切点,∴OB⊥AB,即∠OBA=90°,∵∠BAO=40°,∴∠O=50°,∵OB=OC(都是半径),∴∠OCB=\\frac{1}{2}(180°-∠O)=65°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["40°", "50°", "65°", "75°"], "choices": [40.0, 50.0, 65.0, 75.0], "label": 2}
-{"prob_id": 4436, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4436.png", "question": "如图,⊙O与AB切于点C,∠BCE=60°,DC=6,DE=4,则S_{△CDE}为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过C作CF⊥DE,交DE于点F,∵AB与圆O相切,CE为圆O的弦,∴∠CDE=∠BCE=60°,在Rt△CDF中,DC=6,∠CDE=60°,∴CF=DCsin60°=3√{3},又DE=4,则S_{△CDE}=\\frac{1}{2}DE•CF=6√{3}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.392304845413264", "org_choices": ["6√{5}", "6√{3}", "6√{2}", "6"], "choices": [13.416, 10.392, 8.485, 6.0], "label": 1}
-{"prob_id": 4440, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4440.png", "question": "如图,AB切⊙O于B,割线ACD经过圆心O,若∠BCD=70°,则∠A的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OB=OC,∠BCD=70°,∴∠OBC=∠BCD=70°,∴∠BOC=180°-∠BCD-∠OBC=40°,∵AB切⊙O于B,∴OB⊥AB,∴∠ABO=90°,∴∠A=90°-∠BOC=50°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["20°", "50°", "40°", "80°"], "choices": [20.0, 50.0, 40.0, 80.0], "label": 1}
-{"prob_id": 4445, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4445.png", "question": "如图,在△ABC中,AB=15,AC=12,BC=9,经过点C且与边AB相切的动圆与CB、CA分别相交于点E、F,则线段EF长度的最小值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:结合题意,易知△ABC为RT△,∠C=90°,即知EF为圆的直径,设圆与AB的切点为D,连接CD,当CD垂直于AB时,即CD是圆的直径的时候,EF长度最小,最小值是\\frac{9×12}{15}=\\frac{36}{5}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "7.2", "org_choices": ["\\frac{12}{5}", "\\frac{36}{5}", "\\frac{15}{2}", "8"], "choices": [2.4, 7.2, 7.5, 8.0], "label": 1}
-{"prob_id": 4458, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4458.png", "question": "如图,BC与⊙O相切于点C,BO的延长线交⊙O于点A,连结AC,若∠ACB=120°,则∠A的度数等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接OC．∵BC与⊙O相切于点C,∴OC⊥BC,即∠OCB=90°．∵A=OC,∴∠A=∠ACO=∠ACB-∠OCB=120°-90°=30°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["30°", "40°", "50°", "60°"], "choices": [30.0, 40.0, 50.0, 60.0], "label": 0}
-{"prob_id": 4473, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4473.png", "question": "如图,一块四边形绿化园地,四角都做有半径为2的圆形喷水池,则这四个喷水池占去的绿化园地的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:圆形喷水池形成四边形,四边形的内角和为360°,阴影部分的面积和为一个圆面积,故圆形喷水池的面积为π•2²=4π．故选:A．", "dataset_name": "Geoqa", "ground_truth": "12.566370614359172", "org_choices": ["4π", "8π", "16π", "不能确定"], "choices": [12.566, 25.133, 50.265], "label": 0}
-{"prob_id": 4475, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4475.png", "question": "如图,在边长为4的正方形ABCD中,先以点A为圆心,AD的长为半径画弧,再以AB边的中点为圆心,AB长的一半为半径画弧,则两弧之间的阴影部分面积是()(结果保留π)．. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:根据题意得,S_{阴影部分}=S_{扇形BAD}-S_{半圆BA},∵S_{扇形BAD}=\\frac{90π\\cdot4^{2}}{360}=4πS_{半圆BA}=\\frac{1}{2}•π•2²=2π,∴S_{阴影部分}=4π-2π=2π．故选:B．", "dataset_name": "Geoqa", "ground_truth": "6.283185307179586", "org_choices": ["π", "2π", "3π", "4π"], "choices": [3.142, 6.283, 9.425, 12.566], "label": 1}
-{"prob_id": 4508, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4508.png", "question": "如图,在△ABC中,DE∥BC,AE=3,AC=9,AD=4,则AB的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴\\frac{AD}{AB}=\\frac{AE}{AC},即\\frac{4}{AB}=\\frac{3}{9},∴AB=12．故选:D．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["6", "8", "9", "12"], "choices": [6.0, 8.0, 9.0, 12.0], "label": 3}
-{"prob_id": 4513, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4513.png", "question": "如图,AB∥CD,AD与BC相交于点O,若AO=2,DO=4,BO=3,则BC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB∥CD,∴\\frac{BO}{CO}=\\frac{AO}{DO}；∵AO=2,DO=4,BO=3,∴\\frac{3}{CO}=\\frac{2}{4},解得:CO=6,∴BC=BO+CO=3+6=9．故选:B．", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["6", "9", "12", "15"], "choices": [6.0, 9.0, 12.0, 15.0], "label": 1}
-{"prob_id": 4528, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4528.png", "question": "如图,已知a∥b∥c,AB=1,BC=2,EF=4,则DE=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵a∥b∥c,AB=1,BC=2,EF=4,∴\\frac{AB}{BC}=\\frac{DE}{EF},即\\frac{1}{2}=\\frac{DE}{4},DE=2,故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["1", "2", "3", "4"], "choices": [1.0, 2.0, 3.0, 4.0], "label": 1}
-{"prob_id": 4534, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4534.png", "question": "如图,直线a、b、c分别与直线m、n交于点A、B、C、D、E、F．已知直线a∥b∥c,若AB=2,BC=3,则\\frac{DE}{EF}的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵直线a∥b∥c,∴\\frac{DE}{EF}=\\frac{AB}{BC}=\\frac{2}{3},故选:A．", "dataset_name": "Geoqa", "ground_truth": "0.6666666666666666", "org_choices": ["\\frac{2}{3}", "\\frac{3}{2}", "\\frac{2}{5}", "\\frac{3}{5}"], "choices": [0.667, 1.5, 0.4, 0.6], "label": 0}
-{"prob_id": 4535, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4535.png", "question": "如图所示,在△ABC中,DE∥BC,若AD=1,DB=2,则\\frac{AE}{AC}的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AD=1,DB=2,∴AB=3,∴\\frac{AD}{AB}=\\frac{1}{3}∵\\frac{AD}{DB}=\\frac{AE}{AC},∴\\frac{AE}{AC}=\\frac{1}{3}；故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.3333333333333333", "org_choices": ["\\frac{2}{3}", "\\frac{1}{3}", "\\frac{1}{4}", "\\frac{1}{2}"], "choices": [0.667, 0.333, 0.25, 0.5], "label": 1}
-{"prob_id": 4539, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4539.png", "question": "如图,在△ABC中,M是AC的中点,E是AB上一点,AE=\\frac{1}{4}AB,连接EM并延长,交BC的延长线于D,则\\frac{BC}{CD}=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,过C点作CP∥AB,交DE于P,∵PC∥AE,∴△AEM∽△CPM,∴\\frac{PC}{AE}=\\frac{CM}{AM},∵M是AC的中点,∴AM=CM,∴PC=AE,∵AE=\\frac{1}{4}AB,∴CP=\\frac{1}{4}AB,∴CP=\\frac{1}{3}BE,∵CP∥BE,∴△DCP∽△DBE,∴\\frac{CP}{BE}=\\frac{CD}{BD}=\\frac{1}{3},∴BD=3CD,∴BC=2CD,即\\frac{BC}{CD}=2．故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["\\frac{1}{2}", "2", "\\frac{2}{3}", "\\frac{3}{2}"], "choices": [0.5, 2.0, 0.667, 1.5], "label": 1}
-{"prob_id": 4542, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4542.png", "question": "如图,在矩形ABCD中,AB=3,BC=4,点M在BC边上,且满足BM=1,过D作DN⊥AM交AM于点N,则DN的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接DM,如图所示:∵四边形ABCD是矩形,∴∠B=90°,AD=BC=4,△AMD底边AD上的高为AB,AM=√{AB^{2}+BM^{2}}=√{3^{2}+1^{2}}=√{10},∵△ADM的面积=\\frac{1}{2}AM×DN=\\frac{1}{2}AD×AB,∴DN=\\frac{AD×AB}{AM}=\\frac{4×3}{√{10}}=\\frac{6√{10}}{5}；故选:D．", "dataset_name": "Geoqa", "ground_truth": "3.794733192202055", "org_choices": ["\\frac{7}{2}√{5}", "\\frac{3}{5}√{5}", "\\frac{3}{2}√{10}", "\\frac{6}{5}√{10}"], "choices": [7.826, 1.342, 4.743, 3.795], "label": 3}
-{"prob_id": 4546, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4546.png", "question": "已知如图,在△ABC中,点D、点E分别在AB、BC边上,且DE∥AC,BE=2,CE=1,△BDE的面积为4,则△ABC的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BE=2,CE=1,∴BC=BE+CE=2+1=3,∵DE∥AC,∴△BDE∽△BAC,∴\\frac{BE}{BC}=\\frac{BD}{AB}=\\frac{2}{3},∴\\frac{S△BDE}{S△ABC}=(\\frac{2}{3})^{2}=\\frac{4}{9},∵△BDE的面积为4,∴S△ABC=\\frac{9}{4}×4=9,故选:D．", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["5", "6", "8", "9"], "choices": [5.0, 6.0, 8.0, 9.0], "label": 3}
-{"prob_id": 4553, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4553.png", "question": "如图,在△ABC中,DE∥BC,若AB=7cm,AC=5cm,AD=3cm,则DE=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB=7,AD=3,∴BD=BA-AD=4,∵DE∥BC,∴△BDE∽△BAC,∴\\frac{BD}{BA}=\\frac{DE}{AC},即\\frac{4}{7}=\\frac{DE}{5},解得,DE=\\frac{20}{7}(cm),故选:D．", "dataset_name": "Geoqa", "ground_truth": "2.857142857142857", "org_choices": ["\\frac{15}{4}cm", "\\frac{20}{3}cm", "\\frac{15}{7}cm", "\\frac{20}{7}cm"], "choices": [3.75, 6.667, 2.143, 2.857], "label": 3}
-{"prob_id": 4558, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4558.png", "question": "如图,在▱ABCD中,点E在边AD上,CE交BD于点F,若EF=\\frac{1}{3}FC,则\\frac{AE}{ED}=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在▱ABCD中,∵AD∥BC,AD=BC,∴△DEF∽△BCF,∴\\frac{DE}{BC}=\\frac{EF}{FC}=\\frac{1}{3},∴\\frac{DE}{AD}=\\frac{1}{3},∴\\frac{AE}{ED}=2,故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["\\frac{3}{2}", "2", "\\frac{5}{3}", "3"], "choices": [1.5, 2.0, 1.667, 3.0], "label": 1}
-{"prob_id": 4590, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4590.png", "question": "如图,已知点M为平行四边形ABCD边AB的中点,线段CM交BD于点E,S△BEM=2,则图中阴影部分的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AB=CD,AB∥CD,∴S△DMB=S△CBM,∴S△DEM=S△CEB,∵AM=BM=\\frac{1}{2}AB=\\frac{1}{2}CD,∴\\frac{CE}{EM}=\\frac{CD}{BM}=2,∴S△CEB=2S△BME=4,∴S阴=4+4=8,故选:C．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["5", "4", "8", "6"], "choices": [5.0, 4.0, 8.0, 6.0], "label": 2}
-{"prob_id": 4591, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4591.png", "question": "如图,四边形ABCD中,AD∥BC,对角线AC、BD相交于O,若\\frac{S_{\riangleADO}}{S_{\riangleDOC}}=\\frac{1}{3},则的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵\\frac{S_{\riangleADO}}{S_{\riangleDOC}}=\\frac{1}{3},∴\\frac{OA}{OC}=\\frac{1}{3},∵AD∥BC,∴△ADO∽△CBO,∴\\frac{AD}{BC}=\\frac{OA}{OC}=\\frac{1}{3},故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.3333333333333333", "org_choices": ["\\frac{1}{2}", "\\frac{1}{3}", "\\frac{1}{9}", "\\frac{√{3}}{3}"], "choices": [0.5, 0.333, 0.111, 0.577], "label": 1}
-{"prob_id": 4598, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4598.png", "question": "如图,▱ABCD中,∠C=120°,AB=AE=5,AE与BD交于点F,AF=2EF．则BC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AD=BC,AD∥BC,∴△AFD∽△EFB,∴\\frac{BE}{AD}=\\frac{EF}{AF},∵AF=2EF,∴AD=BC=2BE,∵BE=5,∴BC=10,故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["12", "10", "8", "6"], "choices": [12.0, 10.0, 8.0, 6.0], "label": 1}
-{"prob_id": 4614, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4614.png", "question": "如图,D,E为△ABC的边AB,AC上的点,DE∥BC,若AD:DB=1:3,AE=2,则AC的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴\\frac{AE}{AC}=\\frac{AD}{AB}=\\frac{1}{3+1}=\\frac{1}{4}．∵AE=2,∴AC=8故选:B．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["10", "8", "6", "4"], "choices": [10.0, 8.0, 6.0, 4.0], "label": 1}
-{"prob_id": 4619, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4619.png", "question": "如图,已知AB∥CD∥EF,AD:AF=3:5,BE=15,那么CE的长等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB∥CD∥EF,∴\\frac{BC}{BE}=\\frac{AD}{AF},即\\frac{BC}{15}=\\frac{3}{5},∴BC=9,∴CE=BE-BC=15-9=6．故选:B．", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["9", "6", "\\frac{15}{2}", "\\frac{9}{2}"], "choices": [9.0, 6.0, 7.5, 4.5], "label": 0}
-{"prob_id": 4620, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4620.png", "question": "如图,AD∥BE∥CF,直线l1,l2与这三条平行线分别交于点A,B,C,D,E,F,\\frac{AB}{BC}=\\frac{2}{3},DE=6,则EF的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AD∥BE∥CF,∴\\frac{AB}{BC}=\\frac{DE}{EF},即\\frac{6}{EF}=\\frac{2}{3},∴EF=9．故选:C．", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["4", "6", "9", "12"], "choices": [4.0, 6.0, 9.0, 12.0], "label": 2}
-{"prob_id": 4621, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4621.png", "question": "如图,已知直线a∥b∥c,直线m,n与a,b,c分别交于点A,C,E,B,D,F,若AC=4,AE=10,BD=3,则DF的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵a∥b∥c,∴image_023087.png\\frac{AC}{AE}=\\frac{BD}{BF},即\\frac{4}{10}=\\frac{3}{BF},解得,BF=\\frac{15}{2},则DF=BF-BD=4.5,故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.5", "org_choices": ["4", "4.5", "5", "5.5"], "choices": [4.0, 4.5, 5.0, 5.5], "label": 1}
-{"prob_id": 4642, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4642.png", "question": "如图所示,在△ABC中,DE∥BC,若AD=1,DB=2,则\\frac{AD}{AB}的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AD=1,DB=2,∴AB=3,∴\\frac{AD}{AB}=\\frac{1}{3}；故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.3333333333333333", "org_choices": ["\\frac{2}{3}", "\\frac{1}{4}", "\\frac{1}{3}", "\\frac{1}{2}"], "choices": [0.667, 0.25, 0.333, 0.5], "label": 2}
-{"prob_id": 4652, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4652.png", "question": "如图,直线a∥b∥c,直线m、n与a、b、c分别交于点A、C、E和B、D、F,若AC=4,AE=10,BF=\\frac{15}{2},则DF的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AC=4,AE=10,∴CE=6,∵直线a∥b∥c,∴\\frac{AE}{CE}=\\frac{BF}{DF},即\\frac{10}{6}=\\frac{\\frac{15}{2}}{DF},∴DF=\\frac{9}{2},故选:A．", "dataset_name": "Geoqa", "ground_truth": "4.5", "org_choices": ["\\frac{9}{2}", "10", "3", "\\frac{7}{2}"], "choices": [4.5, 10.0, 3.0, 3.5], "label": 0}
-{"prob_id": 4653, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4653.png", "question": "如图,已知a∥b∥c,AC=6,AB=2,EF=5,则DF的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵直线a∥b∥c,AC=6,AB=2,EF=5,∴\\frac{AB}{AC}=\\frac{DE}{DF},即\\frac{2}{6}=\\frac{DF-5}{DF},解得DF=\\frac{15}{2}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "7.5", "org_choices": ["\\frac{5}{3}", "\\frac{5}{2}", "\\frac{10}{3}", "\\frac{15}{2}"], "choices": [1.667, 2.5, 3.333, 7.5], "label": 3}
-{"prob_id": 4665, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4665.png", "question": "如图,在△ABC中,DE∥BC,\\frac{AD}{DB}=\\frac{1}{2},DE=4,则BC的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵\\frac{AD}{DB}=\\frac{1}{2},∴\\frac{AD}{AB}=\\frac{1}{3},∵在△ABC中,DE∥BC,∴\\frac{DE}{BC}=\\frac{AD}{AB}=\\frac{1}{3},∵DE=4,∴BC=3DE=12．故选:D．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["8", "10", "11", "12"], "choices": [8.0, 10.0, 11.0, 12.0], "label": 3}
-{"prob_id": 4676, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4676.png", "question": "如图,在△ABC中,点D,E分别在边AB,AC上,DE∥BC,已知EC=6,\\frac{AD}{DB}=\\frac{2}{3},则AE的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴\\frac{AD}{DB}=\\frac{AE}{EC},∵EC=6,\\frac{AD}{DB}=\\frac{2}{3},∴\\frac{AE}{6}=\\frac{2}{3},解得:AE=4．故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["1", "4", "5", "9"], "choices": [1.0, 4.0, 5.0, 9.0], "label": 1}
-{"prob_id": 4687, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4687.png", "question": "如图,在△ABC中,D,E分别是AB和AC上的点,满足AD=3,AE=2,EC=1,DE∥BC,则AB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴\\frac{AD}{DB}=\\frac{AE}{EC},∵AD=3,AE=2,EC=1,∴\\frac{3}{DB}=\\frac{2}{1},∴DB=\\frac{3}{2}=1.5,∴AB=AD+DB=3+1.5=4.5,故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.5", "org_choices": ["6", "4.5", "2", "1.5"], "choices": [6.0, 4.5, 2.0, 1.5], "label": 1}
-{"prob_id": 4700, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4700.png", "question": "如图,AB∥CD∥EF,AC与BD相交于点E,若CE=5,CF=4,AE=BC,则\\frac{CD}{AB}的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设AE=x,则BC=x,∵EF∥AB,∴\\frac{CE}{CA}=\\frac{CF}{CB},即\\frac{5}{5+x}=\\frac{4}{x},解得x=20,即AE=20,∵CD∥AB,∴△ECD∽△EAB,∴\\frac{CD}{AB}=\\frac{CE}{AE}=\\frac{5}{20}=\\frac{1}{4}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "0.25", "org_choices": ["\\frac{2}{3}", "\\frac{1}{2}", "\\frac{1}{3}", "\\frac{1}{4}"], "choices": [0.667, 0.5, 0.333, 0.25], "label": 3}
-{"prob_id": 4701, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4701.png", "question": "如图,在△ABC中,点D、E分别在AB、AC边上,DE∥BC．若\\frac{AE}{AC}=\\frac{3}{4},AD=9,则AB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴\\frac{AD}{AB}=\\frac{AE}{AC}=\\frac{3}{4},又AD=9,∴AB=12,故选:C．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["10", "11", "12", "16"], "choices": [10.0, 11.0, 12.0, 16.0], "label": 2}
-{"prob_id": 4711, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4711.png", "question": "如图,直线l_{1}∥l_{2}∥l_{3},已知:AB=4,BC=6,DE=3,则EF=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵l_{1}∥l_{2}∥l_{3},∴\\frac{AB}{BC}=\\frac{DE}{EF},即\\frac{4}{6}=\\frac{3}{EF},∴EF=\\frac{9}{2}．故选:C．", "dataset_name": "Geoqa", "ground_truth": "4.5", "org_choices": ["8", "6", "4.5", "2"], "choices": [8.0, 6.0, 4.5, 2.0], "label": 2}
-{"prob_id": 4739, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4739.png", "question": "如图,平行四边形ABCD中,F是边AB上的点,DF交AC于点E,如果CD=10,\\frac{AE}{EC}=\\frac{2}{5},那么BF的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如右图所示,∵四边形ABCD是▱,∴AB∥CD,∴△AEF∽△CED,∴AE:CE=AF:CD,又∵\\frac{AE}{EC}=\\frac{2}{5},∴AF=4,∴BF=AB-AF=10-4=6．故选:C．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["4", "5", "6", "8"], "choices": [4.0, 5.0, 6.0, 8.0], "label": 2}
-{"prob_id": 4747, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4747.png", "question": "如图,E是平行四边形ABCD的AD边上一点,过点E作EF∥AB交BD于F,若DE:EA=2:3,EF=4,则CD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE:EA=2:3,∴DE:DA=2:5,∵EF∥AB,∴\\frac{DE}{DA}=\\frac{EF}{AB},∵EF=4,∴\\frac{2}{5}=\\frac{4}{AB},解得:AB=10,∵四边形ABCD是平行四边形,∴CD=AB=10．故选:C．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["\\frac{16}{3}", "8", "10", "16"], "choices": [5.333, 8.0, 10.0, 16.0], "label": 2}
-{"prob_id": 4749, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4749.png", "question": "如图,已知l_{1}∥l_{2}∥l_{3},如果AB:BC=2:3,DE=4,则EF的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵l_{1}∥l_{2}∥l_{3},∴\\frac{AB}{BC}=\\frac{DE}{EF},又AB:BC=2:3,DE=4,∴EF=6．故选:B．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["\\frac{10}{3}", "6", "4", "25"], "choices": [3.333, 6.0, 4.0, 25.0], "label": 1}
-{"prob_id": 4758, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4758.png", "question": "如图DE∥BC,AD=3,DB=4,AE=1.5,则EC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵△ABC中,DE∥BC,∴\\frac{AD}{BD}=\\frac{AE}{EC},∵AD=3,DB=6,AE=2,∴\\frac{3}{4}=\\frac{1.5}{EC},∴EC=2．故选:C．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["1", "1.5", "2", "2.5"], "choices": [1.0, 1.5, 2.0, 2.5], "label": 2}
-{"prob_id": 4770, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4770.png", "question": "如图,在△ABC中,点D、E分别在边AB、AC上,DE∥BC,且AE=1,AC=5,AB=6,则AD的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴\\frac{AE}{AC}=\\frac{AD}{AB},∵AE=1,AC=5,AB=6,∴\\frac{1}{5}=\\frac{AD}{6},解得:AD=\\frac{6}{5}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "1.2", "org_choices": ["1", "1.2", "2", "2.5"], "choices": [1.0, 1.2, 2.0, 2.5], "label": 1}
-{"prob_id": 4781, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4781.png", "question": "如图,D、E是△ABC边AB、AC上的点,且DE∥BC,若DE:BC=3:5,AD=6,则AB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴\\frac{DE}{BC}=\\frac{AD}{AB}=\\frac{3}{5},∴\\frac{6}{AB}=\\frac{3}{5},∴AB=10．故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["9", "10", "6", "15"], "choices": [9.0, 10.0, 6.0, 15.0], "label": 1}
-{"prob_id": 4799, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4799.png", "question": "如图,△ABC∽△AED,∠ADE=80°,∠A=60°,则∠B等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ADE+∠A+∠AED=180°,∴∠AED=180°-∠ADE-∠A=180°-80°-60°=40°,又∵△ABC∽△AED,∴∠B=∠AED=40°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "60°", "80°", "100°"], "choices": [40.0, 60.0, 80.0, 100.0], "label": 0}
-{"prob_id": 4817, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4817.png", "question": "如图,Rt△ABC中,∠C=90°,BC=3,AC=4,若△ABC∽△BDC,则CD=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵△ABC∽△BDC,∴\\frac{BC}{CD}=\\frac{AC}{BC},即\\frac{3}{CD}=\\frac{4}{3},解得CD=\\frac{9}{4}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "2.25", "org_choices": ["2", "\\frac{3}{2}", "\\frac{4}{3}", "\\frac{9}{4}"], "choices": [2.0, 1.5, 1.333, 2.25], "label": 3}
-{"prob_id": 4828, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4828.png", "question": "如图,△ABC∽△DEF,相似比为1:2,若EF=2,则BC的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵△ABC∽△DEF,相似比为1:2,∴\\frac{BC}{EF}=\\frac{1}{2},∴BC=\\frac{1}{2}EF=1,故选:A．", "dataset_name": "Geoqa", "ground_truth": "1.0", "org_choices": ["1", "2", "3", "4"], "choices": [1.0, 2.0, 3.0, 4.0], "label": 0}
-{"prob_id": 4846, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4846.png", "question": "如图,DE是△ABC的中位线,已知△ABC的面积为8cm^{2},则△ADE的面积为()cm^{2}．. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE为中位线,∴DE∥BC,DE=\\frac{1}{2}BC,∴△ADE∽△ABC,∴S△ADE:S△ABC=1:4,∵S△ABC=8cm^{2},∴S△ADE=2cm^{2}．故选:A．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["2", "4", "6", "8"], "choices": [2.0, 4.0, 6.0, 8.0], "label": 0}
-{"prob_id": 4859, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4859.png", "question": "如图,D是△ABC的边BC上一点,已知AB=6,AD=3,AC=4,∠DAC=∠B,则BD长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠DAC=∠B,∠C=∠C,∴△ACD∽△BCA,∵AB=6,AD=3,AC=4,∴\\frac{AC}{BC}=\\frac{AD}{AB},即\\frac{4}{BC}=\\frac{3}{6},可得:BC=8,∵△ACD∽△BCA,∴\\frac{CD}{AC}=\\frac{AC}{BC},即\\frac{CD}{4}=\\frac{4}{8},可得；CD=2,∴BD=BC-CD=8-2=6,故选:B．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["4", "6", "8", "9"], "choices": [4.0, 6.0, 8.0, 9.0], "label": 1}
-{"prob_id": 4865, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4865.png", "question": "如图,若△ABC∽△ACD,∠A=60°,∠ACD=40°,则∠BCD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵△ABC∽△ACD,∠A=60°,∠ACD=40°,∴∠B=∠ACD=40°,∴∠ACB=180°-∠A-∠B=80°,∴∠BCD=∠ACB-∠ACD=80°-40°=40°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["30°", "40°", "50°", "30°或50°"], "choices": [30.0, 40.0, 50.0], "label": 1}
-{"prob_id": 4873, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4873.png", "question": "如图,两条直线被三条平行线所截,AB=2,BC=3,则\\frac{EF}{EG}等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AE∥BF∥CG,∴\\frac{EF}{EG}=\\frac{AB}{AC},∵AB=2,BC=3,∴AC=AB+BC=5,∴\\frac{EF}{EG}=\\frac{2}{5},故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.4", "org_choices": ["\\frac{2}{3}", "\\frac{2}{5}", "\\frac{3}{2}", "\\frac{5}{6}"], "choices": [0.667, 0.4, 1.5, 0.833], "label": 1}
-{"prob_id": 4875, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4875.png", "question": "如图所示,在△ABC中,DE∥BC,若\\frac{AD}{AB}=\\frac{1}{3},则\\frac{AE}{AC}=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在△ABC中,∵DE∥BC,\\frac{AD}{AB}=\\frac{1}{3},∴\\frac{AD}{AB}=\\frac{AE}{AC}=\\frac{1}{3},故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.3333333333333333", "org_choices": ["\\frac{1}{2}", "\\frac{1}{3}", "\\frac{2}{3}", "\\frac{1}{4}"], "choices": [0.5, 0.333, 0.667, 0.25], "label": 1}
-{"prob_id": 4906, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4906.png", "question": "如图,C、M是线段AB上的两点,且点M是线段AC的中点,若AB=8cm,BC=2cm,则AM的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】:由图形可知AC=AB-BC=8-2=6cm,∵M是线段AC的中点,∴AM=AC=3cm．故AM的长为3cm．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["2cm", "3cm", "4cm", "6cm"], "choices": [2.0, 3.0, 4.0, 6.0], "label": 1}
-{"prob_id": 4918, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4918.png", "question": "如图,C,D是线段AB上两点,若CB=4cm,DB=7cm,且D是AC的中点,则AC的长等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:由线段的和差,得DC=DB-CB=7-4=3cm,由D是AC中点,得AC=2DC=6cm．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["14cm", "11cm", "6cm", "3cm"], "choices": [14.0, 11.0, 6.0, 3.0], "label": 2}
-{"prob_id": 4920, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4920.png", "question": "如图,BC=\\frac{1}{2}AB,D为AC的中点,若DC=3,则AB的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵D为AC的中点,DC=3,∴AC=2DC=2×3=6,∵BC=\\frac{1}{2}AB,∴AB=\\frac{2}{3}AC=\\frac{2}{3}×6=4,", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["3", "4", "5", "6"], "choices": [3.0, 4.0, 5.0, 6.0], "label": 1}
-{"prob_id": 4927, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4927.png", "question": "如图,小林从P点向西直走12米后,向左转,转动的角度为α,再走12米,如此重复,小林共走了108米回到点P,则α-5的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:设边数为n,根据题意,n=108÷12=9,∴α=360°÷9=40°．所以α-5=35°,", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["35°", "40°", "50°", "不存在"], "choices": [35.0, 40.0, 50.0], "label": 0}
-{"prob_id": 4929, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4929.png", "question": "如图,已知AD是△ABC的中线,且△ABD的周长比△ACD的周长大3cm,则AB与AC的差为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵AD是△ABC的中线,∴BD=DC,∴△ABD与△ACD的周长之差=(AB+AD+BD)-(AC+AD+CD)=AB-AC,∵△ABD比△ACD的周长大3cm,∴AB与AC的差为3cm．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["2cm", "3cm", "4cm", "6cm"], "choices": [2.0, 3.0, 4.0, 6.0], "label": 1}
-{"prob_id": 4962, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4962.png", "question": "如图,在△ABC中,AB=AC,M,N分别是AB,AC的中点,D,E为BC上的点,连结DN,EM．若AB=13cm,BC=10cm,DE=5cm,则图中阴影部分面积为cm2．(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:连接MN,过点A作AF⊥BC于F,则MN是△ABC的中位线,因此MN=\\frac{1}{2}BC=5cm；则AF=√{AB²-BF²}=12cm．∵图中阴影部分的三个三角形的底长都是5cm,且高的和为12cm；因此S阴影=\\frac{1}{2}×5×12=30cm2．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["25", "35", "30", "42"], "choices": [25.0, 35.0, 30.0, 42.0], "label": 2}
-{"prob_id": 4968, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4968.png", "question": "如图,C是以AB为直径的半圆O上一点,连结AC,BC,分别以AC,BC为边向外作正方形ACDE,BCFG．DE,FG,⁀{\\mathrm{AC}},⁀{\\mathrm{BC}}的中点分别是M,N,P,Q．若MP+NQ=14,AC+BC=18,则AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:连接OP,OQ,∵DE,FG,⁀{\\mathrm{AC}},⁀{\\mathrm{BC}}的中点分别是M,N,P,Q,∴OP⊥AC,OQ⊥BC,∴H、I是AC、BD的中点,∴OH+OI=\\frac{1}{2}(AC+BC)=9,∵MH+NI=AC+BC=18,MP+NQ=14,∴PH+QI=18-14=4,∴AB=OP+OQ=OH+OI+PH+QI=9+4=13,", "dataset_name": "Geoqa", "ground_truth": "13.0", "org_choices": ["9√{2}", "\\frac{90}{7}", "13", "16"], "choices": [12.728, 12.857, 13.0, 16.0], "label": 2}
-{"prob_id": 4985, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4985.png", "question": "如图,在四边形ABCD中,点P是对角线BD的中点,点E、F分别是AB、CD的中点,AD=BC,∠FPE=136°,则∠PFE的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵P是对角线BD的中点,E是AB的中点,∴EP=\\frac{1}{2}AD,同理,FP=\\frac{1}{2}BC,∵AD=BC,∴PE=PF,∵∠FPE=136°,∴∠PFE=∠PEF=22°,", "dataset_name": "Geoqa", "ground_truth": "22.0", "org_choices": ["15°", "20°", "22°", "44°"], "choices": [15.0, 20.0, 22.0, 44.0], "label": 2}
-{"prob_id": 4990, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/4990.png", "question": "如图,已知直线a∥b∥c,直线d与它们分别垂直且相交于A,B,C三点,若AB=3,AC=8,则平行线b,c之间的距离是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵直线a∥b∥c,直线d与它们分别垂直且相交于A,B,C三点,∴AB长为直线a和b之间的距离,BC长为直线b和c之间的距离,AC长为直线a和c之间的距离,又∵AB=3,AC=8,∴BC=8-3=5,即直线b与直线c之间的距离为5．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["3", "5", "8", "11"], "choices": [3.0, 5.0, 8.0, 11.0], "label": 1}
-{"prob_id": 500, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/500.png", "question": "如图,已知∠1＋∠2=100°,则∠3=()．. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠1+∠2=100^{°},∠1=∠2,∴∠1=50^{°},∴∠3=180°-∠1=130°,故选C.", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["50°", "80°", "130°", "120°"], "choices": [50.0, 80.0, 130.0, 120.0], "label": 2}
-{"prob_id": 501, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/501.png", "question": "如图,有一池塘,要测池塘两端A,B间的距离,可先在平地上取一个不经过池塘可以直接到达点A和B的点C,连接AC并延长至D,使CD=CA,连接BC并延长至E,使CE=CB,连接ED．若量出DE=58米,则A,B间的距离为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:在△ABC和△DEC中,AC=CD⊥∠ACD=∠DCEBC=CE△ABC\\omega△DEC(SAS),∴AB=DE=58{米},故选B.", "dataset_name": "Geoqa", "ground_truth": "58.0", "org_choices": ["29米", "58米", "60米", ".116米A120°"], "choices": [29.0, 58.0, 60.0, 120.0], "label": 1}
-{"prob_id": 520, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/520.png", "question": "如图,平行线a、b被直线c所截,若∠1=50°,则∠2的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵直线a//b,∠1=50°,∴∠3=∠1=50°,∴∠2=180^{°}-∠3=180^{°}-50^{°}=130°故选B.", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["150°", "130°", "110°", "100°"], "choices": [150.0, 130.0, 110.0, 100.0], "label": 1}
-{"prob_id": 521, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/521.png", "question": "如图,已知∠1=60°,∠A+∠B+∠C+∠D+∠E+∠F=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠1+∠B+∠C+∠D+∠E=180°,∠1+∠A+∠F=180°,∠1=60°,∴∠B+∠C+∠D+∠E=120°,∠A+∠F=120°,∴∠A+∠B+∠C+∠D+∠E+∠F=240°.故选:C", "dataset_name": "Geoqa", "ground_truth": "240.0", "org_choices": ["360°", "540°", "240°", "280°"], "choices": [360.0, 540.0, 240.0, 280.0], "label": 2}
-{"prob_id": 540, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/540.png", "question": "如图,等腰三角形ABC中,AB=AC,BD是AC边上的高,若∠A=36°,则∠DBC的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB=AC,∠A=36^{°},∴∠ABC=∠ACB=72^{°}.∵BD是AC边上的高,∴BD⊥AC,∴∠DBC=90^{°}-72^{°}=18^{°}故选A.", "dataset_name": "Geoqa", "ground_truth": "18.0", "org_choices": ["18°", "36°", "54°", "72°"], "choices": [18.0, 36.0, 54.0, 72.0], "label": 0}
-{"prob_id": 550, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/550.png", "question": "如图,若a∥b,∠1=115°,则∠2=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵a//b,∴∠1+∠2=180°,∵∠1=115°,∴∠2=65°故选C.", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["55°", "60°", "65°", "75°"], "choices": [55.0, 60.0, 65.0, 75.0], "label": 2}
-{"prob_id": 551, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/551.png", "question": "如图,在△ABC中∠A=80°．点D是BC延长线上一点,∠ACD=150°,则∠B=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠ACD=∠A+∠B,∠A=80°,∠ACD=150°,∴∠B=70°.故选C.", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["60°", "50°", "70°", "165°"], "choices": [60.0, 50.0, 70.0, 165.0], "label": 2}
-{"prob_id": 569, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/569.png", "question": "如图,a∥b,点B在直线a上,且AB⊥BC,∠1=35°,那么∠2=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:如图∵AB⊥BC,∠1=35°,∴∠3=90^{°}-35^{°}=55^{°}.∵a//b,∴∠2=∠3=55^{°}.故选C.", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["45°", "50°", "55°", "60°"], "choices": [45.0, 50.0, 55.0, 60.0], "label": 2}
-{"prob_id": 576, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/576.png", "question": "如图,直线AB与CD相交于E,在∠CEB的平分线上有一点F,FM∥AB．当∠3=10°时,∠F的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠1+∠2+∠3=180°,∠3=10°,∴∠1+∠2=170°,即∠CEB=170,∵EF平分∠CEB,∴∠1=∠2=85°,∴FM//AB,∴∠F=∠2=85°.故选D.", "dataset_name": "Geoqa", "ground_truth": "85.0", "org_choices": ["80°", ".82°", "83°", "85°"], "choices": [80.0, 0.82, 83.0, 85.0], "label": 3}
-{"prob_id": 580, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/580.png", "question": "如图,已知直线a、b被直线c所截．若a∥b,∠1=120°,则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:如图,∠3=180°-∠1=180°-120°=60°,∵a//b,∴∠2=∠3=60°.故选B.", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["50°", "60°", "120°", "130°"], "choices": [50.0, 60.0, 120.0, 130.0], "label": 1}
-{"prob_id": 587, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/587.png", "question": "如图,C、D是以线段AB为直径的⊙O上两点,若CA=CD,且∠CAB=25°,则∠ACD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵CD是直径,∴∠ACB=90°,∵∠CAB=25°,∴∠ABC=65°,∴∠ADC=65°,∵CA=CD,∴∠CAD=∠ADC=65°,∴∠ACD=180°-2×65°=50°故选D.", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["25°", "30°", "40°", "50°"], "choices": [25.0, 30.0, 40.0, 50.0], "label": 3}
-{"prob_id": 593, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/593.png", "question": "如图,AB∥EF,CD⊥EF于点D,若∠BCD=140°,则∠ABC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "过点C作CG//AB,由题意可得:AB//EF//CG,故∠B=∠BCG,∵CD⊥EF于点D,∴∠GCD=90°∵∠BCD=140°.∴∠BCG=50^{°},∴∠ABC=50^{°},故选:B.", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["60°", "50°", "40°", "30°"], "choices": [60.0, 50.0, 40.0, 30.0], "label": 1}
-{"prob_id": 596, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/596.png", "question": "如图,在△ABC中,∠B=40°,过点C作CD∥AB,∠ACD=65°,则∠ACB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵CD//AB,∴∠A=∠ACD=65°,∴∠ACB=180°-∠A-∠B=180°-65°-40°=75°,即∠ACB的度数为75°.故选D.", "dataset_name": "Geoqa", "ground_truth": "75.0", "org_choices": ["60°", "65°", "70°", "75°"], "choices": [60.0, 65.0, 70.0, 75.0], "label": 3}
-{"prob_id": 598, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/598.png", "question": "将一副直角三角板如图放置,使含30°角的三角板的直角边和含45°角的三角板的一条直角边在同一条直线上,则∠1的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "方法一:∠1的对顶角所在的三角形中另两个角的度数分别为60°,45°,∴∠1=180°-(60°+45°)=75°.方法二:∠1可看作是某个三角形的外角,根据三角形的外角等于与它不相邻的两个内角的和计算.故选A.", "dataset_name": "Geoqa", "ground_truth": "75.0", "org_choices": ["75°", "65°", "45°", "30°"], "choices": [75.0, 65.0, 45.0, 30.0], "label": 0}
-{"prob_id": 603, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/603.png", "question": "已知直线a∥b,一块直角三角板如图所示放置,若∠1=37°,则∠2的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "作直线AB//a,∵a//b∴AB//a//b,∵AB//a,∴∠1=∠3,∵AB//b,∴∠2=∠4,∵∠3+∠4=90°,∴∠1+∠2=90°,∵∠1=37°,∴∠2=90^{°}-37^{°}=53^{°}故选B", "dataset_name": "Geoqa", "ground_truth": "53.0", "org_choices": ["37°", "53°", "63°", "27°"], "choices": [37.0, 53.0, 63.0, 27.0], "label": 1}
-{"prob_id": 620, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/620.png", "question": "如图所示,矩形ABCD的对角线AC、BD相交于点O,CE∥BD,DE∥AC,若AB=4,BC=3,则四边形CODE的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "首先由CE||BD,DE||AC,可证得四边形CODE是平行四边形,又由四边形ABCD是矩形,根据矩形的性质,易得OC=OD=2,即可判定四边形CODE是菱形,继而求得答案.解:∵CE||BD1DE||AC,∴四边形CODE是平行四边形,.四边形ABCD是矩形,∴AC=BD=4,OA=OC,OB=OD,∴OD=OC,AC=√{AB²+BC²}=√{4²+3²}=5.∴四边形CODE是菱形,且OC=\\frac{1}{2}AC=2.5∴四边形CODE的周长为:2.5×4=10.故选A", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["10", "12", "18", "24"], "choices": [10.0, 12.0, 18.0, 24.0], "label": 0}
-{"prob_id": 631, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/631.png", "question": "如图,将含30°角的三角板的直角顶点放在直尺的一边上,若∠1=35°,则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图,∵∠1=35°,∠3=30°,∴∠4=115°,∵∠2+∠4=180°,∴∠2=65°.故选B.", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["80°", "65°", "60°", "55°"], "choices": [80.0, 65.0, 60.0, 55.0], "label": 1}
-{"prob_id": 654, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/654.png", "question": "如图,在▱ABCD中,F是AD上的一点,CF=CD.若∠B=72°,则∠AFC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "已知四边形ABCD是平行四边形,根据平行四边形的性质可得∠D=∠B=72°,再因CF=CD,根据等腰三角形的性质可得∠DFC=∠D=72°,所以∠AFC=180°∠DFC=108°1故选B", "dataset_name": "Geoqa", "ground_truth": "108.0", "org_choices": ["144°", "108°", "102°", ".78°A菱形的对角线互相垂直"], "choices": [144.0, 108.0, 102.0], "label": 1}
-{"prob_id": 691, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/691.png", "question": "从棱长为4的正方体毛坯的一角,挖去一个棱长为2的小正方体,得到一个如图所示的零件,则这个零件的表面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:棱长为4的正方体毛坯的一角挖去一个棱长为2的小正方体,得到的图形与原图形表面积相等,则表面积是4×4×6=96,故答案为:96", "dataset_name": "Geoqa", "ground_truth": "96.0", "org_choices": ["90", "92", "94", "96"], "choices": [90.0, 92.0, 94.0, 96.0], "label": 3}
-{"prob_id": 703, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/703.png", "question": "如图,点B,O,D在同一直线上,若∠1=15°,∠2=105°,则∠AOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠2=105°,∴∠BOC=180^{°}-∠2=75^{°}∴∠AOC=∠1+∠BOC=15^{°}+75^{°}=90^{°}故选C.", "dataset_name": "Geoqa", "ground_truth": "90.0", "org_choices": ["70", "80", "90", "100"], "choices": [70.0, 80.0, 90.0, 100.0], "label": 2}
-{"prob_id": 717, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/717.png", "question": "如图,将两块三角板的直角顶点重合后叠放在一起,若∠1=40°,则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图:∵∠1+∠BOC=90^{°},∠2+∠BOC=90^{°},∴∠2=∠1=40^{°},故选:C.", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["60°", "50°", "40°", "30°"], "choices": [60.0, 50.0, 40.0, 30.0], "label": 2}
-{"prob_id": 722, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/722.png", "question": "如图所示,一辆汽车经过一段公路两次拐弯后,和原来的行驶方向相同,也就是拐弯前后的两条路互相平行.第一次拐的角∠B等于142°,第二次拐的角∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵拐弯前后的两条路互相平行,∴∠C=∠B=142°(两直线平行,内错角相等).故选B", "dataset_name": "Geoqa", "ground_truth": "142.0", "org_choices": ["38°", "142°", "130°", "140°"], "choices": [38.0, 142.0, 130.0, 140.0], "label": 1}
-{"prob_id": 728, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/728.png", "question": "如图△ABC中,∠ACB=90°,AD平分∠BAC交BC于D,DE垂直AB于E,若DE=1.5cm,BD=3cm,则BC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∠ACB=90^{°},DE垂直AB于E,AD平分∠BAC交BC于D,所以DC=DE=1.5.BD=3cm∴BC=4.5cm所以选D.", "dataset_name": "Geoqa", "ground_truth": "4.5", "org_choices": ["3cm", "7.5cm", "6cm", "4.5cm"], "choices": [3.0, 7.5, 6.0, 4.5], "label": 3}
-{"prob_id": 731, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/731.png", "question": "如图所示,AB=AC,AD=AE,∠BAC=∠DAE,∠1=25°,∠2=30°,则∠3=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:∵∠BAC=∠DAE,∴∠BAC-∠DAC=∠DAE-∠DAC∴∠1=∠EAC,在△BAD和△EAC中,AB=AC∠BAD=∠EACAD=AE∴△BAD≌△EAC(SAS),∠2=∠ABD=30^{°},∵∠1=25°∴∠3=∠1+∠AB∠ABD=25^{°}+30^{°}=55^{°}故选B.", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["60°", "55°", "50°", "无法计算"], "choices": [60.0, 55.0, 50.0], "label": 1}
-{"prob_id": 734, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/734.png", "question": "如图,在△ABC中,∠B=46°,∠C=54°,AD平分∠BAC,交BC于D,则∠BAD的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠B=46°∠C=54°.∠BAC=180°-∠B-∠C=180^{°}-46^{°}-54^{°}=80^{°},AD平分∠BAC,∠BAD=40°所以选C.", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["45°", "54°", "40°", "50°"], "choices": [45.0, 54.0, 40.0, 50.0], "label": 2}
-{"prob_id": 735, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/735.png", "question": "如图,已知D为BC上一点,∠B=∠1,∠BAC=78°,则∠2=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠2=∠B+∠BAD,∠BAC=∠1+∠BAD,又∵∠B=∠1,∴∠2=∠BAC,∵∠BAC=78°,∴∠2=78°.故选A.", "dataset_name": "Geoqa", "ground_truth": "78.0", "org_choices": ["78°", "80°", "50°", "60°"], "choices": [78.0, 80.0, 50.0, 60.0], "label": 0}
-{"prob_id": 758, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/758.png", "question": "如图,在△ABC中,∠ACB=90°,沿CD折叠△CBD,使点B恰好落在AC边上的点E处．若∠A=24°,则∠BDC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "在△ABC中,∠ACB=90°,∠A=24°,∠B=90^{°}-∠A=66^{°}.由折叠的性质可得:∠BCD=\\frac{1}{2}∠ACB=45^{°}∴∠BDC=180°-∠BCD-∠B=69°故选C.", "dataset_name": "Geoqa", "ground_truth": "69.0", "org_choices": ["42°", "66°", "69°", "77°"], "choices": [42.0, 66.0, 69.0, 77.0], "label": 2}
-{"prob_id": 777, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/777.png", "question": "如图,DE为△ABC的边BC的垂直平分线,交BC于E,交AB于D,且∠B=40°,∠A=60°,则∠ACD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:∵∠B=40°,∠A=60°,∴∠ACB=180^{°}-60^{°}-40^{°}=80^{°},∵DE为△ABC边BC的垂直平分线,∴∠BCD=∠B=40°,∴∠ACD=∠ACB-angleBCD=80^{°}-40^{°}=40^{°}.故选A.", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "50°", "30°", "45°"], "choices": [40.0, 50.0, 30.0, 45.0], "label": 0}
-{"prob_id": 829, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/829.png", "question": "如图,在半径为5cm的⊙O中,AB为一条弦,OC⊥AB于点C,且OC=3cm,则AB的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "连接OA,OC⊥AB,点O是圆心,∴AB=2AC,∠ACO=90°,∴AC=√{OA²-OC²}=√{5²-3²}=4cm,∴AB=8cm,故选D", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["3cm", "4cm", "6cm", "8cm"], "choices": [3.0, 4.0, 6.0, 8.0], "label": 3}
-{"prob_id": 869, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/869.png", "question": "已知如图,在⊙O中,OA⊥OB,∠A=35°,则弧CD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC,∵OA⊥OB,∴∠AOB=90°,∵∠A=35°,∴∠OBC=∠OCB=55°,∴OB=OC,∴∠OBC=∠OCB=55°,∴∠COB=70°,∴弧CD的度数为20°,故选:A.", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["20°", "25°", "30°", "35°"], "choices": [20.0, 25.0, 30.0, 35.0], "label": 0}
-{"prob_id": 884, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/884.png", "question": "如图,在△ABC中,DE是AC的垂直平分线,AE=3cm,△ABD的周长为13cm,则△ABC的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵DE是AC的垂直平分线,AE=3cm,∴AE=CE=3cm,AD=DC,又△ABD的周长为13cm,即AB+BD+AD=13cm,△ABC的周长=AB+BC+AC=AB+BD+DC+2AE=AB+BD+AD+2AE=13+6=19cm故选C.", "dataset_name": "Geoqa", "ground_truth": "19.0", "org_choices": ["16cm", "13cm", "19cm", "10cm"], "choices": [16.0, 13.0, 19.0, 10.0], "label": 2}
-{"prob_id": 887, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/887.png", "question": "如图,⊿ABC内接于⊙O,若∠OAB=28°则∠C的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "连接OB,∵OA=OB,∠OAB=28°∠OBA=∠OAB=28°,∴∠AOB=180°-28°-28°=124°,∵∠ACB、∠AOB是\\hat{AB}所对的圆周角和圆心角,∴∠ACB=\\frac{1}{2}∠AOB=62^{°},故选C", "dataset_name": "Geoqa", "ground_truth": "62.0", "org_choices": ["56°", "60°", "62°", "28°"], "choices": [56.0, 60.0, 62.0, 28.0], "label": 2}
-{"prob_id": 907, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/907.png", "question": "如图,已知PA、PB是⊙O的切线,A、B为切点,AC是⊙O的直径,∠P=40°,则∠BAC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BC,OB,AC是直径,则∠ABC=90°PA、PB是⊙O的切线,A、B为切点,则∠OAP=∠OBP=90°,∴∠AOB=180°-∠P=140°由圆周角定理知,∠C=\\frac{1}{2}∠AOB=70^{°},∴∠BAC=90°-∠C=20°.故选B.", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["10°", "20°", "30°", "40°"], "choices": [10.0, 20.0, 30.0, 40.0], "label": 1}
-{"prob_id": 936, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/936.png", "question": "如图,在Rt△ABC中,∠B=90°,AB=6,AC=10将△ABC沿ED折叠,使点C与点A重合,则△ABE的周长等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "在直角△ABC中,BC=√{AC²-AB²}=√{10²-6²}=8cm∵AE=EC,∴△ABE的周长=AB+BE+AE=AB+BE+EC=AB+BC=6+8=14(cm).故选A.", "dataset_name": "Geoqa", "ground_truth": "14.0", "org_choices": ["14", "12", "10", "15"], "choices": [14.0, 12.0, 10.0, 15.0], "label": 0}
-{"prob_id": 942, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/942.png", "question": "如图,一把矩形直尺沿直线断开并错位,点E、D、B、F在同一条直线上,若∠ADE=125°,则∠DBC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "延长CB,延长CB,∵AD//CB,∴∠1=∠ADE=145°,∴∠DBC=180^{°}-∠1=180^{°}-125^{°}=55^{°}.故答案选:D.", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["125°", "75°", "65°", "55°"], "choices": [125.0, 75.0, 65.0, 55.0], "label": 3}
-{"prob_id": 948, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/948.png", "question": "如图,圆心角∠AOB=60∘,则圆周角∠ACB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠AOB=60°∴∠ACB=\\frac{1}{2}∠AOB=30^{°}故选A.", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["30°", "60°", "90°", "120°"], "choices": [30.0, 60.0, 90.0, 120.0], "label": 0}
-{"prob_id": 964, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/964.png", "question": "如图,△ABC中,∠A=90°,AB=AC,BD平分∠ABE,DE⊥BC,如果BC=10cm,则△DEC的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BD平分∠ABE,DE⊥BC,DA⊥ABAD=DE又∵BD=BD,∴△BAD≌△BED(HL)AB=BE又∵AB=ACBE=ACBC=BE+EC=AC+EC=AD+DC+EC=DE+DC+EC=10cm∴△DEC的周长是10cm,故选B.", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["8cm", "10cm", "11cm", "12cm"], "choices": [8.0, 10.0, 11.0, 12.0], "label": 1}
-{"prob_id": 968, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/968.png", "question": "如图,圆外切等腰梯形ABCD的中位线EF=15cm,那么等腰梯形ABCD的周长等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "根据梯形的中位线等于两底和的一,得梯形的两底和等于梯形的中位线的2倍,即30cm;根据圆外切四边形的两组对边和相等,得梯形的两腰的和等于两底和,即30cm.则梯形的周长等于30+30=60(cm).故选:D.", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["15cm", "20cm", "30cm", "60cm"], "choices": [15.0, 20.0, 30.0, 60.0], "label": 3}
-{"prob_id": 970, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/970.png", "question": "如图,若CB=4cm,DB=7cm,且D是AC的中点,则AC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵CB=4cm,DB=7cm∴CD=7-4=3(cm);∵D是AC的中点,∴AD=CD=3cm,∴AC=AD+DC=3+3=6(cm).故选:A.", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["6cm", "7cm", "4cm", "5cm"], "choices": [6.0, 7.0, 4.0, 5.0], "label": 0}
-{"prob_id": 979, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/979.png", "question": "如图,在△ABC中,∠ABC=120°,若DE、FG分别垂直平分AB、BC,那么∠EBF的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE、FG分别垂直平分AB、BC,∴AE=BE,BF=CF,∴∠A=∠ABE,∠C=∠CBF,∵∠A+∠C+∠ABC=180°,∠ABC=120°,∴∠A+∠C=60°∴∠ABE+∠CBF=60°∴∠EBF=120°60°=60°,故选C.", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["30°", "45°", "60°", "75°"], "choices": [30.0, 45.0, 60.0, 75.0], "label": 2}
-{"prob_id": 996, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/996.png", "question": "如图,在Rt△ABC中,∠BAC=90°,将△ABC绕点A顺时针旋转90°后得到△AB′C′(点B的对应点是点B′,点C的对应点是点C′),连接CC′,若∠CC′B′=33°,则∠B的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵将△ABC绕点A顺时针旋转90°后得到△AB'C'∴AC=AC',∠CAC'=90°,∠AB'C'=∠B∴∠ACC'=45°∵∠AB'C'=∠ACC'+∠CC'B'∴∠AB'C=45°+33°=78°∴∠B=78°故选D.", "dataset_name": "Geoqa", "ground_truth": "78.0", "org_choices": ["33°", "45°", "57°", "78°"], "choices": [33.0, 45.0, 57.0, 78.0], "label": 3}
-{"prob_id": 5012, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5012.png", "question": "如图,点C在线段AB上,点D是AC的中点,如果CD=3cm,AB=10cm,那么BC的长度是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵点D是AC的中点,∴AC=2CD=2×3=6cm,∴BC=AB-AC=10-6=4cm．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["3cm", "4cm", "6cm", "7cm"], "choices": [3.0, 4.0, 6.0, 7.0], "label": 1}
-{"prob_id": 5049, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5049.png", "question": "如图,AD是△ABC的中线,已知△ABD的周长为22cm,AB比AC长3cm,则△ACD的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:由题意得,AB=AC+3,∵AD是△ABC的中线,∴BD=DC,∵△ABD的周长为22,∴AB+BD+AD=AC+3+DC+AD=22,则AC+DC+AD=19,∴△ACD的周长=AC+DC+AD=19(cm),", "dataset_name": "Geoqa", "ground_truth": "19.0", "org_choices": ["19cm", "22cm", "25cm", "31cm"], "choices": [19.0, 22.0, 25.0, 31.0], "label": 0}
-{"prob_id": 5059, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5059.png", "question": "如图,线段AB=20,C为AB的中点,D为CB上一点,E为DB的中点,且EB=3,则CD等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵E为DB的中点,且EB=3,∴BD=2BE=6,∵线段AB=20,C为AB的中点,∴CB=AC=10,∵CD=BC-BD∴CD=4", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["10", "6", "4", "2"], "choices": [10.0, 6.0, 4.0, 2.0], "label": 2}
-{"prob_id": 5073, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5073.png", "question": "如图,C,D是线段AB上两点．若CB=4cm,DB=7cm,且D是AC的中点,则AB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵CB=4cm,DB=7cm,∴CD=7-4=3(cm)；∵D是AC的中点,∴AD=CD=3cm,∴AB=AD+DB=3+7=10(cm)．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["10cm", "11cm", "12cm", "14cm"], "choices": [10.0, 11.0, 12.0, 14.0], "label": 0}
-{"prob_id": 5075, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5075.png", "question": "如图,一辆超市购物车放置在水平地面上,其侧面四边形ABCD与地面某条水平线在同一平面内,且AB∥l,若∠A=93°,∠D=111°,则直线CD与l所夹锐角的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:如图所示,根据题意可知直线CD与l所夹锐角即为∠AED,据题意可得∠ADE=180°-∠ADC=69°,∠DAE=180°-∠BAD=87°,∴∠AED=180°-∠ADE-∠DAE=24°．", "dataset_name": "Geoqa", "ground_truth": "24.0", "org_choices": ["15°", "18°", "21°", "24°"], "choices": [15.0, 18.0, 21.0, 24.0], "label": 3}
-{"prob_id": 5082, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5082.png", "question": "如图,在△ABC中,∠B=∠C,D为BC边上一点,E点在AC边上,∠ADE=∠AED,若∠BAD=24°,则∠CDE=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵∠ADC是△ABD的外角,∴∠ADC=∠B+∠BAD=∠B+24°,∵∠AED是△CDE的外角,∴∠AED=∠C+∠EDC,∵∠B=∠C,∠ADE=∠AED,∴∠C+∠EDC=∠ADC-∠EDC=∠B+24°-∠EDC,解得∠EDC=12°．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["24°", "20°", "15°", "12°"], "choices": [24.0, 20.0, 15.0, 12.0], "label": 3}
-{"prob_id": 5096, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5096.png", "question": "如图,AB是⊙O的弦,OC⊥AB于点D,交⊙O于点C,若半径为5,OD=3,则弦AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:连接AO,∵OC⊥AB,∴D为AB的中点,即AD=BD=\\frac{1}{2}AB,在Rt△AOD中,OA=5,OD=3,根据勾股定理得:AD=√{AO²-DO²}=4,则AB=2AD=8．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["5", "6", "7", "8"], "choices": [5.0, 6.0, 7.0, 8.0], "label": 3}
-{"prob_id": 5112, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5112.png", "question": "如图,AB是⊙O的直径,O是圆心,弦CD⊥AB于E,AB=10,CD=8,则OE的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:连接OC,∵直径AB=10,∴OC=5,∵CD⊥AB,AB为直径,∴CD=2CE=8,∠OEC=90°,∴CE=4,由勾股定理得:OE=√{5²-4²}=3．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["2", "3", "4", "5"], "choices": [2.0, 3.0, 4.0, 5.0], "label": 1}
-{"prob_id": 5118, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5118.png", "question": "如图,⊙O的半径为OA=5,以A为圆心,OA为半径的弧交⊙O于B,C两点,则弦BC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:连接AB,OB,∵⊙O的半径为OA=5,以A为圆心,OA为半径的弧交⊙O于B,C两点,∴OA=AB=OB,BC⊥OA,∴∠BOA=60°,∵BC⊥OA,∴BC=5√{3}．", "dataset_name": "Geoqa", "ground_truth": "8.660254037844387", "org_choices": ["5√{3}", "\\frac{5}{2}√{3}", "8", "5√{2}"], "choices": [8.66, 4.33, 8.0, 7.071], "label": 0}
-{"prob_id": 5159, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5159.png", "question": "如图,C、D是线段AB上两点,若BC=3cm,BD=5cm,且D是AC的中点,则AC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵BC=3cm,BD=5cm,∴CD=BD-BC=2cm,∵D是AC的中点,∴AC=2CD=4cm,", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["2cm", "4cm", "8cm", "13cm"], "choices": [2.0, 4.0, 8.0, 13.0], "label": 1}
-{"prob_id": 5181, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5181.png", "question": "如图,在⊙O中,AB是弦,OC⊥AB,垂足为C,若AB=16,OC=6,则⊙O的直径等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵在⊙O中,AB是弦,OC⊥AB,垂足为C,AB=16,∴AC=\\frac{1}{2}AB=\\frac{1}{2}×16=8,在Rt△AOC中,∵OC=6,AC=8,∴OA=√{OC²+AC²}=√{6²+8²}=10,∴⊙O的直径=2OA=2×10=20．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["16", "20", "10", "8"], "choices": [16.0, 20.0, 10.0, 8.0], "label": 1}
-{"prob_id": 5184, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5184.png", "question": "如图,在半径为10的⊙O中,半径OC垂直于弦AB于点D,AB=16,则CD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:连接OA,∵半径OC垂直于弦AB,AB=16,∴AD=8,∠ADO=90°,∵OA=10,∴在Rt△ADO中,由勾股定理得:OD=6,∴CD=10-6=4,", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["2", "4", "6", "8"], "choices": [2.0, 4.0, 6.0, 8.0], "label": 1}
-{"prob_id": 5192, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5192.png", "question": "如图所示,P是⊙O的弦AB上的一点,AB=10cm,AP=4cm,OP=5cm,则⊙O的半径为cm．(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:过O作OD⊥AB,D为垂足,连接OB,∵AB=10cm,AP=4cm,∴BD=5cm,DP=1cm,在Rt△ODP中,OD=√{OP²-DP²}=√{5²-1²}=2√{6}；在Rt△ODB中,OB=√{OD²+BD²}=√{(2√{6})²+5²}=7cm．", "dataset_name": "Geoqa", "ground_truth": "7.0", "org_choices": ["5", "7", "6", "6.5"], "choices": [5.0, 7.0, 6.0, 6.5], "label": 1}
-{"prob_id": 5193, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5193.png", "question": "如图,矩形与⊙O相交,若AB=4,BC=5,DE=3,则EF的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:作OM⊥BC于M,交EF于N点,则OM⊥EF．∵OM⊥BC,∴BM=CM=\\frac{1}{2}BC=2.5,∴AM=AB+BM=6.5,由题意得:四边形ADNM是矩形,∴DN=AM=6.5,∴EN=3.5,∵ON⊥EF,∴EF=2EN=7,", "dataset_name": "Geoqa", "ground_truth": "7.0", "org_choices": ["3.5", "6.5", "7", "8"], "choices": [3.5, 6.5, 7.0, 8.0], "label": 2}
-{"prob_id": 5195, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5195.png", "question": "如图,AB是⊙O的直径,CD是弦,AB⊥CD,垂足为点E,连接OD、CB、AC,∠DOB=60°,EB=2,那么CD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵∠DOB=60°,∴∠BCE=30°．在Rt△BCE中,∵BE=2,∠BCE=30°,∴BC=4,CE=√{BC²-BE²}=√{4²-3²}=2√{3},∵AB是⊙O的直径,AB⊥CD,∴CD=2CE=4√{3},", "dataset_name": "Geoqa", "ground_truth": "6.928203230275509", "org_choices": ["√{3}", "2√{3}", "3√{3}", "4√{3}"], "choices": [1.732, 3.464, 5.196, 6.928], "label": 3}
-{"prob_id": 5198, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5198.png", "question": "如图,AB是⊙O的直径,CD是弦,AB⊥CD于点E,若半径为5,OE=3,则CD的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵AB是⊙O的直径,CD是弦,AB⊥CD于点E,∴CE=\\frac{1}{2}CD．在Rt△OCE中,∵OC=5,OE=3,∴CE=√{OC²-OE²}=√{5²-3²}=4,∴CD=2CE=8．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["4", "6", "8", "7"], "choices": [4.0, 6.0, 8.0, 7.0], "label": 2}
-{"prob_id": 5215, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5215.png", "question": "如图,半径为5的圆O中,弦AB的长为8,则圆心O到弦AB的距离为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:连接AO,∵OC⊥AB,OC过O,∴AC=BC=\\frac{1}{2}AB=4,在Rt△OAC中,由勾股定理得:OC=√{5²-4²}=3,", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["3", "4", "5", "6"], "choices": [3.0, 4.0, 5.0, 6.0], "label": 0}
-{"prob_id": 5225, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5225.png", "question": "如图,AB=8cm,AD=BC=5cm,则CD等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵AB=8cm,AD=5cm,∴BD=AB-AD=3cm,∵BC=5cm,∴CD=CB-BD=2cm,", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["1cm", "2cm", "3cm", "4cm"], "choices": [1.0, 2.0, 3.0, 4.0], "label": 1}
-{"prob_id": 5251, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5251.png", "question": "如图,C,D是线段AB上两点,若CB=4cm,DB=7cm,且D是AC的中点,则AB的长等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵CB=4cm,DB=7cm,∴CD=7-4=3(cm)；∵D是AC的中点,∴AD=CD=3cm,∴AB=AD+DB=3+7=10(cm)．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["6cm", "7cm", "10cm", "11cm"], "choices": [6.0, 7.0, 10.0, 11.0], "label": 2}
-{"prob_id": 5301, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5301.png", "question": "如图,点C在线段AB上,点E是AC中点,点D是BC中点．若ED=6,则线段AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵点E是AC中点,点D是BC中点,∴AE=CE=\\frac{1}{2}AC,CD=BD=\\frac{1}{2}BC,∴CE+CD=\\frac{1}{2}AC+\\frac{1}{2}BC,即ED=\\frac{1}{2}(AC+BC)=\\frac{1}{2}AB,∴AB=2ED=12；", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["6", "9", "12", "18"], "choices": [6.0, 9.0, 12.0, 18.0], "label": 2}
-{"prob_id": 5319, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5319.png", "question": "如图,已知∠1=40°,∠A+∠B=140°,则∠C+∠D的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:连接CD,如图:∵∠1=40°,∠1+∠2+∠3=180°,∴∠2+∠3=180°-40°=140°,∵∠A+∠B+∠ADC+∠BCD=360°,∠A+∠B=140°,∴∠ADC+∠BCD=360°-140°=220°,∴∠BCE+∠ADE=(∠ADC+∠BCD)-(∠2+∠3)=220°-140°=80°,", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["40°", "60°", "80°", "100°"], "choices": [40.0, 60.0, 80.0, 100.0], "label": 2}
-{"prob_id": 5350, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5350.png", "question": "如图,四边形ABCD的对角线AC⊥BD,垂足为O,且AC=12,BD=9,则四边形ABCD的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵AC⊥BD,AC=12,BD=9,∴S四边形ABCD=S_{△AOD}+S_{△COD}+S_{△BOC}+S_{△AOB}=\\frac{1}{2}OA\\cdotOD+\\frac{1}{2}OC\\cdotOD+\\frac{1}{2}OC\\cdotOB+\\frac{1}{2}OB\\cdotOA=\\frac{1}{2}OD(OA+OC)+\\frac{1}{2}OB(OA+OC)=\\frac{1}{2}OD\\cdotAC+\\frac{1}{2}OB\\cdotAC=\\frac{1}{2}AC\\cdot(OD+OC)=\\frac{1}{2}AC\\cdotBD=\\frac{1}{2}×12×9=54．", "dataset_name": "Geoqa", "ground_truth": "54.0", "org_choices": ["60", "54", "30", "27"], "choices": [60.0, 54.0, 30.0, 27.0], "label": 1}
-{"prob_id": 5357, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5357.png", "question": "如图,已知△ABC,点D在BC的延长线上,∠ACD=140°,∠ABC=50°,则∠A的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵∠ACD=∠A+∠ABC,∴∠A=∠ACD-∠ABC,∵∠ACD=140°,∠ABC=50°,∴∠A=140°-50°=90°", "dataset_name": "Geoqa", "ground_truth": "90.0", "org_choices": ["50°", "140°", "120°", "90°"], "choices": [50.0, 140.0, 120.0, 90.0], "label": 3}
-{"prob_id": 5360, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5360.png", "question": "如图,点O在直线AB上,若∠2=140°,则∠1的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵∠1+∠2=180°且∠2=140°,∴∠1=40°,", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "60°", "140°", "150°"], "choices": [40.0, 60.0, 140.0, 150.0], "label": 0}
-{"prob_id": 5366, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5366.png", "question": "如图所示,线段AB=10,M为线段AB的中点,C为线段MB的中点,N为线段AM的一点,且MN=1,线段NC的长(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵线段AB=10,M为线段AB的中点,∴MB=\\frac{1}{2}AB=5,∵C为线段MB的中点,∴MC=\\frac{1}{2}BM=2.5,∴NC=NM+MC=3.5．", "dataset_name": "Geoqa", "ground_truth": "3.5", "org_choices": ["2", "2.5", "3", "3.5"], "choices": [2.0, 2.5, 3.0, 3.5], "label": 3}
-{"prob_id": 5369, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5369.png", "question": "设BF交AC于点P,AE交DF于点Q．若∠APB=126°,∠AQF=100°,则∠A-∠F=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:如图:∵∠1=∠APB-∠A=126°-∠A,∠2=180°-∠AQF-∠F=180°-100°-∠F=80°-∠F；∵∠1=∠2,∴126°-∠A=80°-∠F；∴∠A-∠F=46°．", "dataset_name": "Geoqa", "ground_truth": "46.0", "org_choices": ["60°", "46°", "26°", "45°"], "choices": [60.0, 46.0, 26.0, 45.0], "label": 1}
-{"prob_id": 5376, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5376.png", "question": "如图,BD,CE分别是△ABC的高线和角平分线,且相交与点O,若∠BCA=70°,则∠BOE的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵B⊥AC,∴∠BDC=90°,∵CE平分∠ACB,∠ACB=70°,∴∠DCO=35°,∴∠BOE=∠COD=90°-35°=55°,", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["60°", "55°", "50°", "40°"], "choices": [60.0, 55.0, 50.0, 40.0], "label": 1}
-{"prob_id": 5380, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5380.png", "question": "如图,已知点A、B、C在同一直线上,AB=7,BC=3,点D为线段AC的中点,线段DB的长度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵AB=7,BC=3,∴AC=AB+BC=10．∵点D为线段AC的中点,∴CD=\\frac{1}{2}AC=5,∴DB=CD-BC=2．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["2", "4", "6", "8"], "choices": [2.0, 4.0, 6.0, 8.0], "label": 0}
-{"prob_id": 5389, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5389.png", "question": "如图,在四边形ABCD中,∠DAB的角平分线与∠ABC的外角平分线相交于点P,且∠∠D+∠C=200°,则∠P=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:如图,∵∠D+∠C=200°,∠DAB+∠ABC+∠C+∠D=360°,∴∠DAB+∠ABC=160°．又∵∠DAB的角平分线与∠ABC的外角平分线相交于点P,∴∠PAB+∠ABP=\\frac{1}{2}∠DAB+∠ABC+\\frac{1}{2}(180°-∠ABC)=90°+\\frac{1}{2}(∠DAB+∠ABC)=170°,∴∠P=180°-(∠PAB+∠ABP)=10°．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["10°", "20°", "30°", "40°"], "choices": [10.0, 20.0, 30.0, 40.0], "label": 0}
-{"prob_id": 5458, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5458.png", "question": "如图,BP平分∠ABC交CD于点F,DP平分∠ADC交AB于点E,若∠A=40°,∠P=38°,则∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵BP平分∠ABC,DP平分∠ADC,∴∠ADP=∠PDF,∠CBP=∠PBA,∵∠A+∠ADP=∠P+∠ABP,∠C+∠CBP=∠P+∠PDF,∴∠A+∠C=2∠P,∵∠A=40°,∠P=38°,∴∠C=2×38°-40°=36°,", "dataset_name": "Geoqa", "ground_truth": "36.0", "org_choices": ["36°", "39°", "38°", "40°"], "choices": [36.0, 39.0, 38.0, 40.0], "label": 0}
-{"prob_id": 5465, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5465.png", "question": "如图,延长长度为8的线段AB到C,使BC=4,M、N分别是AB、BC的中点,则MN的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵M、N分别是AB、BC的中点,∴MB=\\frac{1}{2}AB=4,BN=\\frac{1}{2}BC=2,∴MN=MB+BN=4+2=6．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["2", "4", "6", "4或6"], "choices": [2.0, 4.0, 6.0], "label": 2}
-{"prob_id": 5470, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5470.png", "question": "如图,A,B,C,D四点都在⊙O上,∠BOD=110°,则∠BCD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由圆周角定理得,∠A=\\frac{1}{2}∠BOD=55°,∵四边形ABCD是圆内接四边形,∴∠BCD=180°-∠A=125°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "125.0", "org_choices": ["70°", "110°", "125°", "130°"], "choices": [70.0, 110.0, 125.0, 130.0], "label": 2}
-{"prob_id": 5474, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5474.png", "question": "如图,四边形ABCD为⊙O的内接四边形,∠BCD=110°,则∠BOD的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD为⊙O的内接四边形,∠BCD=110°,∴∠A=180°-∠BCD=70°,由圆周角定理得,∠BOD=2∠A=140°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["70°", "120", "140°", "160°"], "choices": [70.0, 120.0, 140.0, 160.0], "label": 2}
-{"prob_id": 5487, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5487.png", "question": "如图,某货船以24海里/时的速度从A处向正东方向的D处航行,在点A处测得某岛C在北偏东60°的方向．该货船航行30分钟后到达B处,此时测得该岛在北偏东30°的方向上．则货船在航行中离小岛C的最短距离是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作CE⊥AB交AB的延长线于E,由题意得,AB=24×\\frac{1}{2}=12,∠CBE=60°,∠CAE=30°,∴∠ACB=30°,∴∠CAE=∠ACB,∴BC=AB=12,在Rt△CBE中,sin∠CBE=\\frac{CE}{BC},∴CE=BC×sin∠CBE=12×\\frac{√{3}}{2}=6√{3}(海里),故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.392304845413264", "org_choices": ["12海里", "6√{3}海里", "12√{3}海里", "24√{3}海里"], "choices": [12.0, 10.392, 20.785, 41.569], "label": 1}
-{"prob_id": 5501, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5501.png", "question": "如图,PA,PB切⊙O于点A,B,点C是⊙O上一点,且∠P=36°,则∠ACB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图所示,连接OA、OB．p<(\\phi,7)∵PA、PB都为圆O的切线,∴∠PAO=∠PBO=90°．∵∠P=36°,∴∠AOB=144°．∴∠C=\\frac{1}{2}∠AOB=\\frac{1}{2}=72°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "72.0", "org_choices": ["54°", "72°", "108°", "144°"], "choices": [54.0, 72.0, 108.0, 144.0], "label": 1}
-{"prob_id": 5508, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5508.png", "question": "如图,PA,PB分别与⊙O相切于A,B两点,∠C=55°,则∠P等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB、OA,如图,∵PA、PB分别与圆O相切于A、B两点,∴OA⊥PA,OB⊥PB,∴∠OAP=∠OBP=90°,∴∠AOB=180°-∠P,∵∠C=55°,∴∠AOB=2∠C=110°,∴∠P=180°-110°=70°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["110°", "70°", "140°", "55°"], "choices": [110.0, 70.0, 140.0, 55.0], "label": 1}
-{"prob_id": 5544, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5544.png", "question": "如图,在边长为1的正方形网格中,连接格点D、N和E、C,DN和EC相交于点P,tan∠CPN为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接格点MN、DM,如图所示:则四边形MNCE是平行四边形,△DAM和△MBN都是等腰直角三角形,∴EC∥MN,∠DMA=∠NMB=45°,DM=√{2}AD=2√{2},MN=√{2}BM=√{2},∴∠CPN=∠DNM,∴tan∠CPN=tan∠DNM,∵∠DMN=180°-∠DMA-∠NMB=180°-45°-45°=90°,∴tan∠CPN=tan∠DNM=\\frac{DM}{MN}=\\frac{2√{2}}{√{2}}=2,故选:B．\\lbrack\\frac{D}{M}\\rbrack:\\frac{c}{\\omega}≥q\\rbrace", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["1", "2", "√{3}", "√{5}"], "choices": [1.0, 2.0, 1.732, 2.236], "label": 1}
-{"prob_id": 5576, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5576.png", "question": "如图,在Rt△ABC中,∠C=90°,AB=10,AC=8,则sinB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,在Rt△ABC中,∠C=90°,AB=10,AC=8．所以sinB=\\frac{AC}{AB}=\\frac{8}{10}=\\frac{4}{5}．故选:A．", "dataset_name": "Geoqa", "ground_truth": "0.8", "org_choices": ["\\frac{4}{5}", "\\frac{3}{5}", "\\frac{3}{4}", "\\frac{4}{3}"], "choices": [0.8, 0.6, 0.75, 1.333], "label": 0}
-{"prob_id": 5596, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5596.png", "question": "如图,四边形ABCD是⊙O的外切四边形,且AB=10,CD=12,则四边形ABCD的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是⊙O的外切四边形,∴AD+BC=AB+CD=22,∴四边形ABCD的周长=AD+BC+AB+CD=44,故选:A．", "dataset_name": "Geoqa", "ground_truth": "44.0", "org_choices": ["44", "42", "46", "47"], "choices": [44.0, 42.0, 46.0, 47.0], "label": 0}
-{"prob_id": 5609, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5609.png", "question": "已知水平放置的圆柱形排水管道,管道截面半径是1m,若水面高0.2m．则排水管道截面的水面宽度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作OC⊥AB于C,交⊙O于D,连接OB,如图所示:则AB=2BC,∠OCB=90°,OB=OD=1m,CD=0.2m,∴OC=OD-CD=0.8m,∴BC=√{0B^{2}-0c^{2}}=√{1^{2}-0.8^{2}}=0.6(m),∴AB=2AC=1.2m,∴排水管道截面的水面宽度为1.2m,故选:C．", "dataset_name": "Geoqa", "ground_truth": "1.2", "org_choices": ["0.6m", "0.8m", "1.2m", "1.6m"], "choices": [0.6, 0.8, 1.2, 1.6], "label": 2}
-{"prob_id": 5621, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5621.png", "question": "如图,A,B,C是⊙O上的三点,AB,AC的圆心O的两侧,若∠ABO=20°,∠ACO=30°,则∠BOC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过A作⊙O的直径,交⊙O于D．在△OAB中,OA=OB,则∠BOD=∠ABO+∠OAB=2×20°=40°,同理可得:∠COD=∠ACO+∠OAC=2×30°=60°,故∠BOC=∠BOD+∠COD=100°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["100°", "110°", "125°", "130°"], "choices": [100.0, 110.0, 125.0, 130.0], "label": 0}
-{"prob_id": 5668, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5668.png", "question": "如图,在直角坐标系xOy中,点A在y轴正半轴上,点B、C在x正半轴上,且∠BAC=∠ACB=30°,AC=4,点D是x轴上的一个动点,点D关于直线AB、AC的对称点为E、F,则线段EF的最小值等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接AD,AE．AF．由题意,AD=AE=AF,∠DAB=∠BAE,∠DAC=∠CAF,∵∠BAC=∠ACB=30°,AC=4,∠AOC=90°,∴OA=≥ft.\\begin{array}{l}{x_{1}^{′}\\cdots\\cdots\\cdotsf^{r}}\\\\{\\frac{i}{o}:;}{√[3]{f}AC=2,∠OAC=60°,∠CAE+∠EAB=30°,∴∠EAF=∠CAE+∠CAF=∠CAE+∠CAE+∠DAE=2(∠CAE+∠BAE)=60°,∵AE=AF,∴△AEF是等边三角形,轨迹垂线段最短可知,当点D与O重合时,AD的值最小,∴AE的最小值=OA=2,∴EF的最小值为2,故选:A．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["2", "3", "4", "5"], "choices": [2.0, 3.0, 4.0, 5.0], "label": 0}
-{"prob_id": 5675, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5675.png", "question": "如图,∠BAC=110°,若A,B关于直线MP对称,A,C关于直线NQ对称,则∠PAQ的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BAC=110°,∴∠B+∠C=70°,∵A,B关于直线MP对称,A,C关于直线NQ对称,又∵MP,NQ为AB,AC的垂直平分线,∴∠BAP=∠B,∠QAC=∠C,∴∠BAP+∠CAQ=70°,∴∠PAQ=∠BAC-∠BAP-∠CAQ=110°-70°=40°故选:C．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["70°", "55°", "40°", "30°"], "choices": [70.0, 55.0, 40.0, 30.0], "label": 2}
-{"prob_id": 5677, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5677.png", "question": "如图,AB∥CD,BE垂直平分AD,DC=BC,若∠A=70°,则∠C=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BE垂直平分AD,∴AB=DB,∴∠ABE=∠DBE,又∵∠A=70°,∴∠ABE=20°,∴∠ABD=40°,又∵AB∥CD,∴∠CDB=∠ABD=40°,又∵DC=BC,∴∠C=180°-2×40°=100°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["100°", "110°", "115°", "120°"], "choices": [100.0, 110.0, 115.0, 120.0], "label": 0}
-{"prob_id": 5682, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5682.png", "question": "如图,在△ABC中,AB=10cm,AC=18cm,点M从点A出发以每秒2cm的速度向点B运动,点N从点C出发以每秒3cm的速度向点A运动,其中一个动点到达端点,另一个动点也随之停止,当△AMN是以MN为底边的等腰三角形时,运动的时间是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设运动的时间为x,在△ABC中,AB=10cm,AC=18cm,点M从点A出发以每秒2cm的速度向点B运动,点N从点C出发以每秒3cm的速度向点A运动,当△AMN是等腰三角形时,AM=AN,AN=18-3x,AM=2x即18-3x=2x,解得x=3.6．故选:D．", "dataset_name": "Geoqa", "ground_truth": "3.6", "org_choices": ["1.6秒", "2秒", "2.4秒", "3.6秒"], "choices": [1.6, 2.0, 2.4, 3.6], "label": 3}
-{"prob_id": 5704, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5704.png", "question": "如图,在△ABC中,∠ABC=110°,AM=AN,CN=CP,则∠MNP=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ABC=110°,∴∠A+∠C=180°-110°=70°．∵AM=AN,CN=CP,∴∠ANM=\\frac{180^{°}-∠A}{2},∠CNP=\\frac{180^{°}-∠C}{2},∴∠MNP=180°-\\frac{180^{°}-∠A}{2}-\\frac{180^{°}-∠C}{2}=180°-90°+\\frac{1}{2}∠A-90°+\\frac{1}{2}∠C=\\frac{1}{2}(∠A+∠C)=\\frac{1}{2}×70°=35°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["25°", "30^°^", "35°", "45°"], "choices": [25.0, 30.0, 35.0, 45.0], "label": 2}
-{"prob_id": 5713, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5713.png", "question": "如图,已知▱ABCD的四个内角的平分线分别相交于点E、F、G、H,连接AC．若EF=2,FG=GC=5,则AC的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,作AP⊥CH交CH的延长线与P．∵四边形ABCD是平行四边形,▱ABCD的四个内角的平分线分别相交于点E、F、G、H,∴易证四边形EFGH是矩形,四边形AEHP是矩形,△ABE≌△CDG,可得PA=FG=5,AE=PH=CG=5,CP=CG+PH+GH=2+10=12,在Rt△APC中,AC=∠\\beta=∠ZZN=√{PA^{2}+PC^{2}}=13．故选:B．", "dataset_name": "Geoqa", "ground_truth": "13.0", "org_choices": ["12", "13", "6√{5}", "8√{3}"], "choices": [12.0, 13.0, 13.416, 13.856], "label": 1}
-{"prob_id": 5719, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5719.png", "question": "如图,▱ABCD中,点E、F分别在AD、AB上,依次连接EB、EC、FC、FD,图中阴影部分的面积分别为S~1~、S~2~、S~3~、S~4~,已知S~1~=2、S~2~=12、S~3~=3,则S~4~的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设平行四边形的面积为S,则S~△CBE~=S~△CDF~=\\frac{1}{2}S,由图形可知,△CDF面积+△CBE面积+(S~1~+S~4~+S~3~)-S~2~=平行四边形ABCD的面积∴S=S~△CBE~+S~△CDF~+2+S~4~+3-12,即S=\\frac{1}{2}S+\\frac{1}{2}S+2+S~4~+3-12,解得S~4~=7,故选:D．", "dataset_name": "Geoqa", "ground_truth": "7.0", "org_choices": ["4", "5", "6", "7"], "choices": [4.0, 5.0, 6.0, 7.0], "label": 3}
-{"prob_id": 5725, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5725.png", "question": "如图,在▱ABCD中,对角线AC,BD相交于点O,点E,F分别是AB,AO的中点,连接EF,若EF=3,则BD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵点E,F分别是AB,AO的中点,连接EF,EF=3,∴EF是△OAB的中位线,则OB=2EF=6,∵在▱ABCD中,∴BD=2OB=12,故选:C．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["6", "9", "12", "15"], "choices": [6.0, 9.0, 12.0, 15.0], "label": 2}
-{"prob_id": 5728, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5728.png", "question": "如图,▱ABCD的对角线AC,BD相交于O,EF经过点O,分别交AD,BC于E,F,已知▱ABCD的面积是20cm^2^,则图中阴影部分的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AD∥BC,OA=OC,∴∠OAE=∠OCF,∵∠AOE=∠COF,∴△AOE≌△COF,∴S~阴~=S~△BOC~=\\frac{1}{4}S~平行四边形ABCD~=5(cm^2^),故选:D．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["12cm^2^", "10cm^2^", "8cm^2^", "5cm^2^"], "choices": [12.0, 10.0, 8.0, 5.0], "label": 3}
-{"prob_id": 5729, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5729.png", "question": "如图,在▱ABCD中,∠BCD的平分线交AD于点E,交BA的延长线于点F,BF=4AF,BC=12,则AF的长度是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD为平行四边形,∴AD∥BC,AB∥DC,AB=CD,AD=BC=12,∴∠DEC=∠ECB,∵CF平分∠BCD,∴∠ECD=∠ECB,∴∠DEC=∠ECD,∴DE=DC,∴AE=AD-DE=12-DE,∵BF∥CD,∴△AEF∽△DEC,∵BF=4AF,∴\\frac{AF}{CD}=\\frac{AE}{DE},即\\frac{1}{3}=\\frac{12-DE}{DE},则DE=9．∴DE=DC=AB=9,∴AF=3,故选:D．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["6", "5", "4", "3"], "choices": [6.0, 5.0, 4.0, 3.0], "label": 3}
-{"prob_id": 5739, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5739.png", "question": "如图,在▱ABCD中,AB=10cm,AD=15cm,AC、BD相交于点O．OE⊥BD交AD于E,则△ABE的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在▱ABCD中,点O是BD中点,EO⊥BD,∴EO是线段BD的中垂线,∴BE=ED,∴△ABE的周长=AB+AE+BE=AB+AD=10+15=25(cm)．故选:C．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["20cm", "22cm", "25cm", "30cm"], "choices": [20.0, 22.0, 25.0, 30.0], "label": 2}
-{"prob_id": 5740, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5740.png", "question": "如图,平行四边形ABCD中,E,F分别是AD,BC的中点,P是边DC上的动点,G,H分别是PE,PF的中点,已知DC=10cm,则GH的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接EF,∵四边形ABCD是平行四边形,∴AB=CD,AD=BD,AD∥BC,∵E,F分别是AD,BC的中点,∴AE=BF,∴四边形ABFE是平行四边形,∴AB=EF=10cm,∵G,H分别是PE,PF的中点,∴GH是△PEF的中位线,∴GH=\\frac{1}{2}EF=\\frac{1}{2}×10=5cm,故选:C．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["7cm", "6cm", "5cm", "4cm"], "choices": [7.0, 6.0, 5.0, 4.0], "label": 2}
-{"prob_id": 5761, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5761.png", "question": "如图,在平行四边形ABCD中,对角线AC、BD相交于点O,点E是边CD的中点,连接OE．若平行四边形ABCD的周长为24,BD=8,则△DOE的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵平行四边形ABCD的周长为24,∴BC+CD=12．∵O是BD中点,E是CD中点,∴OE=\\frac{1}{2}BC,DE=\\frac{1}{2}CD,OD=\\frac{1}{2}BD=4∴△DOE周长=OE+DE+OD=6+4=10．故选:A．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["10", "12", "14", "16"], "choices": [10.0, 12.0, 14.0, 16.0], "label": 0}
-{"prob_id": 5763, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5763.png", "question": "如图,在平行四边形ABCD中,点E是AB边上一点,连接DE、CE．若DE、CE分别是∠ADC、∠BCD的角平分线,且AB=4,则平行四边形ABCD的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE、CE分别是∠ADC、∠BCD的平分线,∴∠ADE=∠CDE,∠DCE=∠BCE,∵四边形ABCD是平行四边形,∴AB∥DC,AD=BC,CD=AB=4,∴∠CDE=∠DEA,∠DCE=∠CEB,∴∠ADE=∠AED,∠BCE=∠CEB,∴AD=AE,BE=BC,∴AD+BC=AE+BE=AB=4,∴平行四边形ABCD的周长=2(AB+AD)=3AB=12；故选:D．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["10", "8√{2}", "5√{5}", "12"], "choices": [10.0, 11.314, 11.18, 12.0], "label": 3}
-{"prob_id": 5768, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5768.png", "question": "如图,过三角形内一点分别作三边的平行线,如果三角形的周长为6cm,则图中三个阴影三角形的周长和为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵EN∥BC,PM∥AB,DQ∥AC,∴四边形EFBP,FQCN,ADFM是平行四边形,∴DF=AM,FM=AD,EF=BP,PF=BE,FQ=NC,FN=CQ,∴三个阴影三角形的周长和为:DE+EF+FD+FM+FN+MN+FP+PQ+FQ=DE+BP+AM+AD+QC+MN+BE+PQ+NC=(AD+DE+BE)+(BP+PQ+CQ)+(NC+MN+AM)=AB+BC+AC=6(cm)．故选:A．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["6cm", "8cm", "9cm", "10cm"], "choices": [6.0, 8.0, 9.0, 10.0], "label": 0}
-{"prob_id": 5781, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5781.png", "question": "如图,在△ABC中,过顶点A的直线DE∥BC,∠ABC、∠ACB的平分线分别交DE于点E、D,若AC=3,AB=4,则DE的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由分析得:∠EBC=∠ABE,∠ACD=∠DCB；根据平行线的性质得:∠DCB=∠CDE,∠EBC=∠BED；所以∠ADC=∠ACD,∠ABE=∠AEB,则AD=AC,AB=AE；所以DE=AD+AE=AB+AC=3+4=7；故选:B．", "dataset_name": "Geoqa", "ground_truth": "7.0", "org_choices": ["6", "7", "8", "9"], "choices": [6.0, 7.0, 8.0, 9.0], "label": 1}
-{"prob_id": 5783, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5783.png", "question": "如图所示．△ABC中,∠B=∠C,D在BC上,∠BAD=50°,AE=AD,则∠EDC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,∠AED=∠EDC+∠C,∠ADC=∠B+∠BAD,∵AD=AE,∴∠AED=∠ADE,∵∠B=∠C,∴∠B+∠BAD=∠EDC+∠C+∠EDC,即∠BAD=2∠EDC,∵∠BAD=50°,∴∠EDC=25°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["15°", "25°", "30°", "50°"], "choices": [15.0, 25.0, 30.0, 50.0], "label": 1}
-{"prob_id": 5791, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5791.png", "question": "如图,在四边形ABCD中,AD∥BC,BF平分∠ABC,交AD于点F,CE平分∠BCD,交AD于点E,AB=8,CD=6,EF=2,则AD长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BF平分∠ABC、CE平分∠BCD,∴∠ABF=∠CBF、∠DCE=∠BCE,∵AD∥BC,∴∠CBF=∠AFB、∠DEC=∠BCE,∴∠ABF=∠AFB、∠DCE=∠DEC,∴AB=AF=8、CD=DE=6,∵EF=2,∴AD=AF+DE-EF=8+6-2=12,故选:C．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["8", "10", "12", "14"], "choices": [8.0, 10.0, 12.0, 14.0], "label": 2}
-{"prob_id": 5797, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5797.png", "question": "如图,在△ABC中,AB=10,AC=6,过点A的直线DE∥CB,∠ABC与∠ACB的平分线分别交DE于E,D,则DE的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴∠E=∠EBC．∵BE平分∠ABC,∴∠ABE=∠EBC,∴∠E=∠ABE,∴AB=AE=10．同理可得:AD=AC=6,∴DE=AD+AE=AB+AC=16．故选:B．", "dataset_name": "Geoqa", "ground_truth": "16.0", "org_choices": ["14", "16", "10", "12"], "choices": [14.0, 16.0, 10.0, 12.0], "label": 1}
-{"prob_id": 5806, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5806.png", "question": "如图,已知等腰△ABC的一腰AB长为4厘米,过底边BC上任意一点D作两腰的平行线,分别交两腰于E、F,则四边形AEDF的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥AC,DF∥AB,∴∠EDB=∠C,∠FDC=∠B,∵AB=AC,∴∠B=∠C,∴∠EDB=∠B,∠FDC=∠C,∴DE=BE,DF=FC,∴四边形AEDF的周长是AE+ED+DF+AF=AE+BE+CF+AF=AB+AC=2AB=2×4=8厘米．故选:B．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["4厘米", "8厘米", "12厘米", "16厘米"], "choices": [4.0, 8.0, 12.0, 16.0], "label": 1}
-{"prob_id": 5827, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5827.png", "question": "如图,在等边△ABC中,BD平分∠ABC交AC于点D,过点D作DE⊥BC于点E,且CE=1.5,则AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵△ABC是等边三角形,∴∠ABC=∠C=60°,AB=BC=AC,∵DE⊥BC,∴∠CDE=30°,∵EC=1.5,∴CD=2EC=3,∵BD平分∠ABC交AC于点D,∴AD=CD=3,∴AB=AC=AD+CD=6．故选:C．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["3", "4.5", "6", "7.5"], "choices": [3.0, 4.5, 6.0, 7.5], "label": 2}
-{"prob_id": 5854, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5854.png", "question": "一艘轮船由海平面上A地出发向南偏西40°的方向行驶40海里到达B地,再由B地向北偏西20°的方向行驶40海里到达C地,则A、C两地相距(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意得∠ABC=60°,AB=BC,∴△ABC是等边三角形,∴AC=AB=40海里．故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["30海里", "40海里", "50海里", "60海里"], "choices": [30.0, 40.0, 50.0, 60.0], "label": 1}
-{"prob_id": 5861, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5861.png", "question": "如图是\"人字形\"钢架,其中斜梁AB=AC,顶角∠BAC=120°,跨度BC=10m,AD为支柱(即底边BC的中线),两根支撑架DE⊥AB,DF⊥AC,则DE+DF等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB=AC,∠BAC=120°,∴∠B=∠C=30°,∵DE⊥AB,DF⊥AC,垂足为E,F,∴DE=\\frac{1}{2}BD,DF=\\frac{1}{2}DC,∴DE+DF=\\frac{1}{2}BD+\\frac{1}{2}DC=\\frac{1}{2}(BD+DC)\\frac{1}{2}BC．∴DE+DF=\\frac{1}{2}BC=\\frac{1}{2}×10=5m．故选:B．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["10m", "5m", "2.5m", "9.5m"], "choices": [10.0, 5.0, 2.5, 9.5], "label": 1}
-{"prob_id": 5868, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5868.png", "question": "将△ABC沿CB向右平移得到△DEF,若四边形ABED的面积等于32,则平移距离等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设平移的距离为x,即AD=BE=x,∵∠C=90°,∠ABC=30°,∴AC=\\frac{1}{2}AB=8,由平移的性质可知,四边形ABED的平行四边形,则8x=32,解答,x=4,故选:A．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["4", "6", "8", "16"], "choices": [4.0, 6.0, 8.0, 16.0], "label": 0}
-{"prob_id": 5879, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5879.png", "question": "如图,在△ABC中,∠ACB=90°,∠ABC=60°,BD平分∠ABC,P点是BD的中点,若BD=6,则CP的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ACB=90°,∠ABC=60°,∴∠A=30°,∵BD平分∠ABC,∴∠CBD=∠DBA=30°,∴BD=AD=6,∵P点是BD的中点,∴CP=\\frac{1}{2}BD=3,故选:A．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["3", "3.5", "4", "4.5"], "choices": [3.0, 3.5, 4.0, 4.5], "label": 0}
-{"prob_id": 5889, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5889.png", "question": "如图,一辆货车车厢底板离地面的高度为\\frac{3}{2}米,为了方便下货,常用一块木板搭成一个斜面,要使斜面与水平地面的夹角不大于30°,则这块木板的长度至少为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图:AC为车厢底板离地面的高度\\frac{3}{2}米,AB是要求木板的长度,因为在直角三角形ABC中,∠B=30°,所以AB=2AC=2×\\frac{3}{2}=3(米)．故选:A．z=\\lambda^{2}-|➝{ZI}|^{-2}", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["3米", "2.5米", "2.6米", "0.87米"], "choices": [3.0, 2.5, 2.6, 0.87], "label": 0}
-{"prob_id": 5905, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5905.png", "question": "如图,在Rt△ABC中,∠ACB=90°,AC=6,BC=8,AD是∠BAC的平分线．若P,Q分别是AD和AC上的动点,则PC+PQ的最小值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,过点C作CM⊥AB交AB于点M,交AD于点P,过点P作PQ⊥AC于点Q,∵AD是∠BAC的平分线．∴PQ=PM,这时PC+PQ有最小值,即CM的长度,∵AC=6,BC=8,∠ACB=90°,∴AB=√{AC^{2}+BC^{2}}=√{6^{2}+8^{2}}=10．∵S~△ABC~=\\frac{1}{2}AB•CM=\\frac{1}{2}AC•BC,∴CM=\\frac{AC\\cdotBC}{AB}=\\frac{6×8}{10}=\\frac{24}{5},即PC+PQ的最小值为\\frac{24}{5}．故选:C．", "dataset_name": "Geoqa", "ground_truth": "4.8", "org_choices": ["\\frac{12}{5}", "4", "\\frac{24}{5}", "5"], "choices": [2.4, 4.0, 4.8, 5.0], "label": 2}
-{"prob_id": 5914, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5914.png", "question": "如图,在四边形ABCD中,∠BAD=130°,∠B=∠D=90°,点E,F分别是线段BC,DC上的动点．当△AEF的周长最小时,则∠EAF的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作A关于BC和CD的对称点A′,A″,连接A′A″,交BC于E,交CD于F,则A′A″即为△AEF的周长最小值．作DA延长线AH,∵∠DAB=130°,∴∠HAA′=50°,∴∠AA′E+∠A″=∠HAA′=50°,∵∠EA′A=∠EAA′,∠FAD=∠A″,∴∠EAA′+∠A″AF=50°,∴∠EAF=130°-50°=80°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["90°", "80°", "70°", "60°"], "choices": [90.0, 80.0, 70.0, 60.0], "label": 1}
-{"prob_id": 5919, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5919.png", "question": "如图,△ABC的周长为16．点D是AB边的中点,BD=2,过点D作AB的垂线l,E是l上任意一点,则△AEC的周长最小值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵点D是AB边的中点,BD=2,∴AB=2BD=4,∵△ABC的周长为16,∴AC+BC=12,如图,连接BE,∵点D是AB边的中点,l⊥AB,∴l是AB的垂直平分线,∴AE=BE,∴AE+CE=BE+CE,∵BE+CE≥BC,∴当B,E,C在同一直线上时,BE+CE的最小值等于BC的长,而AC长不变,∴△AEC的周长最小值等于AC+BC=12,故选:A．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["12", "14", "16", "18"], "choices": [12.0, 14.0, 16.0, 18.0], "label": 0}
-{"prob_id": 5927, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5927.png", "question": "如图,OA、OB分别是线段MC、MD的垂直平分线,MD=5cm,MC=7cm,CD=10cm,一只小蚂蚁从点M出发爬到OA边上任意一点E,再爬到OB边上任意一点F,然后爬回M点处,则小蚂蚁爬行的路径最短可为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设CD与OA的交点为E,与OB的交点于F,∵OA、OB分别是线段MC、MD的垂直平分线,∴ME=CE,MF=DF,∴小蚂蚁爬行的路径最短=CD=10cm,故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["12cm", "10cm", "7cm", "5cm"], "choices": [12.0, 10.0, 7.0, 5.0], "label": 1}
-{"prob_id": 5942, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5942.png", "question": "如图,在△ABC中,BF平分∠ABC,过A点作AF⊥BF,垂足为F并延长交BC于点G,D为AB中点,连接DF延长交AC于点E．若AB=12,BC=20,则线段EF的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在△BFA和△BFG中,≥ft\\lbrace\\begin{array}{l}{∠ABF=∠GBF}\\\\{BF=BF}\\\\{∠BFA=∠BFG}\\end{array}\\right.,∴△BFA≌△BFG(ASA)∴BG=AB=12,AF=FG,∴GC=BC-BG=8,∵AF=FG,AE=EC,∴EF=\\frac{1}{2}GC=4,故选:C．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["2", "3", "4", "5"], "choices": [2.0, 3.0, 4.0, 5.0], "label": 2}
-{"prob_id": 5946, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5946.png", "question": "如图,在△ABC中,点D、E分别是AB、AC的中点,若DE=1.5,则BC的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵点D、E分别是AB、AC的中点,∴BC=2DE=3,故选:A．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["3", "4", "2", "1"], "choices": [3.0, 4.0, 2.0, 1.0], "label": 0}
-{"prob_id": 5958, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5958.png", "question": "如图,在△ABC中,BD、CE是角平分线,AM⊥BD于点M,AN⊥CE于点N．△ABC的周长为30,BC=12．则MN的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "证明:∵△ABC的周长为30,BC=12．∴AB+AC=30-BC=18．延长AN、AM分别交BC于点F、G．如图所示:∵BN为∠ABC的角平分线,∴∠CBN=∠ABN,∵BN⊥AG,∴∠ABN+∠BAN=90°,∠G+∠CBN=90°,∴∠BAN=∠AGB,∴AB=BG,∴AN=GN,同理AC=CF,AM=MF,∴MN为△AFG的中位线,GF=BG+CF-BC,∴MN=\\frac{1}{2}(AB+AC-BC)=\\frac{1}{2}(18-12)=3．故选:D．z\\in\\hat{x}(\\lambda)", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["15", "9", "6", "3"], "choices": [15.0, 9.0, 6.0, 3.0], "label": 3}
-{"prob_id": 5965, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5965.png", "question": "如图,△ABC中,D,E分别是BC,AC的中点,BF平分∠ABC,交DE于点F,若BC=6,则DF的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵D,E分别是BC,AC的中点,∴DE∥AB,∴∠BFD=∠ABF,∵BF平分∠ABC,∴∠DBF=∠ABF,∴∠BFD=∠DBF,∴DF=DB=\\frac{1}{2}BC=3,故选:A．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["3", "4", "5", "6"], "choices": [3.0, 4.0, 5.0, 6.0], "label": 0}
-{"prob_id": 5984, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5984.png", "question": "同学们都玩过跷跷板的游戏,如图是一个跷跷板的示意图,立柱OC与地面垂直,OA=OB．当跷跷板的一头A着地时,∠AOA′=50°,则当跷跷板的另一头B着地时,∠COB′等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA=OB=\\frac{1}{2}AB,∴OA′=OB′=\\frac{1}{2}A′B′,∵AB=A′B′,∴OA=OB′,∵∠AOA′=50°,∴∠AOB′=180°-50°=130°,∵OC⊥AB′,∴∠COB′=\\frac{1}{2}∠AOB′=65°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["25°", "50°", "65°", "130°"], "choices": [25.0, 50.0, 65.0, 130.0], "label": 2}
-{"prob_id": 5985, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/5985.png", "question": "如图,在△ABC中,AB=AC,∠A=40°,DE垂直平分AC,则∠BCD的度数等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB=AC,∠A=40°,∴∠ABC=∠ACB=70°．∵DE垂直平分AC,∴AD=CD,∴∠A=∠ACD=40°∴∠BCD=∠ACB-∠ACD=30°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["20°", "30°", "40°", "50°"], "choices": [20.0, 30.0, 40.0, 50.0], "label": 1}
-{"prob_id": 6528, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/6528.png", "question": "如图,PA、PB是半径为1的⊙O的两条切线,点A、B分别为切点,∠APB=60°,OP与弦AB交于点C,与⊙O交于点D．则图中阴影部分的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA、PB是半径为1的⊙O的两条切线,∴OA⊥PA,OB⊥PB,OP平分∠APB,而∠APB=60°,∴∠APO=30°,∠POA=90°-30°=60°,又∵OP垂直平分AB,∴△AOC≌△BOC,∴S~△AOC~=S~△BOC~,∴S~阴影部分~=S~扇形OAD~=\\frac{60π×1^{2}}{360}=\\frac{π}{6}．故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.5235987755982989", "org_choices": ["\\frac{1}{3}π", "\\frac{1}{3}π-\\frac{√{3}}{4}", "\\frac{1}{6}π", "\\frac{1}{6}π-\\frac{√{3}}{4}"], "choices": [1.047, 0.614, 0.524, 0.091], "label": 2}
-{"prob_id": 6563, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/6563.png", "question": "如图,在△ABC中,∠A=90°,AB=AC=3,现将△ABC绕点B逆时针旋转一定角度,点C′恰落在边BC上的高所在的直线上,则边BC在旋转过程中所扫过的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作高AD,则C′点在AD的反向延长线上,如图,∵∠A=90°,AB=AC=3,∴△ABC为等腰直角三角形,∴BC=√{2}AB=3√{2},BD=CD,∵△ABC绕点B逆时针旋转一定角度,点C′恰落在边BC上的高所在的直线上,∴BC′=BC=3√{2},∴BD=\\frac{1}{2}BC′,∴∠BC′D=30°,∴∠DBC′=60°,∴边BC在旋转过程中所扫过的面积=\\frac{60\\cdotπ\\cdot(3√{2})^{2}}{360}=3π．故选:C．", "dataset_name": "Geoqa", "ground_truth": "9.42477796076938", "org_choices": ["π", "2π", "3π", "4π"], "choices": [3.142, 6.283, 9.425, 12.566], "label": 2}
-{"prob_id": 6711, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/6711.png", "question": "如图,圆心角都是90°的扇形OAB与扇形OCD叠放在一起,OA=3,OC=1,分别连接AC、BD,则图中阴影部分的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由图可知,将△OAC顺时针旋转90°后可与△ODB重合,∴S~△OAC~=S~△OBD~；因此S_{阴影}=S~扇形OAB~+S~△OBD~-S~△OAC~-S~扇形OCD~=S~扇形OAB~-S~扇形OCD~=\\frac{1}{4}π×(9-1)=2π．故选:C．", "dataset_name": "Geoqa", "ground_truth": "6.283185307179586", "org_choices": ["\\frac{1}{2}π", "π", "2π", "4π"], "choices": [1.571, 3.142, 6.283, 12.566], "label": 2}
-{"prob_id": 6717, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/6717.png", "question": "如图,为了绿化环境,在矩形空地的四个角划出四个半径为1的扇形空地进行绿化,则绿化的总面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:利用扇形面积可得,一个小扇形的面积=\\frac{90π×1}{360}=\\frac{π}{4},则四个图形的面积就是π,故选B．", "dataset_name": "Geoqa", "ground_truth": "3.141592653589793", "org_choices": ["\\frac{π}{2}", "π", "2π", "\\frac{π}{4}"], "choices": [1.571, 3.142, 6.283, 0.785], "label": 1}
-{"prob_id": 6770, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/6770.png", "question": "某楼梯的侧面如图所示,已测得AB的长为3米,楼梯斜坡BC的坡度比是1:2,则该楼梯的斜坡BC长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB的长为3米,楼梯斜坡BC的坡度比是1:2,∴$\\frac{AB}{AC}=\\frac{1}{2}$,∴AC=2AB=6米,∴BC$=√{AB^{2}+BC^{2}}=√{3^{2}+6^{2}}=$3$√{5}$(米)．故选:D．", "dataset_name": "Geoqa", "ground_truth": "6.708203932499369", "org_choices": ["3米", "6米", "3√{3}米", "3√{5}米"], "choices": [3.0, 6.0, 5.196, 6.708], "label": 3}
-{"prob_id": 6818, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/6818.png", "question": "某时刻海上点P处有一客轮,测得灯塔A位于P的北偏东30°方向,且相距50海里．客轮以60海里/小时的速度沿北偏西60°方向航行$\\frac{2}{3}$小时到达B处,那么tan∠BAP=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵灯塔A位于客轮P的北偏东30°方向,且相距50海里．∴AP=50,∵客轮以60海里/小时的速度沿北偏西60°方向航行$\\frac{2}{3}$小时到达B处,∴∠APB=90°,BP=60$×\\frac{2}{3}=$40,∴tan∠BAP$=\\frac{BP}{AP}=\\frac{40}{50}=\\frac{4}{5}$；故选:A．", "dataset_name": "Geoqa", "ground_truth": "0.8", "org_choices": ["\\frac{4}{5}", "\\frac{6}{5}", "\\frac{√{5}}{5}", "\\frac{2√{5}}{5}"], "choices": [0.8, 1.2, 0.447, 0.894], "label": 0}
-{"prob_id": 6833, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/6833.png", "question": "如图,已知灯塔M方圆一定范围内有镭射辅助信号,一艘轮船在海上从南向北方向以一定的速度匀速航行,轮船在A处测得灯塔M在北偏东30°方向,行驶1小时后到达B处,此时刚好进入灯塔M的镭射信号区,测得灯塔M在北偏东45°方向,则轮船通过灯塔M的镭射信号区的时间为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接MC,过M点作MD⊥AC于D．在Rt△ADM中,∵∠MAD=30°,∴AD$=√{3}$MD,在Rt△BDM中,∵∠MBD=45°,∴BD=MD,∴BC=2MD,∴BC:AB=2MD:($√{3}-$1)MD=2:$√{3}+$1．故轮船通过灯塔M的镭射信号区的时间为($√{3}+$1)小时．故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.732050807568877", "org_choices": ["(√{3}-1)小时", "(√{3}+1)小时", "2小时", "√{3}小时"], "choices": [0.732, 2.732, 2.0, 1.732], "label": 1}
-{"prob_id": 6834, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/6834.png", "question": "如图,上午8时,一艘船从A处出发,以15海里/时的速度向正北方向航行,9时40分到达B处,从A处测得灯塔C在北偏西26°方向,从B处测得灯塔C在北偏西52°方向,则B处到灯塔C的距离是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:据题意得,∠A=26°,∠DBC=52°,∵∠DBC=∠A+∠C,∴∠A=∠C=26°,∴AB=BC,∵AB=15×\\frac{5}{3}=25,∴BC=25(海里)．故选:B．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["36海里", "25海里", "20海里", "21海里"], "choices": [36.0, 25.0, 20.0, 21.0], "label": 1}
-{"prob_id": 6835, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/6835.png", "question": "上午9时,一船从A处出发,以每小时40海里的速度向正东方向航行,9时30分到达B处,如图所示,从A,B两处分别测得小岛M在北偏东45°和北偏东15°方向,那么B处与小岛M的距离为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由已知得,AB=40$×\\frac{1}{2}=$20海里,∠ABM=105°．过点B作BN⊥AM于点N．在直角△ABN中,BN=AB•sin45°=10$√{2}$；在直角△BNM中,∠MBN=60°,则∠M=30°,∴BM=2BN=20$√{2}$(海里)．故选:B．", "dataset_name": "Geoqa", "ground_truth": "28.284271247461902", "org_choices": ["20海里", "20√{2}海里", "15海里", "20海里"], "choices": [20.0, 28.284, 15.0, 20.0], "label": 1}
-{"prob_id": 6839, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/6839.png", "question": "为了测量两岸平行的河宽AB,测得∠ACB=30°,∠ADB=60°,CD=60m,则河宽AB为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ACB=30°,∠ADB=60°,∴∠CAD=30°,∴AD=CD=60m,在Rt△ABD中,AB=AD•sin∠ADB=60$×\\frac{√{3}}{2}=$30$√{3}$(m)．故选:B．", "dataset_name": "Geoqa", "ground_truth": "51.96152422706632", "org_choices": ["30m", "30√{3}m", "(30√{3}+30)m", "(30√{3}-30)m"], "choices": [30.0, 51.962, 81.962, 21.962], "label": 1}
-{"prob_id": 6852, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/6852.png", "question": "如图,已知一渔船上的渔民在A处看见灯塔M在北偏东60°方向,这艘渔船以28海里/时的速度向正东方向航行,半小时后到达B处,在B处看见灯塔M在北偏东15°方向,此时灯塔M与渔船的距离是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由已知得,AB=\\frac{1}{2}×28=14海里,∠A=30°,∠ABM=105°．过点B作BN⊥AM于点N．∵在直角△ABN中,∠BAN=30°∴BN=\\frac{1}{2}AB=7海里．在直角△BNM中,∠MBN=45°,则直角△BNM是等腰直角三角形．即BN=MN=7海里,∴BM=√{BN^{2}+MN^{2}}=√{7^{2}+7^{2}}=7√{2}海里．故选:A．", "dataset_name": "Geoqa", "ground_truth": "9.899494936611665", "org_choices": ["7√{2}海里", "14√{2}海里", "7海里", "14海里"], "choices": [9.899, 19.799, 7.0, 14.0], "label": 0}
-{"prob_id": 7508, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7508.png", "question": "如图,已知\\frac{OA}{DO}=\\frac{BO}{CO}=\\frac{1}{2},△AOB的面积是100cm²,则△DOC的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵\\frac{OA}{DO}=\\frac{BO}{CO}=\\frac{1}{2},∠AOB=∠COD,∴△AOB∽△COD,∴\\frac{S_{\\bigtriangleupAOB}}{S_{\\bigtriangleupCOD}}=(\\frac{OA}{DO})²,∴S~△DOC~=400故选:C．", "dataset_name": "Geoqa", "ground_truth": "400.0", "org_choices": ["200cm²", "300cm²", "400cm²", "500cm²"], "choices": [200.0, 300.0, 400.0, 500.0], "label": 2}
-{"prob_id": 7522, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7522.png", "question": "如图所示,△ABC中,∠BAC=90°,AD⊥BC于D,若AB=3,BC=5,则DC的长度(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠B=∠B,∠ADB=∠CAB=90°,∴△ABD∽△ABC,∴AB²=BD•BC,∴BD=\\frac{9}{5}∴DC=BC-BD=5-\\frac{9}{5}=\\frac{16}{5}故选:A．", "dataset_name": "Geoqa", "ground_truth": "3.2", "org_choices": ["\\frac{16}{5}", "\\frac{4}{5}", "\\frac{8}{5}", "\\frac{22}{5}"], "choices": [3.2, 0.8, 1.6, 4.4], "label": 0}
-{"prob_id": 7544, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7544.png", "question": "如图,在平行四边形ABCD中,AE:EB=1:2,S~△AEF~=3,则S~△FCD~为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,AE:EB=1:2,∴AE:CD=1:3,∵AB∥CD,∴∠EAF=∠DCF,∵∠DFC=∠AFE,∴△AEF∽△CDF,∵S~△AEF~=3,∴\\frac{S_{\\bigtriangleupAEF}}{S_{\\bigtriangleupFCD}}=\\frac{3}{S_{\\bigtriangleupFCD}}=(\\frac{1}{3})²,解得S~△FCD~=27．故选:B．", "dataset_name": "Geoqa", "ground_truth": "27.0", "org_choices": ["3", "27", "6", "12"], "choices": [3.0, 27.0, 6.0, 12.0], "label": 1}
-{"prob_id": 7573, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7573.png", "question": "如图,在平行四边形ABCD中,AE=EB,AF=2,则FC的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AB=CD,AB∥CD,∴∠CDE=∠AED,∠DCA=∠CAB,∴△AEF∽△CDF,∴AF:CF=AE:CD,∵AE=EB,∴AE=\\frac{1}{2}AB,∴AE=\\frac{1}{2}CD,即AE:CD=1:2,∵AF=2,∴CF=4,故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["5", "4", "3", "2"], "choices": [5.0, 4.0, 3.0, 2.0], "label": 1}
-{"prob_id": 7578, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7578.png", "question": "如图,在Rt△ABC中,∠BAC=90°,AD⊥BC于D,DE⊥AB于E,AD=3,DE=2,则CD的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AD⊥BC,DE⊥AB,∴∠ADC=∠AED=90°,∵∠BAC=90°,∴∠DAE=∠C,∴Rt△ACD∽Rt△DAE,∴\\frac{AD}{AC}=\\frac{DE}{AD},∵AD=3,DE=2,∴\\frac{3}{AC}=\\frac{2}{3},∴AC=\\frac{9}{2},在Rt△ACD中,CD²+AD²=AC²,∴CD=√{(\\frac{9}{2})²-3²}=\\frac{3√{5}}{2},故选:D．", "dataset_name": "Geoqa", "ground_truth": "3.3541019662496847", "org_choices": ["\\frac{21}{2}", "\\frac{√{15}}{2}", "\\frac{9}{2}", "\\frac{3√{5}}{2}"], "choices": [10.5, 1.936, 4.5, 3.354], "label": 3}
-{"prob_id": 7600, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7600.png", "question": "如图,已知点D是AB边的中点,AF∥BC,CG:GA=3:1,BC=8,则AF等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AF∥BC,∴△AFD∽△BED,∴AF:BE=AD:BD,∵D为AB中点,∴AF:BE=1,即AF=BE,∵AF∥BC,∴△AFG∽△CEG,∴CE:AF=CG:GA=3:1,∴CE=3AF,∴BC=2AF=8,∴AF=4,故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["2", "4", "16", "8"], "choices": [2.0, 4.0, 16.0, 8.0], "label": 1}
-{"prob_id": 7603, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7603.png", "question": "如图,已知⊙O的半径为6,M是⊙O外一点,且OM=12,过M的直线与⊙O交于A、B,点A、B关于OM的对称点分别为C、D,AD与BC交于点P,则OP的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图所示,连接AC,与MO交于点N,连接OA,OC,根据对称性可知:MN⊥AC且AN=CN,∴点P在MN上；则AP=CP,∴∠APN=∠CPN,∴∠BPM=∠APO,根据垂径定理知:∠AON=∠CON=\\frac{1}{2}∠AOC,又∠ABC=\\frac{1}{2}∠AOC(同弧圆周角是圆心角的一半),∴∠AON=∠ABC,∵∠AON=180°-(∠OAM+∠AMO),∠ABC=180°-(∠BPM+∠AMO),∴∠OAM=∠BPM,∴∠OAM=∠APO．又∠AOP=∠MOA,∵△AOP∽△MOA,∴\\frac{OP}{OA}=\\frac{OA}{OM}；即\\frac{OP}{6}=\\frac{6}{12},解得:OP=3．故选:C．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["4", "3.5", "3", "2.5"], "choices": [4.0, 3.5, 3.0, 2.5], "label": 2}
-{"prob_id": 7612, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7612.png", "question": "如图,在▱ABCD中,E为CD的中点,AE交BD于点O,S~△DCE~=12,则S~△AOD~等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在▱ABCD中,E为CD中点,∴DE∥AB,DE=\\frac{1}{2}AB,在△DOE与△BOA中,∠DOE=∠BOA,∠OBA=∠ODE,∴△DOE∽△BOA,∴\\frac{EO}{AO}=\\frac{DE}{BA}=\\frac{1}{2},∴S~△AOD~=2S~△DOE~=2×12=24．故选:A．", "dataset_name": "Geoqa", "ground_truth": "24.0", "org_choices": ["24", "36", "48", "60"], "choices": [24.0, 36.0, 48.0, 60.0], "label": 0}
-{"prob_id": 7618, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7618.png", "question": "如图,在△ABC中,∠ACB=90°,D是AB上一点,连接CD,∠ACD=∠B,若BC=13cm,CD=5cm,则BD=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠A=∠A,∠ACD=∠B,∴△ADC∽△ACB；∴∠BDC=∠ACB=90°,∴BD=√{BC²-CD²}=√{13²-5²}=12,故选:D．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["8cm", "9cm", "10cm", "12cm"], "choices": [8.0, 9.0, 10.0, 12.0], "label": 3}
-{"prob_id": 7761, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7761.png", "question": "如图,已知D、E分别是△ABC中AB、AC边上的点,DE∥BC且\\frac{AD}{AB}=\\frac{1}{3},△ADE的周长2,则△ABC的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴△ADE∽△ABC,∴\\frac{AD+DE+AE}{AB+BC+AC}=\\frac{AD}{AB}=\\frac{1}{3}∵AD+DE+AE=2,∴AB+BC+AC=6．故选:B．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["4", "6", "8", "18"], "choices": [4.0, 6.0, 8.0, 18.0], "label": 1}
-{"prob_id": 7770, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7770.png", "question": "如图所示,在△ABC中D为AC边上一点,若∠DBC=∠A,BC=3,AC=6,则CD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠DBC=∠A,∠C=∠C,∴△BCD∽△ACB,∴\\frac{CD}{BC}=\\frac{BC}{AC},∴\\frac{CD}{3}=\\frac{3}{6}∴CD=\\frac{3}{2},故选:C．", "dataset_name": "Geoqa", "ground_truth": "1.5", "org_choices": ["1", "2", "\\frac{3}{2}", "\\frac{5}{2}"], "choices": [1.0, 2.0, 1.5, 2.5], "label": 2}
-{"prob_id": 7802, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7802.png", "question": "如图,DE∥BC,BD,CE相交于O,\\frac{EO}{OC}=\\frac{1}{3},AE=3,则EB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴△EOD∽△COB,△AED∽△ABC,∴\\frac{DE}{BC}=\\frac{EO}{OC}=\\frac{1}{3},\\frac{DE}{BC}=\\frac{AE}{AB},又∵AE=3,∴BE=6．故选:A．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["6", "9", "12", "15"], "choices": [6.0, 9.0, 12.0, 15.0], "label": 0}
-{"prob_id": 7806, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7806.png", "question": "如图,一束光线从点A(-3,3)出发,经过y轴上的点C反射后经过点B(-1,0),则光线从点A到点B经过的路线长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图所示,延长AC交x轴于B′．则点B、B′关于y轴对称,CB=CB′．作AD⊥x轴于D点．则AD=3,DB′=3+1=4．∴AB′=AC+CB′=AC+CB=√{3²+4²}=5．即光线从点A到点B经过的路径长为5．故选:C．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["3", "\\frac{7}{2}", "5", "6"], "choices": [3.0, 3.5, 5.0, 6.0], "label": 2}
-{"prob_id": 7807, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7807.png", "question": "如图,在△ABC中,若DE∥BC,\\frac{AD}{AB}=\\frac{1}{3},DE=4cm,则BC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴△ADE∽△ABC,∴\\frac{AD}{AB}=\\frac{DE}{BC},∴\\frac{4}{BC}=\\frac{1}{3},∴BC=12．故选:C．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["8cm", "10cm", "12cm", "11cm"], "choices": [8.0, 10.0, 12.0, 11.0], "label": 2}
-{"prob_id": 7828, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7828.png", "question": "如图,已知D、E、F分别为等腰△ABC边BC、CA、AB上的点,如果AB=AC,∠FDE=∠B,BD=2,CD=3,CE=4,AE=1,那么AF的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB=AC,∴∠B=∠C；又∵∠FDE=∠B,∴∠BFD+∠BDF=∠BDF+∠CDE,∴∠BFD=∠CDE,而∠B=∠C,∴△BDF∽△CED,∴BD:CE=BF:DC,而BD=2,CD=3,CE=4,∴BF=1.5,∵AB=AC=1+4=5,∴AF=5-1.5=3.5．故选:A．", "dataset_name": "Geoqa", "ground_truth": "3.5", "org_choices": ["3.5", "4", "4.5", "5"], "choices": [3.5, 4.0, 4.5, 5.0], "label": 0}
-{"prob_id": 7842, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7842.png", "question": "如图,一小型水库堤坝的横断面为直角梯形,坝顶BC宽6m,坝高14m,斜坡CD的坡度i=1:2,则坝底AD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过点C作CE⊥AD于点E,∵BC=6m,坝高为14m,∴AE=6m,CE=14m,∵斜坡CD的坡度i=1:2,∴CE:DE=1:2,∴DE=28m,则AD=AE+DE=6+28=34(m)．故选:B．", "dataset_name": "Geoqa", "ground_truth": "34.0", "org_choices": ["13m", "34m", "(6+14√{3})m", "40m"], "choices": [13.0, 34.0, 30.249, 40.0], "label": 1}
-{"prob_id": 7884, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7884.png", "question": "如图,传送带和地面所成斜坡的坡度为1:2,它把物体从地面点A处送到离地面2米高的B处,则物体从A到B所经过的路程为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图:由已知得:BC=8,\\frac{BC}{AC}=\\frac{1}{2},∴AC=4,BC=2,∴AB=√{AC²+BC²}=2√{5},故选B．", "dataset_name": "Geoqa", "ground_truth": "4.47213595499958", "org_choices": ["4", "2√{5}", "√{5}", "2√{3}"], "choices": [4.0, 4.472, 2.236, 3.464], "label": 1}
-{"prob_id": 7898, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7898.png", "question": "如图,△ABC中,AB=AC=18,BC=12,正方形DEFG的顶点E,F在△ABC内,顶点D,G分别在AB,AC上,AD=AG,DG=6,则点F到BC的距离为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过点A作AM⊥BC于点M,交DG于点N,延长GF交BC于点H,∵AB=AC,AD=AG,∴AD:AB=AG:AC,∵∠BAC=∠DAG,∴△ADG∽△ABC,∴∠ADG=∠B,∴DG∥BC,∵四边形DEFG是正方形,∴FG⊥DG,∴FH⊥BC,AN⊥DG,∵AB=AC=18,BC=12,∴BM=\\frac{1}{2}BC=6,∴AM=√{AB²-BM²}=12√{2},∴\\frac{AN}{AM}=\\frac{DG}{BC},∴\\frac{AN}{12√{2}}=\\frac{6}{12},∴AN=6√{2},∴MN=AM-AN=6√{2},∴FH=MN-GF=6√{2}-6．故选:D．", "dataset_name": "Geoqa", "ground_truth": "2.4852813742385704", "org_choices": ["1", "2", "12√{2}-6", "6√{2}-6"], "choices": [1.0, 2.0, 10.971, 2.485], "label": 3}
-{"prob_id": 7914, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7914.png", "question": "如图,在边长为9的正方形ABCD中,F为AB上一点,连接CF．过点F作FE⊥CF,交AD于点E,若AF=3,则AE等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是正方形,∴AD=AB=BC=9,∠A=∠B=90°,∵FE⊥CF,∴∠EFC=90°,∴∠AEF+∠EFA=90°,∠AFE+∠CFB=90°,∴∠AEF=∠CFB,∴△AEF∽△BFC,∴\\frac{AE}{BF}=\\frac{AF}{BC},∴\\frac{AE}{9-3}=\\frac{3}{9},∴AE=2,故选:C．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["1", "1.5", "2", "2.5"], "choices": [1.0, 1.5, 2.0, 2.5], "label": 2}
-{"prob_id": 7924, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7924.png", "question": "如图,在Rt△ABC中,∠BAC=90°,AB=2,AC=3,D为BC的中点,动点E,F分别在AB,AC上,分别过点EG∥AD∥FH,交BC于点G、H,若EF∥BC,则EF+EG+FH的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BAC=90°,AB=2,AC=3,∴BC=√{AB²+AC²}=√{13},∵∠BAC=90°,D为BC的中点,∴DA=DB=DC,∴∠B=∠DAB,∠C=∠DAC,∵EF∥BC,EG∥AD∥FH,∴∠BEG=∠DAB,∠CFH=∠DAC,EF=GH,∴∠B=∠BEG,∠C=∠CFH,∴BG=EG,FH=HC,∴EF+EG+FH=GH+BG+HC=BC=√{13}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "3.605551275463989", "org_choices": ["√{10}", "√{13}", "2√{10}", "2√{13}"], "choices": [3.162, 3.606, 6.325, 7.211], "label": 1}
-{"prob_id": 7926, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7926.png", "question": "如图,在△ABC中,D、E分别是AB、AC上的点,且DE∥BC,若AD=5,DB=3,DE=4,则BC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴△ADE∽△ABC,∴\\frac{AD}{AB}=\\frac{DE}{BC},∵AD=5,DB=3,DE=4,∴AB=AD+DB=8,∴BC=\\frac{AB\\cdotDE}{AD}=\\frac{32}{5}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "6.4", "org_choices": ["\\frac{12}{5}", "\\frac{15}{4}", "\\frac{20}{3}", "\\frac{32}{5}"], "choices": [2.4, 3.75, 6.667, 6.4], "label": 3}
-{"prob_id": 7939, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7939.png", "question": "如图,平行四边形ABCD中,E为DC的中点,△DEF的面积为2,则△ABF的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AB∥CD,AB=CD,∴△DEF∽△BAF,∴\\frac{S_{\\bigtriangleupDEF}}{S_{\\bigtriangleupBAF}}={(\\frac{DE}{AB})}²,∵E为DC的中点,∴DE=\\frac{1}{2}CD,∴DE:AB=1:2,∴\\frac{S_{\\bigtriangleupDEF}}{S_{\\bigtriangleupBAF}}={(\\frac{1}{2})}²,∵△DEF的面积为2,∴△ABF的面积为8．故选:D．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["2", "4", "6", "8"], "choices": [2.0, 4.0, 6.0, 8.0], "label": 3}
-{"prob_id": 7941, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7941.png", "question": "如图,AB∥CD,\\frac{AO}{OD}=\\frac{2}{3},则△AOB的周长与△DOC的周长比是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB∥CD,∴∠A=∠D,∠B=∠C,∴△AOB∽△DOC,∴\\frac{C_{\\bigtriangleupAOB}}{C_{\\bigtriangleupDOC}}=\\frac{AO}{OD}=\\frac{2}{3},故选:D．", "dataset_name": "Geoqa", "ground_truth": "0.6666666666666666", "org_choices": ["\\frac{2}{5}", "\\frac{3}{2}", "\\frac{4}{9}", "\\frac{2}{3}"], "choices": [0.4, 1.5, 0.444, 0.667], "label": 3}
-{"prob_id": 7959, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7959.png", "question": "如图,AB∥CD,AC、BD交于O,BO=6,DO=3,AC=12,则AO长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB∥CD,∴∠C=∠A,∠B=∠D,∴△DOC∽△BOA,∴\\frac{DO}{BO}=\\frac{OC}{AO},∴\\frac{3}{6}=\\frac{12-OA}{AO},∴AO=8．故选:C．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["4", "6", "8", "10"], "choices": [4.0, 6.0, 8.0, 10.0], "label": 2}
-{"prob_id": 7999, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7999.png", "question": "如图,△ABC中,E、F分别是AB,AC的中点,若△AEF的面积为1,则四边形EBCF的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵E、F分别是AB,AC的中点,∴EF∥BC,∴△AEF∽△ABC,∴\\frac{S_{\\bigtriangleupAEF}}{S_{\\bigtriangleupABC}}={(\\frac{EF}{BC})}²={(\\frac{1}{2})}²=\\frac{1}{4},∵△AEF的面积为1,∴△ABC的面积是4,∴四边形EBCF的面积是4-1=3,故选:C．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["1", "2", "3", "4"], "choices": [1.0, 2.0, 3.0, 4.0], "label": 2}
-{"prob_id": 8019, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8019.png", "question": "如图,梯形ABCD中,AD∥BC,对角线AC、BD相交于O点,若S~△AOD~:S~△OCD~=1:2,则S~△AOD~:S~△BOC~=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设点D到AC边的距离为h,则S~△AOD~:S~△OCD~=(\\frac{1}{2}×OA×h):(\\frac{1}{2}×OC×h)=OA:OC=1:2．∵AD∥BC,∴∠DAO=∠BCO,∠ADO=∠CBO,∴△AOD∽△COB,∴S~△AOD~:S~△BOC~=(OA:OC)²=1:4．故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.25", "org_choices": ["\\frac{1}{6}", "\\frac{1}{3}", "\\frac{1}{4}", "\\frac{√{6}}{6}"], "choices": [0.167, 0.333, 0.25, 0.408], "label": 2}
-{"prob_id": 8121, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8121.png", "question": "如图所示,在山坡上种树,已知∠A=30°,AC=3m,相邻两株树的坡面距离AB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:AB=\\frac{AC}{cosA}=\\frac{3}{cos30{^°}}=2√{3}．故选C．", "dataset_name": "Geoqa", "ground_truth": "3.4641016151377544", "org_choices": ["6m", "√{3}m", "2√{3}m", "2√{2}m"], "choices": [6.0, 1.732, 3.464, 2.828], "label": 2}
-{"prob_id": 8203, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8203.png", "question": "如图,热气球从空中的A处看一栋楼的顶部仰角为30°,看这栋楼的俯角为60°．热气球与楼的水平距离为120m．这栋楼的高度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意可得,∠BAD=30°,∠DAC=60°,AD=120m,∴tan30°=\\frac{BD}{120},tan60°=\\frac{CD}{120},解得,BD=40√{3},CD=120√{3},∴BC=BD+CD=160√{3},故选:B．", "dataset_name": "Geoqa", "ground_truth": "277.1281292110204", "org_choices": ["160m", "160√{3}m", "(160-160√{3})m", "360m"], "choices": [160.0, 277.128, -117.128, 360.0], "label": 1}
-{"prob_id": 8236, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8236.png", "question": "如图,某教学兴趣小组想测量一棵树CD的高度,他们先在点A处测得树顶C的仰角为30°,然后沿AD方向前行10m,到达B点,在B处测得树顶C的仰角高度为60°(A、B、D三点在同一直线上)则这棵树CD的高度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠CBD=60°,∠CBD=∠A+∠ACB,∴∠ACB=∠CBD-∠A=60°-30°=30°,∵∠A=30°,∴∠A=∠ACB,∵AB=10,∴BC=AB=10,在R△BCD中,CD=BC•sin∠CBD=10×\\frac{√{3}}{2}=5√{3}．故选:C．", "dataset_name": "Geoqa", "ground_truth": "8.660254037844387", "org_choices": ["10m", "5m", "5√{3}m", "10√{3}m"], "choices": [10.0, 5.0, 8.66, 17.321], "label": 2}
-{"prob_id": 8240, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8240.png", "question": "如图,为了测得电视塔的高度AB,在D处用高为1米的测角仪CD,测得电视塔顶端A的仰角为30°,再向电视塔方向前进120米达到F处,又测得电视塔顶端A的仰角为60°,则这个电视塔的高度AB(单位:米)为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意得,CE=DF=120m,∠EAC=∠AEG-∠ACE=30°,∴∠EAC=∠ECA,∴AE=DF=120m,∴AG=AE×sin∠AEG=60√{3}m,∴AB=AG+GB=(60√{3}+1)m．故选:C．", "dataset_name": "Geoqa", "ground_truth": "104.92304845413264", "org_choices": ["60√{3}", "61", "60√{3}+1", "121"], "choices": [103.923, 61.0, 104.923, 121.0], "label": 2}
-{"prob_id": 8243, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8243.png", "question": "如图,在一次数学课外实践活动中,小文在点C处测得树的顶端A的仰角为37°,BC=20m,则树的高度AB为()(参考数据:sin37°≈0.60,cos37°≈0.80,tan37°≈0.75). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:tanC=\\frac{AB}{BC},∴AB=BC•tanC=20×0.75=15m,∴树的高度AB为15m,故选:B．", "dataset_name": "Geoqa", "ground_truth": "15.0", "org_choices": ["20m", "15m", "12m", "16m"], "choices": [20.0, 15.0, 12.0, 16.0], "label": 1}
-{"prob_id": 8258, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8258.png", "question": "如图,某地修建高速公路,要从B地向C地修一座隧道(B、C在同一水平面上)．为了测量B、C两地之间的距离,某工程师乘坐热气球从C地出发,垂直上升100m到达A处,在A处观察B地的俯角为30°,则B、C两地之间的距离为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:根据题意得:∠ABC=30°,AC⊥BC,AC=100m,在Rt△ABC中,BC=\\frac{AC}{tan∠ABC}=\\frac{100}{\\frac{√{3}}{3}}=100√{3}(m)．故选:A．", "dataset_name": "Geoqa", "ground_truth": "173.20508075688772", "org_choices": ["100√{3}m", "50√{2}m", "50√{3}m", "\\frac{100√{3}}{3}m"], "choices": [173.205, 70.711, 86.603, 57.735], "label": 0}
-{"prob_id": 8273, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8273.png", "question": "数学实践探究课中,老师布置同学们测量学校旗杆的高度．如图所示,小明所在的学习小组在距离旗杆底部10米的地方,用测角仪测得旗杆顶端的仰角为60°,则旗杆的高度是()米．. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,根据题意得:AC=10米,∠ACB=60°,∵∠A=90°,∴在Rt△ABC中,AB=AC•tan∠ACB=10×tan60°=10×√{3}=10√{3}(米)．故选:D．", "dataset_name": "Geoqa", "ground_truth": "17.320508075688775", "org_choices": ["10√{2}", "20", "\\frac{10√{3}}{3}", "10√{3}"], "choices": [14.142, 20.0, 5.774, 17.321], "label": 3}
-{"prob_id": 8336, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8336.png", "question": "如图,要测量底部不能到达的一座塔的高度AB,甲、乙两名同学分别在C,D两处进行了测量．已知点B,C,D在同一直线上,且AB⊥BD,CD=12米,∠ACB=60°,∠ADB=30°,则塔的高度AB为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:根据题意得:∠ABC=90°,∵∠ACB=60°,∠ADB=30°,∴∠CAD=∠ACB-∠ADB=30°,∴∠CAD=∠ADB,∴AC=CD=12米,在Rt△ABC中,AB=AC•sin60°=12$×\\frac{√{3}}{2}=$6$√{3}$(米),故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.392304845413264", "org_choices": ["12√{3}米", "6√{3}米", "12米", "6米"], "choices": [20.785, 10.392, 12.0, 6.0], "label": 1}
-{"prob_id": 8368, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8368.png", "question": "如图1表示一个时钟的钟面垂直固定于水平桌面上,其中分针上有一点A,且当钟面显示3点30分时,分针垂直于桌面,A点距桌面的高度为10公分．如图2,若此钟面显示3点45分时,A点距桌面的高度为16公分,则钟面显示3点50分时,A点距桌面的高度为多少公分(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作A″M⊥OA′,垂足为点M,∵当钟面显示3点30分时,分针垂直于桌面,A点距桌面的高度为10公分．∴AD=10,∵钟面显示3点45分时,A点距桌面的高度为16公分,∴A′C=16,∴AO=A″O=6,则钟面显示3点50分时,∠A″OA′=30°,∴MA″=3,∴A点距桌面的高度为:16+3=19公分．故选:D．", "dataset_name": "Geoqa", "ground_truth": "19.0", "org_choices": ["22-3√{3}", "16+π", "18", "19"], "choices": [16.804, 19.142, 18.0, 19.0], "label": 3}
-{"prob_id": 8398, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8398.png", "question": "如图,PA、PB是⊙O的切线,AC是⊙O的直径,∠P=50°,则∠BOC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA、PB是⊙O的切线,∴∠OAP=∠OBP=90°,而∠P=50°,∴∠AOB=360°-90°-90°-50°=130°,又∵AC是⊙O的直径,∴∠BOC=180°-130°=50°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["50°", "25°", "40°", "60°"], "choices": [50.0, 25.0, 40.0, 60.0], "label": 0}
-{"prob_id": 8406, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8406.png", "question": "如图,在Rt△ABC中,AD⊥BC于D,DE⊥AB于E,若AD=3,DE=2,则AC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在Rt△ABC中,AD⊥BC于D,DE⊥AB于E,∴∠ADC=∠AED=∠BAC=90°,∴∠EAD+∠DAC=90°,∠C+∠CAD=90°,∴∠C=∠EAD,∴sin∠EAD=sin∠C=\\frac{DE}{AD}=\\frac{AD}{AC}∵AD=3,DE=2,∴\\frac{2}{3}=\\frac{3}{AC},解得:AC=\\frac{9}{2}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "4.5", "org_choices": ["\\frac{21}{2}", "\\frac{√{15}}{2}", "√{15}", "\\frac{9}{2}"], "choices": [10.5, 1.936, 3.873, 4.5], "label": 3}
-{"prob_id": 8422, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8422.png", "question": "如图,在△ABC中,AB=BC=2,以AB为直径的⊙O与BC相切于点B,则AC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BC是⊙O的切线,且切点为B,∴∠ABC=90°,故△ABC是等腰直角三角形；由勾股定理,得:AC=√{AB²+BC²}=√{2BC²}=2√{2}；故选C．", "dataset_name": "Geoqa", "ground_truth": "2.8284271247461903", "org_choices": ["√{2}", "√{3}", "2√{2}", "2√{3}"], "choices": [1.414, 1.732, 2.828, 3.464], "label": 2}
-{"prob_id": 8423, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8423.png", "question": "定义:定点A与⊙O上任意一点之间的距离的最小值称为点A与⊙O之间的距离．现有一矩形ABCD(如图),AB=14cm,BC=12cm,⊙K与矩形的边AB,BC,CD分别切于点E,F,G,则点A与⊙K的距离为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接KE,KF,KG、AK,交⊙K于H点,∵ABCD是矩形,⊙K与矩形的边AB,BC,CD分别切于点E,F,G,∴EK=FK=KG,∴四边形BEKF、四边形FKGC均为正方形,∴BF=FC=EK=6cm；∵AB=14cm,∴AE=8cm,AK=10cm,∴AH=AK-KH=10-6=4cm,∴点A与⊙K的距离为4cm．故选:A．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["4cm", "8cm", "10cm", "12cm"], "choices": [4.0, 8.0, 10.0, 12.0], "label": 0}
-{"prob_id": 8434, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8434.png", "question": "如图,⊙O是△ABC的外接圆,∠BOC=3∠AOB,若∠ACB=20°,则∠BAC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ACB=20°,∴∠AOB=2∠ACB=40°,∵∠BOC=3∠AOB,∴∠BOC=120°,∴∠BAC=\\frac{1}{2}∠BOC=60°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["120°", "80°", "60°", "30°"], "choices": [120.0, 80.0, 60.0, 30.0], "label": 2}
-{"prob_id": 8437, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8437.png", "question": "如图,AB是⊙O的直径,C、D是⊙O上两点,CD⊥AB,若∠DAB=70°,则∠BOC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵CD⊥AB．∠DAB=70°,∴∠ADC=90°-∠DAB=20°,∴∠AOC=2∠ADC=40°,∴∠BOC=180°-∠AOC=140°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["70°", "130°", "140°", "160°"], "choices": [70.0, 130.0, 140.0, 160.0], "label": 2}
-{"prob_id": 8452, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8452.png", "question": "如图,A,B,C都是⊙O上的点,若∠ABC=110°,则∠AOC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∠1=2∠ABC=2×110°=220°,则∠AOC=360°-∠1=360°-220°=140°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["70°", "110°", "135°", "140°"], "choices": [70.0, 110.0, 135.0, 140.0], "label": 3}
-{"prob_id": 8456, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8456.png", "question": "点B在⊙O上,点C是⊙O上异于A、B的一点,若∠AOB=50°,则∠ACB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,∵∠AOB=50°,∴∠ACB=\\frac{1}{2}∠AOB=25°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["25°", "65°", "30°", "25°、155°"], "choices": [25.0, 65.0, 30.0, 155.0], "label": 0}
-{"prob_id": 8474, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8474.png", "question": "如图,已知点A、B、C在⊙O上,∠AOB=100°,则∠ACB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠AOB和∠ACB是弧AB所对的角,∴∠AOB=2∠ACB,∵∠AOB=100°,∴∠ACB=50°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["50°", "80°", "100°", "200°"], "choices": [50.0, 80.0, 100.0, 200.0], "label": 0}
-{"prob_id": 8476, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8476.png", "question": "如图,AB是⊙O的直径,CD是⊙O的弦,∠ABD=59°,则∠C等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB是⊙O的直径,∴∠ADB=90°,∵∠ABD=59°,∴∠A=90°-∠ABD=31°,∴∠C=∠A=31°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "31.0", "org_choices": ["29°", "31°", "59°", "62°"], "choices": [29.0, 31.0, 59.0, 62.0], "label": 1}
-{"prob_id": 9059, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9059.png", "question": "如图,正方形ABCD中,AB=8,Q是CD的中点,设∠DAQ=α,在CD上取一点P,使∠BAP=2α,则CP的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:取BC的中点E,连接AE,作EF⊥AP,则△ABE≌△ADQ,得EB=EC=4,由≥ft\\{\\begin{matrix}AE=AE\\\\∠EFA=∠EBA\\\\∠BAE=∠FAE\\\\\\end{matrix}\\right.\\得:△ABE≌△AFE,∴∠AEB=∠AEF,得EF=EB=EC,∵PE=PE,∴∠ECP=∠EFP=90°,∴△EPC≌△EPF,∴∠FEP=∠PEC,∴∠AEP=∠AEF+∠FEP=90°,∴∠PEF=∠PEC=∠EAP=∠EAB,∴△CEP∽△BAE,∴\\frac{PC}{EC}=\\frac{BE}{AB}=\\frac{4}{8}=\\frac{1}{2},即PC=2,故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["1", "2", "3", "√{3}"], "choices": [1.0, 2.0, 3.0, 1.732], "label": 1}
-{"prob_id": 9088, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9088.png", "question": "如图,矩形的两条对角线的一个交角为60°,AC+BD=20cm,则AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是矩形,∴AC=BD,OA=OC=OD=OB,∵AC+BD=20,∴OA=OB=5,∵∠AOB=60°,∴△AOB是等边三角形,∴AB=OA=5,故选:D．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["10cm", "8cm", "6cm", "5cm"], "choices": [10.0, 8.0, 6.0, 5.0], "label": 3}
-{"prob_id": 9119, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9119.png", "question": "如图,在菱形ABCD中,∠BAD=120°,对角线AC的长为3,则菱形ABCD的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图所示,∵四边形ABCD是菱形,AC是对角线,∴AB=BC=CD=AD,∠BAC=∠CAD=\\frac{1}{2}∠BAD,∴∠BAC=60°,∴△ABC是等边三角形,∴AB=BC=3,∴AB=BC=CD=AD=3,∴菱形ABCD的周长是12．故选:D．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["3", "6", "9", "12"], "choices": [3.0, 6.0, 9.0, 12.0], "label": 3}
-{"prob_id": 9124, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9124.png", "question": "如图,∠MON=90°,动点A、B分别位于射线OM、ON上,矩形ABCD的边AB=6,BC=4,则线段OC长的最大值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:取AB中点E,连接OE、CE,如图所示:则BE=\\frac{1}{2}AB=3,∵∠MON=90°,∴OE=\\frac{1}{2}AB=3．在Rt△BCE中,利用勾股定理可得CE=√{3²+4²}=5．在△OCE中,根据三角形三边关系可知CE+OE＞OC,∴当O、E、C三点共线时,OC最大为OE+CE=3+5=8．故选:B．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["10", "8", "6", "5"], "choices": [10.0, 8.0, 6.0, 5.0], "label": 1}
-{"prob_id": 9145, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9145.png", "question": "如图,菱形ABCD中,∠BAD=120°,BC=10,则对角线AC的长等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是菱形,且∠BAD=120°,∴AB=BC,∠BAC=∠DAC=\\frac{1}{2}∠BAD=60°,∴△ABC是等边三角形,∴AC=BC=10．故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["5", "10", "15", "20"], "choices": [5.0, 10.0, 15.0, 20.0], "label": 1}
-{"prob_id": 9155, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9155.png", "question": "如图,菱形ABCD的周长是16,∠A=60°,则对角线BD的长度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵菱形ABCD的周长是16,∴AB=AD=CD=BC=4,∵∠A=60°,∴△ABD是等边三角形,∴AB=AD=BD=4．∴对角线BD的长度为4．故选:C．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["2", "2√{3}", "4", "4√{3}"], "choices": [2.0, 3.464, 4.0, 6.928], "label": 2}
-{"prob_id": 9165, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9165.png", "question": "如图,在菱形ABCD中,AB=5,∠B=60°,则对角线AC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB=BC,∠B=60°,∴△ABC为等边三角形∴AC=AB=5．故选:D．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["20", "15", "10", "5"], "choices": [20.0, 15.0, 10.0, 5.0], "label": 3}
-{"prob_id": 9171, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9171.png", "question": "如图,菱形ABCD中,AB=15,∠ADC=120°,则B、D两点之间的距离为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BD,∵∠ADC=120°,∴∠A=180°-120°=60°,∵AB=AD,∴△ABD是等边三角形,∴BD=AB=15．故选:A．", "dataset_name": "Geoqa", "ground_truth": "15.0", "org_choices": ["15", "\\frac{15}{2}√{3}", "7.5", "15√{3}"], "choices": [15.0, 12.99, 7.5, 25.981], "label": 0}
-{"prob_id": 9175, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9175.png", "question": "如图,在菱形ABCD中,两条对角线AC=12,BD=16,则此菱形的边长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是菱形,∴OA=\\frac{1}{2}AC=\\frac{1}{2}×12=6,OB=\\frac{1}{2}BD=\\frac{1}{2}×16=8,AC⊥BD,∴AB=√{OA²{+OB}²}=10．∴此菱形的边长为10．故选:A．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["10", "8", "6", "5"], "choices": [10.0, 8.0, 6.0, 5.0], "label": 0}
-{"prob_id": 9188, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9188.png", "question": "如图,在菱形ABCD中,∠BAD=80°,AB的垂直平分线交对角线AC于点F,E为垂足,连接DF,则∠CDF等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BD,BF,∵∠BAD=80°,∴∠ADC=100°,又∵EF垂直平分AB,AC垂直平分BD,∴AF=BF,BF=DF,∴AF=DF,∴∠FAD=∠FDA=40°,∴∠CDF=100°-40°=60°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["60°", "65°", "70°", "80°"], "choices": [60.0, 65.0, 70.0, 80.0], "label": 0}
-{"prob_id": 9198, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9198.png", "question": "如图,菱形ABCD中,∠B=60°,AB=2cm,E、F分别是BC、CD的中点,连接AE、EF、AF,则△AEF的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是菱形,∴AB=AD=BC=CD,∠B=∠D,∵E、F分别是BC、CD的中点,∴BE=DF,在△ABE和△ADF中,≥ft\\{\\begin{matrix}AB=AD\\\\∠B=∠D\\\\BE=DF\\\\\\end{matrix}\\right.\\∴△ABE≌△ADF(SAS),∴AE=AF,∠BAE=∠DAF．连接AC,∵∠B=∠D=60°,∴△ABC与△ACD是等边三角形,∴AE⊥BC,AF⊥CD(等腰三角形底边上的中线与底边上的高线重合),∴∠BAE=∠DAF=30°,∴∠EAF=60°,∴△AEF是等边三角形．∴AE=√{3}cm,∴周长是3√{3}cm．故选:B．", "dataset_name": "Geoqa", "ground_truth": "5.196152422706632", "org_choices": ["2√{3}cm", "3√{3}cm", "4√{3}cm", "3cm"], "choices": [3.464, 5.196, 6.928, 3.0], "label": 1}
-{"prob_id": 9230, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9230.png", "question": "如图,在▱ABCD中,BC=BD,∠C=65°,则∠ADB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BC=BD,∠C=65°,∴∠BDC=∠C=65°,∴∠DBC=180°-∠C-∠BDC=50°,∵四边形ABCD是平行四边形,∴AD∥BC,∴∠ADB=∠DBC=50°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["25°", "35°", "50°", "60°"], "choices": [25.0, 35.0, 50.0, 60.0], "label": 2}
-{"prob_id": 9239, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9239.png", "question": "如图,在▱ABCD中,AB=6,BC=8,∠C的平分线交AD于E,交BA的延长线于F,则AE+AF的值等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AB∥CD,AD=BC=8,CD=AB=6,∴∠F=∠DCF,∵CF平分∠BCD,∴∠FCB=∠DCF,∴∠F=∠FCB,∴BF=BC=8,同理:DE=CD=6,∴AF=BF-AB=2,AE=AD-DE=2,∴AE+AF=4；故选:C．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["2", "3", "4", "6"], "choices": [2.0, 3.0, 4.0, 6.0], "label": 2}
-{"prob_id": 9268, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9268.png", "question": "如图,在▱ABCD中,AE⊥BC于E,AF⊥DC交DC的延长线于点F,且∠EAF=60°,则∠B等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在▱ABCD中,AF⊥CD,∴BA⊥AF,∴∠BAF=90°,∵∠EAF=60°,∴∠BAE=30°,∵AE⊥BC,∴∠B=90°-30°=60°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["60°", "50°", "70°", "65°"], "choices": [60.0, 50.0, 70.0, 65.0], "label": 0}
-{"prob_id": 9270, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9270.png", "question": "如图,▱ABCD中,AE平分∠BAD,若CE=3cm,AB=4cm,则▱ABCD的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AD=BC=10,AB=DC,AD∥BC,∴∠DAE=∠BEA,∵AE平分∠BCD,∴∠BAE=∠DAE,∴∠BEA=∠BAE,∴BE=AB=4cm,∴BC=BE+CE=7cm,∴▱ABCD的周长=2(DC+BC)=2(4+7)=22cm；故选:C．", "dataset_name": "Geoqa", "ground_truth": "22.0", "org_choices": ["20cm", "21cm", "22cm", "23cm"], "choices": [20.0, 21.0, 22.0, 23.0], "label": 2}
-{"prob_id": 9272, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9272.png", "question": "如图,在▱ABCD中,AE平分∠BAD,已知∠AEB=63°,则∠D的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:四边形ABCD是平行四边形,∴AD∥BC,∴∠DAB+∠B=180°,∠B=∠D,∴∠AEB=∠DAE=63°,∵AE平分∠BAD,∴∠DAB=2∠DAE=2×63°=126°,∴∠B=180°-126°=54°∴∠D=∠B=54°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "54.0", "org_choices": ["63°", "72°", "54°", "60°"], "choices": [63.0, 72.0, 54.0, 60.0], "label": 2}
-{"prob_id": 9276, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9276.png", "question": "如图,在▱ABCD中,对角线AC、BD相交于点O,AC=10,BD=6,AD=4,则▱ABCD的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,且AC=10,BD=6,∴OA=OC=\\frac{1}{2}AC=5,OB=OD=\\frac{1}{2}BD=3,∵AD=4,∴AD²+DO²=OA²,∴△ADO是直角三角形,且∠BDA=90°,即AD⊥BD,∴▱ABCD面积为:AD•BD=4×6=24．故选:C．", "dataset_name": "Geoqa", "ground_truth": "24.0", "org_choices": ["12", "12√{3}", "24", "30"], "choices": [12.0, 20.785, 24.0, 30.0], "label": 2}
-{"prob_id": 9303, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9303.png", "question": "如图,平行四边形ABCD的对角线交于点O,且AB=6,△OCD的周长为19,则▱ABCD的两条对角线的和是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AB=CD=6,∵△OCD的周长为19,∴OD+OC=19-6=13,∵BD=2DO,AC=2OC,∴平行四边形ABCD的两条对角线的和=BD+AC=2(DO+OC)=26,故选:C．", "dataset_name": "Geoqa", "ground_truth": "26.0", "org_choices": ["13", "25", "26", "38"], "choices": [13.0, 25.0, 26.0, 38.0], "label": 2}
-{"prob_id": 9308, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9308.png", "question": "如图,在平行四边形ABCD中,若∠B=60°,则∠D等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴∠D=∠B=60°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["30°", "45°", "60°", "90°"], "choices": [30.0, 45.0, 60.0, 90.0], "label": 2}
-{"prob_id": 9311, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9311.png", "question": "如图,平行四边形ABCD中,已知∠AOB=90°,AC=8cm,AD=5cm,则BD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴OA=\\frac{1}{2}AC=\\frac{1}{2}×8=4(cm),∵∠AOB=90°,∴∠AOD=180°-∠AOB=90°,∴OD=√{AD²-OA²}=√{5²-4²}=3(cm),∴BD=2OD=6cm．故选:C．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["3cm", "4cm", "6cm", "8cm"], "choices": [3.0, 4.0, 6.0, 8.0], "label": 2}
-{"prob_id": 9313, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9313.png", "question": "如图,▱ABCD中,CE⊥AB,垂足为E,如果∠A=115°,则∠BCE等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AD∥BC,∴∠A+∠B=180°,∴∠B=180°-115°=65°,∵CE⊥AB,∴∠BEC=90°,∴∠BCE=90°-∠B=90°-65°=25°；故选:B．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["65°", "25°", "30°", "15°"], "choices": [65.0, 25.0, 30.0, 15.0], "label": 1}
-{"prob_id": 9328, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9328.png", "question": "如图,在平行四边形ABCD中,CE平分∠BCD交AD边于点E,且DE=3,则AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AB=DC,AD∥BC,∴∠DEC=∠BCE,∵CE平分∠DCB,∴∠DCE=∠BCE,∴∠DEC=∠DCE,∴DE=DC=AB=3,故选:C．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["1", "2", "3", "6"], "choices": [1.0, 2.0, 3.0, 6.0], "label": 2}
-{"prob_id": 9333, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9333.png", "question": "▱ABCD中,对角线AC与BD交于点O,∠DAC=42°,∠CBD=23°,则∠COD是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AD∥BC,∴∠DAC=∠BCA=42°,∴∠COD=∠CBD+∠BCA=65°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["61°", "63°", "65°", "67°"], "choices": [61.0, 63.0, 65.0, 67.0], "label": 2}
-{"prob_id": 9336, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9336.png", "question": "如图,平行四边形ABCD的对角线AC、BD相交于点O,点E是CD的中点,△ABD的周长为16cm,则△DOE的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴O是BD中点,△ABD≌△CDB,又∵E是CD中点,∴OE是△BCD的中位线,∴OE=\\frac{1}{2}BC,即△DOE的周长=\\frac{1}{2}△BCD的周长,∴△DOE的周长=\\frac{1}{2}△DAB的周长．∴△DOE的周长=\\frac{1}{2}×16=8cm．故选:A．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["8cm", "10cm", "12cm", "16cm"], "choices": [8.0, 10.0, 12.0, 16.0], "label": 0}
-{"prob_id": 9338, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9338.png", "question": "如图,在▱ABCD中,BM是∠ABC的平分线交CD于点M,且MC=2,▱ABCD的周长是14,则DM等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BM是∠ABC的平分线,∴∠ABM=∠CBM,∵AB∥CD,∴∠ABM=∠BMC,∴∠BMC=∠CBM,∴BC=MC=2,∵▱ABCD的周长是14,∴BC+CD=7,∴CD=5,则DM=CD-MC=3,故选:C．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["1", "2", "3", "4"], "choices": [1.0, 2.0, 3.0, 4.0], "label": 2}
-{"prob_id": 9341, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9341.png", "question": "如图,P是▱ABCD上一点．已知S~△ABP~=3,S~△PDC~=2,那么平行四边形ABCD的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵P是▱ABCD上一点,∴S~△PBC~=\\frac{1}{2}S~平行四边形ABCD~,∴S~△ABP~+S~△PDC~═\\frac{1}{2}S~平行四边形ABCD~,∵S~△ABP~=3,S~△PDC~=2,∴S~平行四边形ABCD~=(3+2)×2=10,故选:C．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["6", "8", "10", "无法确定"], "choices": [6.0, 8.0, 10.0], "label": 2}
-{"prob_id": 9356, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9356.png", "question": "如图,在▱ABCD中,AE平分∠BAD交边BC于点E,若AD=8,EC=2,则AB的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AD∥BC,AD=BC=8,∵AE平分∠BAD交边BC于点E,∴∠BAE=∠DAE,∵AD∥BC,∴∠DAE=∠BEA,∴∠BAE=∠BEA,∴AB=BE,∴AB=BE=BC-CE=6,故选:C．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["10", "8", "6", "4"], "choices": [10.0, 8.0, 6.0, 4.0], "label": 2}
-{"prob_id": 9358, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9358.png", "question": "如图,在平行四边形ABCD中,过点C的直线CE⊥AB,垂足为E,若∠EAD=54°,则∠BCE的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵CE⊥AB,∴∠E=90°,∵∠EAD=54°,∴∠2=90°-54°=36°,∵四边形ABCD是平行四边形,∴AD∥BC,∴∠ECB=∠2=36°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "36.0", "org_choices": ["54°", "36°", "46°", "126°"], "choices": [54.0, 36.0, 46.0, 126.0], "label": 1}
-{"prob_id": 9359, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9359.png", "question": "如图,在▱ABCD中,BD=CD,∠C=70°,AE⊥BD于点E,则∠BAE的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在△DBC中,∵BD=CD,∠C=70°,∴∠DBC=∠C=70°,又∵在▱ABCD中,AD∥BC,∴∠ADB=∠DBC=70°,又∵AE⊥BD,∴∠DAE=90°-∠ADB=90°-70°=20°．故选:AD．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["20°", "30°", "40°", "50°"], "choices": [20.0, 30.0, 40.0, 50.0], "label": 0}
-{"prob_id": 9363, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9363.png", "question": "如图,P为平行四边形ABCD内一点,过点P分别作AB、AD的平行线交平行四边形于E、F、G、H四点,若S~AHPE~=3,S~PFCG~=5,则S~△PBD~为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:显然EPGD、GPFC、EPHA、PHBF均为平行四边形,∴S~△DEP~=S~△DGP~=\\frac{1}{2}S~平行四边形DEPG~,∴S~△PHB~=S~△PBF~=\\frac{1}{2}S~平行四边形PHBF~,又S~△ADB~=S~△EPD~+S~平行四边形AHPE~+S~△PHB~+S~△PDB~①S~△BCD~=S~△PDG~+S~平行四边形PFCG~+S~△PFB~-S~△PDB~②①-②得0=S~平行四边形AHPE~-S~平行四边形PFCG~+2S~△PDB~,即2S~△PBD~=5-3=2∴S~△PBD~=1．故选:B．", "dataset_name": "Geoqa", "ground_truth": "1.0", "org_choices": ["1.5", "1", "2.5", "3"], "choices": [1.5, 1.0, 2.5, 3.0], "label": 1}
-{"prob_id": 9368, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9368.png", "question": "如图,▱ABCD中,∠A=120°,则∠1=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴∠BCD=∠A=120°,∴∠1=180°-∠BCD=60°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["80°", "60°", "45°", "30°"], "choices": [80.0, 60.0, 45.0, 30.0], "label": 1}
-{"prob_id": 9369, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9369.png", "question": "如图,在▱ABCD中,CE⊥AB,点E为垂足,如果∠D=55°,则∠BCE=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴∠B=∠D=55°,∵CE⊥AB,∴∠BEC=90°,∴∠BCE=90°-∠B=35°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["55°", "35°", "25°", "30°"], "choices": [55.0, 35.0, 25.0, 30.0], "label": 1}
-{"prob_id": 9386, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9386.png", "question": "如图,在▱ABCD中,∠ABC=60°,AB=BC=4cm,点M,N分别在边BC,CD上,且∠MAN=60°,则四边形AMCN的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接AC,∵∠B=60°,∴∠BAD=120°,∵∠MAN=60°,∴∠BAM=∠CAN,∴△ABC为等边三角形,∴AB=AC,∴△ABM≌△ACN,∴四边形AMCN的面积等于平行四边形面积的一半．∵AB=4cm,∴BC边上的高为2√{3},S~菱形ABCD~=4×2√{3}=8√{3}∴四边形AMCN的面积等于\\frac{1}{2}×8√{3}=4√{3}．故选:A．", "dataset_name": "Geoqa", "ground_truth": "6.928203230275509", "org_choices": ["4√{3}cm²", "2√{3}cm²", "8√{3}cm²", "8cm²"], "choices": [6.928, 3.464, 13.856, 8.0], "label": 0}
-{"prob_id": 9387, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9387.png", "question": "如图,在平行四边形ABCD中,AB=4,BC=6,AC的垂直平分线交AD于点E,则△CDE的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AC的垂直平分线交AD于E,∴AE=EC,∵四边形ABCD是平行四边形,∴DC=AB=4,AD=BC=6,∴△CDE的周长为:EC+CD+ED=AD+CD=6+4=10,故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["7", "10", "11", "12"], "choices": [7.0, 10.0, 11.0, 12.0], "label": 1}
-{"prob_id": 9402, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9402.png", "question": "如图,在▱ABCD中,AD=3,DC=5,BD的垂直平分线交BD于点E,则△BCE的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴BC=AD=3,∵BD的垂直平分线交BD于点E,∴DE=BE,∴EB+CE=DC=5,∴△BCE的周长是:5+3=8,故选:B．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["6", "8", "9", "10"], "choices": [6.0, 8.0, 9.0, 10.0], "label": 1}
-{"prob_id": 9415, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9415.png", "question": "如图,▱ABCD的周长为10cm,AC、BD相交于点O,OE⊥AC交AD于E,则△DCE的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵▱ABCD的周长为10cm,∴AD+DC=5cm,∵四边形ABCD是平行四边形,∴AO=CO,∵OE⊥AC交AD于E,∴AE=EC,∴EC+ED+CD=5cm,故选:D．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["4cm", "6cm", "8cm", "5cm"], "choices": [4.0, 6.0, 8.0, 5.0], "label": 3}
-{"prob_id": 9421, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9421.png", "question": "如图,在平行四边形ABCD中,已知AB=6,BC=9,∠B=30°,则平行四边形ABCD的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过点A作AE⊥BC于E,∴∠AEB=90°,∵AB=6,∠B=30°,∴AE=3；又∵BC=9,∴S~平行四边形ABCD~=9×3=27．故选:C．", "dataset_name": "Geoqa", "ground_truth": "27.0", "org_choices": ["12", "18", "27", "54"], "choices": [12.0, 18.0, 27.0, 54.0], "label": 2}
-{"prob_id": 9438, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9438.png", "question": "如图,▱ABCD中,∠AEB=36°,BE平分∠ABC,则∠C等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AD∥BC,∴∠AEB=∠EBC；∵BE平分∠ABC,∠AEB=36°,∴∠ABC=2∠EBC=2∠AEB=72°,又∵AB∥CD,∴∠C+∠ABC=180°,∴∠C=108°；故选:C．", "dataset_name": "Geoqa", "ground_truth": "108.0", "org_choices": ["36°", "72°", "108°", "144°"], "choices": [36.0, 72.0, 108.0, 144.0], "label": 2}
-{"prob_id": 9445, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9445.png", "question": "如图,平行四边形ABCD的对角线交于点O,且AB=5,△OCD的周长为23,则平行四边形ABCD的两条对角线的和是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AB=CD=5,∵△OCD的周长为23,∴OD+OC=23-5=18,∵BD=2DO,AC=2OC,∴平行四边形ABCD的两条对角线的和=BD+AC=2(DO+OC)=36,故选:C．", "dataset_name": "Geoqa", "ground_truth": "36.0", "org_choices": ["18", "28", "36", "46"], "choices": [18.0, 28.0, 36.0, 46.0], "label": 2}
-{"prob_id": 9449, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9449.png", "question": "如图,在▱ABCD中,对角线AC、BD相交于点O,如果AC=12,BD=8,AB=7,那么△OAB的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵▱ABCD,∴OA=OC,OD=OB,∵AC=12,BD=8,∴OA=6,OB=4,∵AB=7,∴△OAB的周长=OA+OB+AB=6+4+7=17．故选:B．", "dataset_name": "Geoqa", "ground_truth": "17.0", "org_choices": ["15", "17", "21", "27"], "choices": [15.0, 17.0, 21.0, 27.0], "label": 1}
-{"prob_id": 9452, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9452.png", "question": "平行四边形ABCD的周长是28cm,AC与BD相交于点O,△AOB的周长比△OBC的周长大4cm,那么AB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵平行四边形ABCD,∴OA=OC,OB=OD,∵平行四边形ABCD的周长是28cm,∴AB=CD,AD=BC,∴AB+BC+CD+AD=2(AB+BC)=28cm,∴AB+BC=14cm,∵△AOB的周长比△OBC的周长大4cm,∴AB+OA+OB-(BC+OB+OC)=AB-BC=4cm,∴AB=9cm．故选:B．", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["8cm", "9cm", "10cm", "11cm"], "choices": [8.0, 9.0, 10.0, 11.0], "label": 1}
-{"prob_id": 9459, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9459.png", "question": "如图,平行四边形ABCD中,对角线AC和BD交于O点,过O点作OE∥BC交DC于点E,若OE=2.5,则AD的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AD=BC,DO=BO,∵OE∥BC,∴DE=CE,∴BC=2OE=2×2.5=5,∴AD=5,故选:B．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["2.5", "5", "10", "15"], "choices": [2.5, 5.0, 10.0, 15.0], "label": 1}
-{"prob_id": 9465, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9465.png", "question": "如图平行四边形ABCD的对角线AC与BD相交于点O,AB=7,AC=10,△ABO周长为16,那么对角线BD的长等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB=7,AC=10,△ABO周长为16,∴AB+OA+0B=16,∴OA+OB=9,∵平行四边形ABCD,∴AC=2OA=10,BD=2OB,∴OA=5,∴OB=4,∴BD=8,故选:D．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["4", "5", "6", "8"], "choices": [4.0, 5.0, 6.0, 8.0], "label": 3}
-{"prob_id": 9466, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9466.png", "question": "如图所示,E是▱ABCD内任一点,若S~四边形ABCD~=6,则图中阴影部分的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设两个阴影部分三角形的底为AB,CD,高分别为h~1~,h~2~,则h~1~+h~2~为平行四边形的高,∴S~△EAB~+S~△ECD~=\\frac{1}{2}AB•h~1~+\\frac{1}{2}CD•h~2~=\\frac{1}{2}AB(h~1~+h~2~)=\\frac{1}{2}S~四边形ABCD~=\\frac{1}{2}×6=3．故选B．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["2", "3", "4", "5"], "choices": [2.0, 3.0, 4.0, 5.0], "label": 1}
-{"prob_id": 9467, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9467.png", "question": "如图,在平行四边形ABCD中,AB=4,∠BAD的平分线与BC的延长线交于点E,与DC交于点F,且点F为边DC的中点,DG⊥AE,垂足为G,若DG=1,则AE的边长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AE为∠DAB的平分线,∴∠DAE=∠BAE,∵DC∥AB,∴∠BAE=∠DFA,∴∠DAE=∠DFA,∴AD=FD,又F为DC的中点,∴DF=CF,∴AD=DF=\\frac{1}{2}DC=\\frac{1}{2}AB=2,在Rt△ADG中,根据勾股定理得:AG=√{3},则AF=2AG=2√{3},∵平行四边形ABCD,∴AD∥BC,∴∠DAF=∠E,∠ADF=∠ECF,在△ADF和△ECF中,≥ft\\{\\begin{matrix}∠DAF=∠E\\\\∠ADF=∠ECF\\\\DF=CF\\\\\\end{matrix}\\right.\\,∴△ADF≌△ECF(AAS),∴AF=EF,则AE=2AF=4√{3}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "6.928203230275509", "org_choices": ["2√{3}", "4√{3}", "4", "8"], "choices": [3.464, 6.928, 4.0, 8.0], "label": 1}
-{"prob_id": 9481, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9481.png", "question": "如图,AB是⊙O的弦,过点A作⊙O的切线AC．如果∠BAC=55°,那么∠AOB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AC为圆O的切线,∴OA⊥AC,∴∠OAC=90°,∵∠BAC=55°,∴∠OAB=∠OAC-∠BAC=35°,∵OA=OB,∴∠OAB=∠OBA=35°,则∠AOB=180°-2×35°=110°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "110.0", "org_choices": ["55°", "90°", "110°", "120°"], "choices": [55.0, 90.0, 110.0, 120.0], "label": 2}
-{"prob_id": 9482, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9482.png", "question": "如图,线段AB过圆心O,交⊙O于点A、C,∠B=30°,直线BD与⊙O切于点D,则∠ADB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OD,∵BD切⊙O于D,∴∠ODB=90°,∵∠B=30°,∴∠DOB=60°,∴∠A=\\frac{1}{2}∠DOB=30°,∴∠ADB=180°-∠B-∠A=180°-30°-30°=120°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["150°", "135°", "120°", "100°"], "choices": [150.0, 135.0, 120.0, 100.0], "label": 2}
-{"prob_id": 9530, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9530.png", "question": "如图,在平行四边形ABCD中,AC,BD为对角线,BC=6,BC边上的高为4,则图中阴影部分的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:通过观察结合平行四边形性质得:S_{阴影}=\\frac{1}{2}×6×4=12．故选:C．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["3", "6", "12", "24"], "choices": [3.0, 6.0, 12.0, 24.0], "label": 2}
-{"prob_id": 9538, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9538.png", "question": "如图,把平行四边形ABCD分成4个平行四边形,已知其中三个面积分别为8、10、30,则第四个平行四边形的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵平行四边形ABCD被分成4个平行四边形,∴AB∥EF∥CD,AD∥MN∥BC,∴四边形AMOE与四边形MBFO同高,底分别为OE与OF,四边形EOND与四边形OFCN同高,底分别为OE与OF,∴\\frac{S_{四边形AEMO}}{S_{四边形MBFO}}=\\frac{OE}{OF}=\\frac{8}{10}=\\frac{4}{5},∴\\frac{S_{四边形EOND}}{S_{四边形OFCN}}=\\frac{OE}{OF},即:\\frac{S_{四边形EOND}}{30}=\\frac{4}{5},∴S~四边形EOND~=24．故选:C．", "dataset_name": "Geoqa", "ground_truth": "24.0", "org_choices": ["28", "26", "24", "22"], "choices": [28.0, 26.0, 24.0, 22.0], "label": 2}
-{"prob_id": 9540, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9540.png", "question": "如图,▱ABCD的对角线AC、BD相交于点O,若AC+BD=10,BC=4,则△BOC的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵ABCD是平行四边形,∴BD=AC,BO=OD,AO=OC,又∵AC+BD=10,∴BO+OC=5,∴△BOC的周长为5+4=9．故选:B．", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["8", "9", "10", "14"], "choices": [8.0, 9.0, 10.0, 14.0], "label": 1}
-{"prob_id": 9549, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9549.png", "question": "如图,在▱ABCD中,AC、BD相交于点O,点E、F分别在边AD、BC上,EF经过点O．如果AB=3,BC=5,EF=AB,那么四边形CDEF的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴CD=AB=3,AD=BC=5,OA=OC,AD∥BC,∴∠EAO=∠FCO,∠AEO=∠CFO,在△AOE和△COF中,≥ft\\{\\begin{matrix}∠EAO=∠FCO&\\\\AEO=∠CFO&\\\\OA=OC&\\\\\\end{matrix}\\right.\\,∴△AOE≌△COF(AAS)．∴OF=OE,CF=AE．∴四边形CDEF的周长=CD+DE+EF+CF=CD+AB+DE+AE=CD+AB+AD=3+3+5=11；故选:D．", "dataset_name": "Geoqa", "ground_truth": "11.0", "org_choices": ["8", "9", "10", "11"], "choices": [8.0, 9.0, 10.0, 11.0], "label": 3}
-{"prob_id": 9556, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9556.png", "question": "如图,平行四边形ABCD的对角线AC的垂直平分线与边BC、DA分别交于E、F,连接CF,若平行四边形ABCD的周长等于18cm,则△CDF的周长等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵EF垂直平分AC,∴AF=CF,∴△CDF的周长=AD+DC=9cm,故选:C．", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["6cm", "8cm", "9cm", "10cm"], "choices": [6.0, 8.0, 9.0, 10.0], "label": 2}
-{"prob_id": 9568, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9568.png", "question": "如图,在△ABC中,AB=AC,∠A=40°,以C为圆心,CB的长为半径画弧,交AB于点D,连接CD,则∠ACD等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB=AC,∠A=40°,∴∠B=∠ACB=70°,∵BC=CD,∴∠CDB=∠B=70°,∴∠BCD=40°,∴∠ACD=30°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["20°", "30°", "40°", "50°"], "choices": [20.0, 30.0, 40.0, 50.0], "label": 1}
-{"prob_id": 9582, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9582.png", "question": "如图,在⊙O中,已知∠AOB=110°,C是圆周上的一点,则∠ACB为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在优弧AB上取点D,连接AD,BD,∵∠D=\\frac{1}{2}∠AOB=\\frac{1}{2}×110°=55°,∴∠ACB=180°-∠D=125°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "125.0", "org_choices": ["130°", "125°", "80°", "50°"], "choices": [130.0, 125.0, 80.0, 50.0], "label": 1}
-{"prob_id": 9591, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9591.png", "question": "如图,CD是⊙O的直径,弦DE∥OA,若∠D的度数是50°,则∠C的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥OA,∴∠AOD=∠D=50°,∴∠C=\\frac{1}{2}∠AOD=25°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["25°", "30°", "40°", "50°"], "choices": [25.0, 30.0, 40.0, 50.0], "label": 0}
-{"prob_id": 9620, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9620.png", "question": "如图,BD是⊙O的直径,点A、C在⊙O上,且BD⊥AC,若⁀{AB}的度数为60°,则∠BDC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC,∵BD是⊙O的直径,BD⊥AC,∴⁀{AB}=⁀{BC},∴∠BOC=∠AOB=60°,∴∠BDC=\\frac{1}{2}∠BOC=30°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["60°", "30°", "35°", "45°"], "choices": [60.0, 30.0, 35.0, 45.0], "label": 1}
-{"prob_id": 9632, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9632.png", "question": "如图,已知AB、AD是⊙O的弦,∠B=20°,点C在弦AB上,连接CO并延长CO交于⊙O于点D,∠D=15°,则∠BAD的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OA,∵OA=OB,∠B=20°,∴∠OAB=∠B=20°．∵OA=OD,∠D=15°,∴∠OAD=∠D=15°,∴∠BAD=∠OAB+∠OAD=20°+15°=35°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["30°", "45°", "20°", "35°"], "choices": [30.0, 45.0, 20.0, 35.0], "label": 3}
-{"prob_id": 9655, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9655.png", "question": "如图,⊙O是△ABC的外接圆,已知∠C=60°,则∠BAO的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB,由圆周角定理得,∠AOB=2∠C=120°,又OA=OB,∴∠BAO=\\frac{1}{2}(180°-120°)=30°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["15°", "30°", "60°", "120°"], "choices": [15.0, 30.0, 60.0, 120.0], "label": 1}
-{"prob_id": 9658, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9658.png", "question": "如图,AB是半圆的直径,∠ABC=50°,点D是⁀{AC}的中点,则∠DAB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连结BD,如图,∵点D是⁀{AC}的中点,即弧CD=弧AD,∴∠ABD=∠CBD,∵∠ABC=50°,∴∠ABD=\\frac{1}{2}×50°=25°,∵AB是半圆的直径,∴∠ADB=90°,∴∠DAB=90°-25°=65°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["40°", "50°", "65°", "70°"], "choices": [40.0, 50.0, 65.0, 70.0], "label": 2}
-{"prob_id": 9676, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9676.png", "question": "如图,AB是⊙O的直径,弦CD与AB相交,且∠ABC=32°,则∠CDB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵线段AB为⊙O的直径,∴∠ACB=90°,∴∠BAC=180°-∠ACB-∠ABC=58°．∵∠CDB与∠BAC均为弦BC的圆周角,∴∠CDB=∠BAC=58°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "58.0", "org_choices": ["58°", "32°", "80°", "64°"], "choices": [58.0, 32.0, 80.0, 64.0], "label": 0}
-{"prob_id": 9677, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9677.png", "question": "如图,⁀{AB}是半圆,连接AB,点O为AB的中点,点C、D在⁀{AB}上,连接AD、CO、BC、BD、OD．若∠COD=62°,且AD∥OC,则∠ABD的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB是半圆的直径,∴∠ADB=90°,∵AD∥OC,∴∠A=∠COD=62°,∴∠ABD=90°-∠A=28°；故选:B．", "dataset_name": "Geoqa", "ground_truth": "28.0", "org_choices": ["26°", "28°", "30°", "32°"], "choices": [26.0, 28.0, 30.0, 32.0], "label": 1}
-{"prob_id": 9716, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9716.png", "question": "如图,AB是⊙O的直径,点C、点D在⊙O上,连结AC、BC、AD、CD,若∠BAC=50°,则∠ADC的度数等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB是⊙O的直径,∴∠ACB=90°,∵∠BAC=50°,∴∠B=40°,∴∠ADC=∠B=40°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["30°", "35°", "40°", "45°"], "choices": [30.0, 35.0, 40.0, 45.0], "label": 2}
-{"prob_id": 9728, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9728.png", "question": "如图,AB是⊙O直径,∠AOC=140°,则∠D为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠AOC=140°,∴∠BOC=180°-140°=40°,∴∠D=\\frac{1}{2}∠BOC=\\frac{1}{2}×40°=20°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["40°", "30°", "20°", "70°"], "choices": [40.0, 30.0, 20.0, 70.0], "label": 2}
-{"prob_id": 9729, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9729.png", "question": "如图,在⊙O中,直径AB⊥弦CD于点H,E是⊙O上的点,若∠BEC=25°,则∠BAD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接AC,∵直径AB⊥弦CD于点H,∴⁀{BC}=⁀{BD}∴∠CAB=∠DAB∵∠BAC=∠BEC=25°,∴∠BAD=∠BAC=25°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["65°", "50°", "25°", "12.5°"], "choices": [65.0, 50.0, 25.0, 12.5], "label": 2}
-{"prob_id": 9736, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9736.png", "question": "如图,AB为⊙O的直径,CD为⊙O的弦,∠ABD=53°,则∠BCD为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接AC,∵AB是圆的直径,∴∠BCA=90°,又∠ACD=∠ABD=53°,∴∠BCD=∠ACB-∠ACD=90°-53°=37°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "37.0", "org_choices": ["37°", "47°", "45°", "53°"], "choices": [37.0, 47.0, 45.0, 53.0], "label": 0}
-{"prob_id": 9760, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9760.png", "question": "如图,⊙O是△ABC的外接圆,∠AOB=60°,则∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵⊙O是△ABC的外接圆,∠AOB=60°,∴∠C=\\frac{1}{2}∠AOB=\\frac{1}{2}×60°=30°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["25°", "30°", "35°", "40°"], "choices": [25.0, 30.0, 35.0, 40.0], "label": 1}
-{"prob_id": 9761, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9761.png", "question": "如图,点A,B,C是⊙O上的三点,∠AOC=110°,则∠ABC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠AOC与∠ABC是同弧所对的圆心角与圆周角,∠AOC=110°,∴∠ABC=\\frac{1}{2}∠AOC=55°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["70°", "65°", "55°", "50°"], "choices": [70.0, 65.0, 55.0, 50.0], "label": 2}
-{"prob_id": 9768, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9768.png", "question": "如图,AB是⊙O的直径,CD为弦,且AB⊥CD,垂足是点E,已知∠COB=60°,则∠DAB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB⊥CD,AB是⊙O的直径,∴⁀{CB}=⁀{BD},∴∠DAB=\\frac{1}{2}∠COB,∵∠COB=60°,∴∠DAB=30°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["60°", "30°", "25°", "35°"], "choices": [60.0, 30.0, 25.0, 35.0], "label": 1}
-{"prob_id": 9773, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9773.png", "question": "如图,已知AB为⊙O的直径,若∠BOC的度数是50°,则∠A的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由圆周角定理得,∠A=\\frac{1}{2}∠BOC=25°,故选:D．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["50°", "40°", "30°", "25°"], "choices": [50.0, 40.0, 30.0, 25.0], "label": 3}
-{"prob_id": 9779, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9779.png", "question": "如图,点A、B、C在⊙O上,∠AOB=140°,∠ACB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在优弧AB上任意找一点D,连接AD,BD．∵∠D=\\frac{1}{2}∠AOB=70°∴∠ACB=180°-40°=110°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "110.0", "org_choices": ["140°", "110°", "70°", "120"], "choices": [140.0, 110.0, 70.0, 120.0], "label": 1}
-{"prob_id": 9798, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9798.png", "question": "如图,AB是⊙O的直径,CD是⊙O的一条弦,且CD⊥AB于E,分别连接AD、BC,已知∠D=65°,则∠OCD=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠B=∠D=65°,CD⊥AB,∴∠BCE=90°-65°=25°,∵OB=OC,∴∠OCB=∠B=65°,∴∠OCD=65°-25°=40°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["30°", "35°", "40°", "45°"], "choices": [30.0, 35.0, 40.0, 45.0], "label": 2}
-{"prob_id": 9803, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9803.png", "question": "如图,AB为⊙O的直径,CD为⊙O的弦,∠ACD=42°,则∠BAD=()°．. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BD,∵∠ACD=42°,∴∠ABD=42°,∵AB为直径,∴∠ADB=90°,∴∠BAD=890°-∠ABD=48°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "48.0", "org_choices": ["42", "48", "60", "45"], "choices": [42.0, 48.0, 60.0, 45.0], "label": 1}
-{"prob_id": 9814, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9814.png", "question": "如图,AB是O的直径,∠AOC=110°,则∠D=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "】解:∵∠AOC=110°,∴∠BOC=180°-110°=70°,∴∠D=\\frac{1}{2}∠BOC=35°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["24°", "22°", "20°", "35°"], "choices": [24.0, 22.0, 20.0, 35.0], "label": 3}
-{"prob_id": 9829, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9829.png", "question": "如图,AB是⊙O的直径,点C在⊙O上,若∠ABC=30°,则∠CAB为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连结BE,如图,∵AB为直径,∴∠ACB=90°,∴∠CAB=90°-∠ABC=90°-30°=60°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["30°", "45°", "60°", "75°"], "choices": [30.0, 45.0, 60.0, 75.0], "label": 2}
-{"prob_id": 9832, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9832.png", "question": "如图,P是⊙O外一点,PA、PB分别交⊙O于C、D两点,已知⁀{AB}和⁀{CD}所对的圆心角分别为90°和50°,则∠P=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵⁀{AB}和⁀{CD}所对的圆心角分别为90°和50°,∴∠A=25°,∠ADB=45°,∵∠P+∠A=∠ADB,∴∠P=∠ADB-∠P=45°-25°=20°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["45°", "40°", "25°", "20°"], "choices": [45.0, 40.0, 25.0, 20.0], "label": 3}
-{"prob_id": 9868, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9868.png", "question": "如图,已知A、B、C三点在⊙O上,AC⊥BO于D,∠B=50°,则∠BOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AC⊥BO,∴∠ADB=90°,∴∠A=90°-∠B=90°-50°=40°,∴∠BOC=2∠A=80°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["80°", "60°", "50°", "40°"], "choices": [80.0, 60.0, 50.0, 40.0], "label": 0}
-{"prob_id": 9874, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9874.png", "question": "如图,⊙O中,弦AB的长为2,OC⊥AB于C,OC=1,若从⊙O外一点P作⊙O的两条切线,切点分别为A、B,则∠APB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连OA,OB．PA,PB是切线,则∠OAP=∠OBP=90°．OC⊥AB⇒AC=BC=1=OC⇒△ACO,△BCO是等腰直角三角形⇒∠AOB=90°⇒四边形AOBP是正方形⇒∠APB=90°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "90.0", "org_choices": ["120°", "90°", "60°", "45°"], "choices": [120.0, 90.0, 60.0, 45.0], "label": 1}
-{"prob_id": 9893, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9893.png", "question": "如图,在△ABC中,AB=10,AC=8,BC=6,经过点C且与边AB相切的动圆与CA、CB分别相交于点P、Q,则线段PQ长度的最小值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,设QP的中点为F,圆F与AB的切点为D,连接FD、CF、CD,则FD⊥AB．∵AB=10,AC=8,BC=6,∴∠ACB=90°,FC+FD=PQ,∴FC+FD＞CD,∵当点F在直角三角形ABC的斜边AB的高CD上时,PQ=CD有最小值,∴CD=BC•AC÷AB=4.8．故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.8", "org_choices": ["4.75", "4.8", "5", "4√{2}"], "choices": [4.75, 4.8, 5.0, 5.657], "label": 1}
-{"prob_id": 9894, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9894.png", "question": "如图,在△ABC中,AB=2,AC=1,以AB为直径的圆与AC相切,与边BC交于点D,则AD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB为直径的圆与AC相切,∴∠CAB=∠ADB=90°,∵AB=2,AC=1,∴BC=√{5},∵AD•BC=AC•AB,∴AD=\\frac{AC\\cdotAB}{BC}=\\frac{2}{5}√{5}．故选:A．", "dataset_name": "Geoqa", "ground_truth": "0.8944271909999159", "org_choices": ["\\frac{2}{5}√{5}", "\\frac{4}{5}√{5}", "\\frac{2}{5}√{3}", "\\frac{4}{5}√{3}"], "choices": [0.894, 1.789, 0.693, 1.386], "label": 0}
-{"prob_id": 9901, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9901.png", "question": "如图,AB是⊙O的直径,点C在AB的延长线上,CD与⊙O相切,切点为D．如果∠A=35°,那么∠C等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BD,AB是⊙O的直径,则∠ADB=90°,∠ABD=90°-∠A=55°∴BDC=∠A=35°,∴∠C=∠ABD-∠BDC=20°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["20°", "30°", "35°", "55°"], "choices": [20.0, 30.0, 35.0, 55.0], "label": 0}
-{"prob_id": 9918, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/9918.png", "question": "如图,Rt△ABC中,∠ACB=90°,AC=4,BC=3,以AC为直径的圆交AB于D,则AD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接CD,∵Rt△ABC中,∠ACB=90°,AC=4,BC=3,∴根据勾股定理得:AB=√{AC²+BC²}=5,∵AC为直径,∴CD⊥AB,∴CD=\\frac{AC\\cdotBC}{AB}=\\frac{12}{5},∴AD=√{AC²-CD²}=\\frac{16}{5}．故选:C．", "dataset_name": "Geoqa", "ground_truth": "3.2", "org_choices": ["\\frac{9}{5}", "\\frac{12}{5}", "\\frac{16}{5}", "4"], "choices": [1.8, 2.4, 3.2, 4.0], "label": 2}
-{"prob_id": 1019, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1019.png", "question": "如图,已知AD与BC相交于点O,AB∥CD,如果∠B=40°,∠D=30°,则∠AOC的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB//CD,∴∠A=∠D=30°由三角形的外角的性质得∠AOC=∠A+∠B=70°故选:B.", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["60°", "70°", "80°", "120°"], "choices": [60.0, 70.0, 80.0, 120.0], "label": 1}
-{"prob_id": 1031, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1031.png", "question": "如图,在△ABC中,AB=AC,D是BC的中点,∠B=40°,则∠BAD=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB=AC,D是BC的中点,∴AD⊥BC,∵∠B=40°,∴∠BAD=90°-40°=50°故选C", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["100°", "80°", "50°", "40°"], "choices": [100.0, 80.0, 50.0, 40.0], "label": 2}
-{"prob_id": 1042, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1042.png", "question": "如图,∠A=70°,∠2=130°,则∠1=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图,∵∠2=130°,∴∠3=180°-∠2=180°-130°=50°,∴∠1=∠A+∠3=70°+50°=120°.故选B", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["130°", "120°", "140°", "110°"], "choices": [130.0, 120.0, 140.0, 110.0], "label": 1}
-{"prob_id": 1053, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1053.png", "question": "如图所示,在四边ABCD中,∠BAD=120°,∠B=∠D=90°,若在BC和CD上分别找一点M,使得△AMN的周长最小,则此时∠AMN+∠ANM的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "作A关于BC和CD的对称点A'\",A\",连接A'A\",交BC于M,交CD于N,则A'A\"即为△AMN的周长最小值.∵∠DAB=120°∴∠AA′M+∠A\"=180^{°}-120^{°}=60^{°},∵∠MA'A=∠MAA',∠NAD=∠A\",且∠MA'A+∠MAA'=∠AMN,∠NAD+∠A\"=∠ANMr∴∠AMN+∠ANM=∠MA'A+∠MAA'+∠NAD+∠A\"=2(∠AA'M+∠A\")=2×60°=120°,故选B.", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["110°", "120°", "140°", "150°"], "choices": [110.0, 120.0, 140.0, 150.0], "label": 1}
-{"prob_id": 1060, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1060.png", "question": "如图,将长方形ABCD沿线段OG折叠到OB'C'G的位置,∠OGC'等于100°,则∠DGC'的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵将长方形ABCD沿线段OG折叠到OB'C'G的位置,∠OGC'等于100°,∴∠OGC=∠OGC'=100°,∴∠OGD=180°-∠OGC=80°,∴∠DGC'=∠OGC-∠OGD=20°故选A.", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["20°", "25°", "30°", "40°"], "choices": [20.0, 25.0, 30.0, 40.0], "label": 0}
-{"prob_id": 1064, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1064.png", "question": "如图,AB是⊙O的直径,若∠BDC=40°,则∠BOC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∠BOC=2∠BDC=80°故选:B.", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["40°", "80°", "14°", "无法确定"], "choices": [40.0, 80.0, 14.0], "label": 1}
-{"prob_id": 1073, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1073.png", "question": "如图,将△ABC折叠,使点A与BC边中点D重合,折痕为MN,若AB=9,BC=6,则△DNB的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵D是BC的中点,BC=6∴BD=3,由折叠的性质可知DN=AN,∴△DNB的周长=DN+BN+BD=AN+BN+BD=AB+BD=9+3=12.故选A.", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["12", "13", "14", "15"], "choices": [12.0, 13.0, 14.0, 15.0], "label": 0}
-{"prob_id": 1076, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1076.png", "question": "如图,▱ABCD的周长为36,对角线AC、BD相交于点O,点E是CD的中点,BD=12,则△DOE的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵\\sqsubsetABCD的周长为36,∴2(BC+CD)=36,则BC+CD=18∵四边形ABCD是平行四边形,对角线AC,BD相交于点O,BD=12又∵点E是CD的中点,DE=\\frac{1}{2}CD,∴OE是△BCD的中位线,∴OE=\\frac{1}{2}BC,∴△DOE的周长=OD+OE+DE=\\frac{1}{2}BD+\\frac{1}{2}(BC+CD)=6+9=15,即△DOE的周长为15.故选A", "dataset_name": "Geoqa", "ground_truth": "15.0", "org_choices": ["15", "18", "21", "24"], "choices": [15.0, 18.0, 21.0, 24.0], "label": 0}
-{"prob_id": 1087, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1087.png", "question": "如图,点A、B、C、D在⊙O上,∠AOC=140°,点B是弧AC的中点,则∠D的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "连接OB,∵点B是弧AC的中点,∴∠AOB=\\frac{1}{2}∠AOC=70^{°},由圆周角定理得,∠D=\\frac{1}{2}∠AOB=35^{°}故答案选:D.", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["70°", "55°", "35.5°", "35°"], "choices": [70.0, 55.0, 35.5, 35.0], "label": 3}
-{"prob_id": 1092, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1092.png", "question": "如图,AB是⊙O的直径,点C,D在⊙O上．若∠ABD=50°,则∠BCD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "连接AD,∵AB是⊙O的直径,∴∠ADB=90°.∠ABD=50°∴∠∠DAB=90^{°}-50^{°}=40^{°}∴∠BCD=∠DAB=40°.故选C.", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["30°", "35°", "40°", "45°"], "choices": [30.0, 35.0, 40.0, 45.0], "label": 2}
-{"prob_id": 1108, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1108.png", "question": "如图,在△ABC中,∠CAB=30°,将△ABC在平面内绕点A逆时针旋转到△AB'C'的位置,且CC'∥AB,则旋转角的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵△ABC在平面内绕点A逆时针旋转到△AB'C'的位置,∴AC=AC,∠CAC为旋转角,∵CC'//AB,∴∠ACC'=∠CAB=30°∵AC=AC'∴∠AC'C=∠ACC'=30°,∴∠CAC'=180°-30°-30°=120°∴旋转角的度数为120°,故选B.", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["100°", "120°", "110°", "130°"], "choices": [100.0, 120.0, 110.0, 130.0], "label": 1}
-{"prob_id": 1128, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1128.png", "question": "如图,O是直线AB上一点,∠1=40°,OD平分∠BOC,则∠2的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠1=40°,∴∠COB=180°-40°=140°.OD平分∠BOC,∴∠2=\\frac{1}{2}∠BOC=\\frac{1}{2}×140^{°}=70^{°}故选:D.", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["20°", "30°", "50°", "70°"], "choices": [20.0, 30.0, 50.0, 70.0], "label": 3}
-{"prob_id": 1131, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1131.png", "question": "如图所示,是一株美丽的勾股树,其中所有的四边形都是正方形,所有的三角形都是直角三角形,若正方形A．B、C、D的面积分别为2,5,1,2．则最大的正方形E的面积是().. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "根据勾股定理,可知,以直角边为边长的正方形的面积和等于以斜边为边的正方形的面积.即S_{A}+S_{B}+S_{C}+S_{D}=S_{E}=2+5+1+2=10故选B", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": [".9", "10", "11", "12"], "choices": [0.9, 10.0, 11.0, 12.0], "label": 1}
-{"prob_id": 1147, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1147.png", "question": "如图,直线AB,CD被BC所截,若AB∥CD,∠1=45°,∠2=35°,则∠3=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB//CD,∠1=45°,∴∠C=∠1=45°∵∠2=35°,∴∠3=∠2+∠C=35°+45°=80°.故选A.", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["80°", "70°", "60°", "90°"], "choices": [80.0, 70.0, 60.0, 90.0], "label": 0}
-{"prob_id": 1150, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1150.png", "question": "如图,在Rt△ABC中,∠BAC=90°,将△ABC绕点A顺时针旋转90°后得到△AB′C′(点B的对应点是点B′,点C的对应点是点C′),连接CC′.若∠CC′B′=32°,则∠AC′B′的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵△ABC绕点A顺时针旋转90°后得到△AB'C',∴AC=AC',∠B=∠AB'C,∠CAC'=90°,∴△ACC为等腰直角三角形,∴∠ACC'=∠AC'C=45°,∵∠CC'B'=32°∴∠AC'B'=∠AC'C-∠CC'B'=45°-32°=13°,∴∠B=13°故答案选:C.", "dataset_name": "Geoqa", "ground_truth": "13.0", "org_choices": ["32°", "45°", "13°", "30°"], "choices": [32.0, 45.0, 13.0, 30.0], "label": 2}
-{"prob_id": 1167, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1167.png", "question": "已知:如图,AB∥CD,BC平分∠ABD,且∠C=40°,则∠D的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB∥CD∴∠ABC=∠C=40°又∵BC平分∠ABD,∴∠DBC=∠ABC=40°∴△BCD中,∠D=180°-40°-40°=100°,故选D.", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["40°", "80°", "90°", "100°"], "choices": [40.0, 80.0, 90.0, 100.0], "label": 3}
-{"prob_id": 1191, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1191.png", "question": "已知直线a∥b,∠1和∠2互余,∠3=121°,那么∠4等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图:∵a∥b,∴∠2+∠5=180°,∵∠3=∠5=121°,∴∠2=59°,∵∠2和∠1互余,∴∠1=90°59°=31°,∵a∥b,∴∠1+∠4=180°,∴∠4=149°,故选B", "dataset_name": "Geoqa", "ground_truth": "149.0", "org_choices": ["159°", "149°", "139°", "21°"], "choices": [159.0, 149.0, 139.0, 21.0], "label": 1}
-{"prob_id": 1215, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1215.png", "question": "在△ABC中,AB=AC,D、E分别在BC、AC上,AD=AE,∠CDE=20°,则∠BAD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠ADC是三角形ABD的外角,∠AED是三角形DEC的一个外角,∠CDE=20°,∴∠ADC=∠BAD+∠B=∠ADE+∠EDC,∠AED=∠EDC+∠C,∠B+∠BAD=∠ADE+20°,∠AED=∠C+20°.∵AB=AC,AD=AE,∠CDE=20°,∴∠B=∠C,∠ADE=∠AED=∠C+20°,∴∠C+∠BAD=∠C+20°+20°,∴∠BAD=40°故选B.", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["36°", "40°", "45°", "50°"], "choices": [36.0, 40.0, 45.0, 50.0], "label": 1}
-{"prob_id": 1228, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1228.png", "question": "如图,直线m∥n,Rt△ABC的顶点A在直线n上,∠C=90°,AB,CB分别交直线m于点D和点E,且DB=DE,若∠B=25°,则∠1的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,∵DB=DE,∠B=25°,∴∠2=25°∴∠3=25°+25°=50°,∵m\\vertn,∴∠4=50°∵∠C=90°∴∠5=65°,∴∠1=180°-50°-65°=65°.故选B.", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["60°", "65°", "70°", "75°"], "choices": [60.0, 65.0, 70.0, 75.0], "label": 1}
-{"prob_id": 1229, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1229.png", "question": "如图,直线a∥b,直线c与直线a,b分别相交于点A,B,AM⊥b,垂足为点M．如果∠1=58°,那么∠2=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵直线a∥b,∠1=58°,∴∠ABM=∠1=58°∵AM⊥b,垂足为点M,∴∠AMB=90°∴∠2=180°-∠1-∠ABM=180°-58°-90°=32°.故选A.", "dataset_name": "Geoqa", "ground_truth": "32.0", "org_choices": ["32°", "58°", "42°", "122°"], "choices": [32.0, 58.0, 42.0, 122.0], "label": 0}
-{"prob_id": 1247, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1247.png", "question": "如图,把一块直角三角板的直角顶点放在直尺的一边上,若∠1=30°,则∠2是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图所示∵∠1+∠3=90°,且∠1=30°∴∠3=90°-∠1=60°∵直尺两边互相平行∴∠2=∠3=60°故选D.", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["45°", "50°", "55°", "60°"], "choices": [45.0, 50.0, 55.0, 60.0], "label": 3}
-{"prob_id": 1248, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1248.png", "question": "如图,AB⊥CD于D,DE⊥DF,若∠BDE=60°,则∠CDF等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB⊥CD,DE⊥DF,∴∠BDC=∠EDF=90°,∴∠CDF+∠CDE=∠CDE+∠BDE=90°,∴∠CDF=∠BDE=60°,故选:C.", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["30°", "45°", "60°", "120°"], "choices": [30.0, 45.0, 60.0, 120.0], "label": 2}
-{"prob_id": 1264, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1264.png", "question": "如图,测得BD=120m,DC=60m,EC=50m,则河宽AB为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ADB=∠EDC,∠ABC=∠ECD=90°,∴△ABD\\sim△ECD,∴\\frac{AB}{EC}=\\frac{BD}{CD},∴AB=\\frac{BD×EC}{CD}=\\frac{120×50}{60}=100(米).则两岸间的大致距离为100米.故选:B.", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["120m", "100m", "75m", "25m"], "choices": [120.0, 100.0, 75.0, 25.0], "label": 1}
-{"prob_id": 1280, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1280.png", "question": "如图,在△ABE中,AE的垂直平分线MN交BE于点C,∠E=30°,且AB=CE,则∠BAE的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:已知在△ABE中,AE的垂直平分线MN交BE于点C,∠E=30°,且AB=CE,故CE=CA=AB,∠ACB=∠ABC=∠CEA+∠CAE=60°,故∠CAB=60°即∠BAE=∠CAB+∠CAE=60+30°=90°.故选C.", "dataset_name": "Geoqa", "ground_truth": "90.0", "org_choices": ["80°", "85°", "90°", "105°"], "choices": [80.0, 85.0, 90.0, 105.0], "label": 2}
-{"prob_id": 1293, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1293.png", "question": "如图,在△ABC中,D、E分别是AB、AC边上的点,DE∥BC,∠ADE=35°,∠C=120°,则∠A为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵DE//BC,∠C=120°,∴∠AED=∠C=120°∵∠ADE=35°,∠ADE+∠AED+∠A=180°,∴∠A=180°-∠AED-∠ADE=180°-120°-35°=25°.故选D.", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["60°", "45°", "35°", "25°"], "choices": [60.0, 45.0, 35.0, 25.0], "label": 3}
-{"prob_id": 1315, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1315.png", "question": "如图,点A,B,C在⊙O上,∠AOB=72°,则∠ACB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "根据圆周角定理可知,∠AOB=2∠ACB=72°,则∠ACB=36°,故选A.", "dataset_name": "Geoqa", "ground_truth": "36.0", "org_choices": ["36°", "54°", "18°", "28°"], "choices": [36.0, 54.0, 18.0, 28.0], "label": 0}
-{"prob_id": 1342, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1342.png", "question": "将一张长方形纸片按如图所示折叠后,再展开．如果∠1=56°,那么∠2等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "根据题意知:折叠所重合的两个角相等.再根据两条直线平行,同旁内角互补,得:2∠1+∠2=180°,解得:∠2=180°-2∠1=68°.故选D.", "dataset_name": "Geoqa", "ground_truth": "68.0", "org_choices": ["56°", "62°", "66°", "68°"], "choices": [56.0, 62.0, 66.0, 68.0], "label": 3}
-{"prob_id": 1346, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1346.png", "question": "如图,直线a∥b,∠1=72°,则∠2的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵直线a//b,∴∠2=∠3,∵∠1=72°∴∠3=108°,∴∠2=108°故选:B.", "dataset_name": "Geoqa", "ground_truth": "108.0", "org_choices": ["118°", "108°", "98°", "72°"], "choices": [118.0, 108.0, 98.0, 72.0], "label": 1}
-{"prob_id": 1354, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1354.png", "question": "如图,一个含有30°角的直角三角板的两个顶点放在一个矩形的对边上,如果∠1=25°,那么∠2的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图,∵四边形ABCD是矩形,∴AD//BC,∴∠2=∠DEF,∵∠1=25^{°},∠GEF=90^{°},∴∠2=25^{°}+90^{°}=115^{°},故选C.", "dataset_name": "Geoqa", "ground_truth": "115.0", "org_choices": ["130°", "105°", "115°", "125°"], "choices": [130.0, 105.0, 115.0, 125.0], "label": 2}
-{"prob_id": 1368, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1368.png", "question": "如图,已知AB、AD是圆O的弦,∠ABO=30°,∠ADO=20°,则∠BAD=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接AO,则AO=BO=DO∠ABO=∠BAO;∠ADO=∠DAO∵∠ABO=30°,∠ADO=20°∴∠BAD=∠BAO+∠DAO=20^{°}+30^{°}=50^{°}.故选C.", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["30°", "40°", "50°", "60°"], "choices": [30.0, 40.0, 50.0, 60.0], "label": 2}
-{"prob_id": 1377, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1377.png", "question": "如图,C、D是线段AB上两点,若CB=4cm,DB=7cm,且D是AC的中点,则AB的长等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BD=7cm,BC=4cm,∴CD=BD-BC=3cm,∵D是AC的中点,∴AC=2CD=6cm,∴AB=AC+BC=10cm,故选:B.", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["9cm", "10cm", "12cm", "14cm"], "choices": [9.0, 10.0, 12.0, 14.0], "label": 1}
-{"prob_id": 1398, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1398.png", "question": "如图所示,C、D是线段AB上两点,若AC=3cm,C为AD中点且AB=10cm,则DB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵点C为AD的中点,AC=3cm,∴CD=3cm.∵AB=10cm,AC+CD+DB=AB,∴BD=10-3-3=4cm.故答案选:A.", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["4cm", "5cm", "6cm", "7cm"], "choices": [4.0, 5.0, 6.0, 7.0], "label": 0}
-{"prob_id": 1417, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1417.png", "question": "如图,⊙O中,AC为直径,MA,MB分别切⊙O于点A,B,∠BAC=25°,则∠AMB的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵MA切⊙O于点A,AC为直径,∴∠MAC=90°,又∠BAC=25°,∠MAB=∠MAC-∠BAC=65°∵MA、MB分别切⊙O于点A、B,∴MA=MB,∴∠MAB=∠MBA=65°,∴∠AMB=180-(∠MAB+∠MBA)=50°故选:D.", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["25°", "30°", "45°", "50°"], "choices": [25.0, 30.0, 45.0, 50.0], "label": 3}
-{"prob_id": 1444, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1444.png", "question": "已知:AB∥CD,∠ABE=120°,∠C=25°,则∠α度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "过点E作EF//CD∴∠C=∠FEC(两直线平行,内错角相等),∴∠FEC=25°∵AB//CD(已知),∴EF//AB(平行于同一直线的两直线平行),∴∠B+∠BEF=180°(两直线平行1同旁内角互补)∴∠BEF=60°∴∠α=∠BEF+∠FEC=85°.故选:C.", "dataset_name": "Geoqa", "ground_truth": "85.0", "org_choices": ["60°", "75°", "85°", "80°"], "choices": [60.0, 75.0, 85.0, 80.0], "label": 2}
-{"prob_id": 1457, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1457.png", "question": "如图,直线AB、CD相交于点O,OD平分∠AOE,∠BOC=50°,则∠EOB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BOC=50°,∴∠AOD=50°,∴∠AOE=100°,∠EOB=180°-100°=80°,故选D.", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["50°", "60°", "70°", "80°"], "choices": [50.0, 60.0, 70.0, 80.0], "label": 3}
-{"prob_id": 1459, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1459.png", "question": "如图一棵大树在离地面9米高的B处断裂,树顶A落在离树底部C的12米处,则大树断裂之前的高度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "由题意得BC=91AC=12,在直角三角形ABC中1根据勾股定理得:AB=√{9²+12²}=15米所以大树的高度是15+9=24米,故选D.", "dataset_name": "Geoqa", "ground_truth": "24.0", "org_choices": ["9米", "15米", "21米", "24米"], "choices": [9.0, 15.0, 21.0, 24.0], "label": 3}
-{"prob_id": 1468, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1468.png", "question": "如图,过⊙O上一点A作⊙O的切线,交直径BC的延长线与点D,连接AB,若∠B=25°,则∠D的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OA∵∠B=25°.∴∠DOA=2∠B=50°.∵AD是⊙的切线,∴∠OAD=90°.∴∠D=180°-90°-50°=40°故选B.", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["25°", "40°", "45°", "50°"], "choices": [25.0, 40.0, 45.0, 50.0], "label": 1}
-{"prob_id": 1472, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1472.png", "question": "如图所示,将含有30°角的三角板(∠A=30°)的直角顶点放在相互平行的两条直线其中一条上,若∠1=38°,则∠2的度数(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图1延长AB交CF于E,∵∠ACB=90°,∠A=30°∴∠ABC=60°,∵∠1=38°,∴∠AEC=∠ABC-∠1=22°,∵GH||EF,∴∠2=∠AEC=22°故选B.", "dataset_name": "Geoqa", "ground_truth": "22.0", "org_choices": ["28°", "22°", "32°", "38°"], "choices": [28.0, 22.0, 32.0, 38.0], "label": 1}
-{"prob_id": 1484, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1484.png", "question": "如图,小明从点A向北偏东80°方向走到B点,又从B点向南偏西25°方向走到点C,则∠ABC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "|N_{2}B,如图,∠1=80°,∵N_{1}A||N_{2}A∴∠1=∠2+∠3=80^{°},∵∠3=25^{°},∴∠2=80^{°}-∠3=80^{°}-25^{°}=55^{°}即∠ABC=55°故选A.", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["55°", "50°", "45°", "40°"], "choices": [55.0, 50.0, 45.0, 40.0], "label": 0}
-{"prob_id": 1485, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/1485.png", "question": "如图,已知直线AB,CD相交于点O,OE⊥AB,∠EOC=30°,则∠BOD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:因为OE⊥AB,∠EOC=30°,所以∠COB=90°-30°=60°,因为∠COB+∠BOD=180°,所以∠BOD=180-60°=120°,故选C.", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["60°", "30°", "120°", "150°"], "choices": [60.0, 30.0, 120.0, 150.0], "label": 2}
-{"prob_id": 7034, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7034.png", "question": "某几何体的三视图如图所示,其中主视图和左视图均为边长为2的等边三角形,则该几何体的表面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由三视图可知:该几何体是一个圆锥,其轴截面是一个边长为2的正三角形．S~表面积~=S~圆锥侧面积~+S~圆~=\\frac{1}{2}×2π×1×2+π×1²=3π．故选:B．", "dataset_name": "Geoqa", "ground_truth": "9.42477796076938", "org_choices": ["4π", "3π", "2π", "π"], "choices": [12.566, 9.425, 6.283, 3.142], "label": 1}
-{"prob_id": 7065, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7065.png", "question": "如图,在直角三角形ABC中,∠C=90°,AB=5,AC=4,则sin∠B的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在直角三角形ABC中,∠C=90°,AB=5,AC=4,∴sin∠B=AC:AB=4:5．故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.8", "org_choices": ["\\frac{3}{5}", "\\frac{4}{5}", "\\frac{3}{4}", "\\frac{4}{3}"], "choices": [0.6, 0.8, 0.75, 1.333], "label": 1}
-{"prob_id": 7100, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7100.png", "question": "如图,在Rt△ABC中,∠C为直角,CD⊥AB于D,已知AC=3,AB=5,则tan∠BCD等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠C为直角,CD⊥AB,∴∠A+∠B=90°,∠BCD+∠B=90°,∴∠BCD=∠A,∵∠C为直角,AC=3,AB=5,∴BC=√{AB²-AC²}=4,∴tanA=\\frac{4}{3},∴tan∠BCD=\\frac{4}{3},故选:B．", "dataset_name": "Geoqa", "ground_truth": "1.3333333333333333", "org_choices": ["\\frac{3}{4}", "\\frac{4}{3}", "\\frac{3}{5}", "\\frac{4}{5}"], "choices": [0.75, 1.333, 0.6, 0.8], "label": 1}
-{"prob_id": 7124, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7124.png", "question": "如图,在△ABC中,DE∥BC,若AD=3,DB=6,DE=2.5,则BC长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴△ADE∽△ABC．∴\\frac{AD}{AB}=\\frac{DE}{BC},即\\frac{3}{9}=\\frac{2.5}{BC},解得BC=7.5．故选:C．", "dataset_name": "Geoqa", "ground_truth": "7.5", "org_choices": ["5", "5.5", "7.5", "10"], "choices": [5.0, 5.5, 7.5, 10.0], "label": 2}
-{"prob_id": 7141, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7141.png", "question": "如图,在Rt△ABC中,∠BAC=90°,AB=3,AC=4,点P为BC上任意一点,连接PA,以PA,PC为邻边作平行四边形PAQC,连接PQ,则PQ的最小值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BAC=90°,AB=3,AC=4,∴BC=√{AC²+AB²}=5,∵四边形APCQ是平行四边形,∴PO=QO,CO=AO,∵PQ最短也就是PO最短,∴过O作BC的垂线OP′,∵∠ACB=∠P′CO,∠CP′O=∠CAB=90°,∴△CAB∽△CP′O,∴\\frac{CO}{BC}=\\frac{OP'}{AB},∴\\frac{2}{5}=\\frac{OP'}{3},∴OP′=\\frac{6}{5},∴则PQ的最小值为2OP′=\\frac{12}{5},故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.4", "org_choices": ["\\frac{6}{5}", "\\frac{12}{5}", "\\frac{5}{3}", "2"], "choices": [1.2, 2.4, 1.667, 2.0], "label": 1}
-{"prob_id": 7161, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7161.png", "question": "如图,AB∥CD,AB=6,CD=9,AD=10,则OD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB∥CD,∴△AOB∽△DOC,∴\\frac{AB}{CD}=\\frac{AO}{OD},∵AB=6,CD=9,AD=10,∴\\frac{6}{9}=\\frac{10-OD}{OD},∴OD=6,故选:C．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["4", "5", "6", "7"], "choices": [4.0, 5.0, 6.0, 7.0], "label": 2}
-{"prob_id": 7165, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7165.png", "question": "如图,在△ABC中,DE∥BC,分别交AB,AC于点D,E．若AD=2,DB=3,BC=6,则DE的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AD=2,DB=3,∴AB=5,∵DE∥BC,∴△ADE∽△ABC,∴\\frac{AD}{AB}=\\frac{DE}{BC},∴\\frac{2}{5}=\\frac{DE}{6},∴DE=\\frac{12}{5},故选:C．．", "dataset_name": "Geoqa", "ground_truth": "2.4", "org_choices": ["4", "2.5", "\\frac{12}{5}", "10"], "choices": [4.0, 2.5, 2.4, 10.0], "label": 2}
-{"prob_id": 7185, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7185.png", "question": "如图,AB为⊙O的直径,C为⊙O上一点,弦AD平分∠BAC,交BC于点E,AB=6,AD=5,则DE的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图1,连接BD、CD,∵AB为⊙O的直径,∴∠ADB=90°,∴BD=√{AB²-AD²}=√{6²-5²}=√{11},∵弦AD平分∠BAC,∴CD=BD=√{11},∴∠CBD=∠DAB,在△ABD和△BED中,≥ft\\{\\begin{matrix}∠BAD=∠EBD\\\\∠ADB=∠BDE\\\\\\end{matrix}\\right.\\∴△ABD∽△BED,∴\\frac{DE}{DB}=\\frac{DB}{AD},即\\frac{DE}{√{11}}=\\frac{√{11}}{5},解得DE=\\frac{11}{5}．故选:A．", "dataset_name": "Geoqa", "ground_truth": "2.2", "org_choices": ["2.2", "2.5", "2", "1.8"], "choices": [2.2, 2.5, 2.0, 1.8], "label": 0}
-{"prob_id": 7190, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7190.png", "question": "如图,在△ABC中,DE∥BC,\\frac{AD}{DB}=\\frac{1}{2},DE=4,则BC的长(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴△ADE∽△ABC,∴\\frac{DE}{BC}=\\frac{AD}{AB},∵\\frac{AD}{DB}=\\frac{1}{2},∴\\frac{AD}{AB}=\\frac{1}{3},∴\\frac{DE}{BC}=\\frac{1}{3},∵DE=4,∴BC=12．故选:C．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["8", "10", "12", "16"], "choices": [8.0, 10.0, 12.0, 16.0], "label": 2}
-{"prob_id": 7198, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7198.png", "question": "如图,AD•AB=AE•AC,∠ADE=80°,∠A=60°,则∠B=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AD•AB=AE•AC,∴\\frac{AD}{AC}=\\frac{AE}{AB},且∠A为公共角,∴△ADE∽△ACB,∴∠C=∠ADE=80°,∴∠B=180°-∠A-∠C=180°-60°-80°=40°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "60°", "80°", "100°"], "choices": [40.0, 60.0, 80.0, 100.0], "label": 0}
-{"prob_id": 7217, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7217.png", "question": "如图,DC∥EF∥AB,若\\frac{EG}{AB}=\\frac{1}{2},DC=6,则GF的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵EF∥AB,∴△DEG∽△DAB,∴\\frac{DG}{DB}=\\frac{EG}{AB}=\\frac{1}{2},即点G为DB的中点,∵DC∥EF,点G为DB的中点,∴GF=\\frac{1}{2}CD=3,故选:B．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["2", "3", "4", "1.5"], "choices": [2.0, 3.0, 4.0, 1.5], "label": 1}
-{"prob_id": 7219, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7219.png", "question": "如右图,△ABC中,DE∥BC,\\frac{AD}{AB}=\\frac{2}{5},DE=3,则BC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴△ADE∽△ABC,∴\\frac{DE}{BC}=\\frac{AD}{AB}=\\frac{2}{5},∴BC=\\frac{5}{2}DE=\\frac{5}{2}×3=\\frac{15}{2}．故选:A．", "dataset_name": "Geoqa", "ground_truth": "7.5", "org_choices": ["7.5", "4.5", "8", "6"], "choices": [7.5, 4.5, 8.0, 6.0], "label": 0}
-{"prob_id": 7220, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7220.png", "question": "如图,在平行四边形ABCD中,E为BC的中点,AE、BD相交于点F．若△BFE的面积为3,则△ABF的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD为平行四边形,∴AD∥BC,AD=BC,∴△AFD∽△EFB,∴\\frac{AF}{EF}=\\frac{AD}{BE},而E为BC的中点,∴BE=\\frac{1}{2}BC=\\frac{1}{2}AD,∴\\frac{AF}{EF}=2,∴\\frac{S_{\\bigtriangleupBAF}}{S_{\\bigtriangleupBEF}}=\\frac{AF}{EF}=2,∴S~△ABF~=2S~△BFE~=6．故选:B．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["3", "6", "9", "12"], "choices": [3.0, 6.0, 9.0, 12.0], "label": 1}
-{"prob_id": 7224, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7224.png", "question": "如图,△ABC中,D、E分别为AB、AC的中点,已知△ADE的面积为1,那么△ABC的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵D、E分别是AB、AC的中点,∴DE是△ABC的中位线,∴DE∥BC,\\frac{DE}{BC}=\\frac{1}{2},∴△ADE∽△ABC,∴\\frac{S_{\\bigtriangleupADE}}{S_{\\bigtriangleupABC}}=(\\frac{1}{2})²=\\frac{1}{4},∵△ADE的面积为1,∴S~△ABC~=4．故选:C．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["2", "3", "4", "5"], "choices": [2.0, 3.0, 4.0, 5.0], "label": 2}
-{"prob_id": 7250, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7250.png", "question": "如图,已知AB、CD、EF互相平行,且AB=1,CD=4,那么EF的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB、CD、EF都与BD垂直,∴AB∥CD∥EF,∴△DEF∽△DAB,△BEF∽△BCD,∴\\frac{EF}{AB}=\\frac{DF}{DB},\\frac{EF}{CD}=\\frac{BF}{BD},∴\\frac{EF}{AB}+\\frac{EF}{CD}=\\frac{DF}{DB}+\\frac{BF}{BD}=\\frac{BD}{BD}=1．∵AB=1,CD=4,∴\\frac{EF}{1}+\\frac{EF}{4}=1,∴EF=\\frac{4}{5}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "0.8", "org_choices": ["\\frac{1}{3}", "\\frac{2}{3}", "\\frac{3}{4}", "\\frac{4}{5}"], "choices": [0.333, 0.667, 0.75, 0.8], "label": 3}
-{"prob_id": 7251, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7251.png", "question": "如图,在△ABC中,DE∥BC,分别交AB,AC于点D,E．若AE=3,EC=6,则\\frac{DE}{BC}的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵△ABC中,DE∥BC,∴\\frac{DE}{BC}=\\frac{AE}{AC}=\\frac{AE}{AE+EC}=\\frac{3}{3+6}=\\frac{1}{3},故选:D．", "dataset_name": "Geoqa", "ground_truth": "0.3333333333333333", "org_choices": ["\\frac{1}{9}", "\\frac{1}{6}", "\\frac{1}{4}", "\\frac{1}{3}"], "choices": [0.111, 0.167, 0.25, 0.333], "label": 3}
-{"prob_id": 7259, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7259.png", "question": "如图,BE,CF为△ABC的两条高,若AB=6,BC=5,EF=3,则AE的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BE,CF为△ABC的两条高,∴∠AEB=∠AFC=90°,∵∠A=∠A,∴△AEB∽△AFC,∴\\frac{AE}{AF}=\\frac{AB}{AC},∵∠A=∠A,∴△AEF∽△ABC,∴\\frac{EF}{BC}=\\frac{AE}{AB},∵AB=6,BC=5,EF=3,∴\\frac{3}{5}=\\frac{AE}{6},∴AE=\\frac{18}{5},故选:A．", "dataset_name": "Geoqa", "ground_truth": "3.6", "org_choices": ["\\frac{18}{5}", "4", "\\frac{21}{5}", "\\frac{24}{5}"], "choices": [3.6, 4.0, 4.2, 4.8], "label": 0}
-{"prob_id": 7302, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7302.png", "question": "如图,长4m的楼梯AB的倾斜角∠ABD为60°,为了改善楼梯的安全性能,准备重新建造楼梯,使其倾斜角∠ACD为45°,则调整后的楼梯AC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在Rt△ABD中,∵sin∠ABD=\\frac{AD}{AB},∴AD=4sin60°=2√{3}(m),在Rt△ACD中,∵sin∠ACD=\\frac{AD}{AC},∴AC=\\frac{2√{3}}{sin45{^°}}=2√{6}(m)．故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.898979485566356", "org_choices": ["2√{3}m", "2√{6}m", "(2√{3}-2)m", "(2√{6}-2)m"], "choices": [3.464, 4.899, 1.464, 2.899], "label": 1}
-{"prob_id": 7303, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7303.png", "question": "如图是拦水坝的横断面,斜坡AB的水平宽度为12m,斜面坡度为1:2,则斜坡AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意可得,AC=12m,BC:AC=1:2,∴BC=6m,又∵∠BCA=90°,∴AB=√{AC²+BC²}=√{12²+6²}=6√{5}m．故选:B．", "dataset_name": "Geoqa", "ground_truth": "13.416407864998739", "org_choices": ["4√{3}m", "6√{5}m", "12√{5}m", "24m"], "choices": [6.928, 13.416, 26.833, 24.0], "label": 1}
-{"prob_id": 7320, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7320.png", "question": "如图,在离地面高度5m处引拉线固定电线杆,拉线和地面成60°角,则拉线AC的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵CD⊥AB且CD=5,∠A=∠B=60°,∴AC=\\frac{CD}{sinA}=\\frac{5}{sin60{^°}}=\\frac{10√{3}}{3}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "5.773502691896257", "org_choices": ["10m", "\\frac{10√{3}}{3}m", "\\frac{5√{2}}{2}m", "5√{3}m"], "choices": [10.0, 5.774, 3.536, 8.66], "label": 1}
-{"prob_id": 7348, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7348.png", "question": "如图,在△ABC中,点D、E分别是AB、AC的中点,若△ADE的面积为4,则△ABC的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在△ABC中,点D、E分别是AB、AC的中点,∴DE∥BC,DE=\\frac{1}{2}BC,∴△ADE∽△ABC,∵\\frac{DE}{BC}=\\frac{1}{2},∴\\frac{S_{\\bigtriangleupADE}}{S_{\\bigtriangleupABC}}=\\frac{1}{4},∵△ADE的面积为4,∴△ABC的面积为:16,故选:D．", "dataset_name": "Geoqa", "ground_truth": "16.0", "org_choices": ["8", "12", "14", "16"], "choices": [8.0, 12.0, 14.0, 16.0], "label": 3}
-{"prob_id": 7354, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7354.png", "question": "如图,矩形ABCD中,AB=4,BC=2,点M在BC上,连接AM,作∠AMN=∠AMB,点N在直线AD上,MN交CD于点E,则BM•AN的最大值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作NH⊥AM于点H,如右图所示,则∠NHM=90°,∵在矩形ABCD中,AB=4,BC=2,点M在BC上,∠AMN=∠AMB,∴AC=2√{5},AD∥BC,∴∠DAM=∠AMB,∴∠DAM=∠AMN,∴△AMN是等腰三角形,∴AN=MN,AH=MH,∵∠ABM=∠NHM=90°,∠AMB=∠NMH,∴△ABM∽△NHM,∴\\frac{BM}{HM}=\\frac{AM}{MN},∴BM•MN=AM•HM,∵点M在边BC上,AM=2HM,∴AM的最大值是AM=AC,此时AM=2√{5},∴BM•MN的最大值是:2√{5}\\cdot√{5}=10,∵MN=AN,∴BM•AN的最大值是10,故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["\\frac{17}{2}", "10", "17", "20"], "choices": [8.5, 10.0, 17.0, 20.0], "label": 1}
-{"prob_id": 7398, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7398.png", "question": "如图,△ABC中,∠ACB=90°,CD⊥AB于D,CD=4,BC=5,则AC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∠ACB=90°,CD⊥AB于D,CD=4,BC=5,由勾股定理得:BD=√{BC²-CD²}=√{5²-4²}=3,∵∠ACB=90°,CD⊥AB于D,∴∠B=90°-∠BCD=∠ACD,∠BDC=∠ADC,∴△BDC∽△CDA,∴\\frac{BC}{AC}=\\frac{BD}{CD},即\\frac{5}{AC}=\\frac{3}{4},解得:AC=\\frac{20}{3},故选:D．", "dataset_name": "Geoqa", "ground_truth": "6.666666666666667", "org_choices": ["3", "4", "\\frac{16}{3}", "\\frac{20}{3}"], "choices": [3.0, 4.0, 5.333, 6.667], "label": 3}
-{"prob_id": 7429, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7429.png", "question": "如图,△ABC中有一正方形DEFG,其中D在AC上,E、F在AB上,直线AG分别交DE、BC于M、N两点．若∠B=90°,AB=8,BC=6,EF=2,则BN的长度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形DEFG为正方形,∴∠AED=∠AFG=∠B=90°．∵∠DAE=∠CAB,∠GAF=∠NAB,∴△DAE∽△CAB,△GAF∽△NAB．∵AB=8,BC=6,EF=2,∴\\frac{AE}{AB}=\\frac{DE}{CB},即\\frac{AE}{8}=\\frac{2}{6},∴AE=\\frac{8}{3},∴AF=AE+EF=\\frac{14}{3}．∵△GAF∽△NAB,∴\\frac{BN}{GF}=\\frac{AB}{AF},即\\frac{BN}{2}=\\frac{8}{\\frac{14}{3}},∴BN=\\frac{24}{7}．故选:C．", "dataset_name": "Geoqa", "ground_truth": "3.4285714285714284", "org_choices": ["\\frac{8}{3}", "\\frac{16}{5}", "\\frac{24}{7}", "\\frac{7}{2}"], "choices": [2.667, 3.2, 3.429, 3.5], "label": 2}
-{"prob_id": 7462, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/7462.png", "question": "如图,在△ABC中,点D,E分别为边AB,AC上的点,且DE∥BC,若AD=5,BD=10,DE=3,则BC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AD=5,BD=10,∴AB=15,∵DE∥BC,∴△ADE∽△ABC,∴\\frac{AD}{AB}=\\frac{DE}{BC},即\\frac{5}{15}=\\frac{3}{BC},∴BC=9,故选:C．", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["3", "6", "9", "12"], "choices": [3.0, 6.0, 9.0, 12.0], "label": 2}
-{"prob_id": 8501, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8501.png", "question": "如图,△ABC内接于⊙O,∠BAC=120°,AB=AC,BD为⊙O的直径,AB=3,则AD的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BAC=120°,AB=AC,∴∠ACB=30°,∴∠ACB=∠ADB=30°,∵BD是⊙O的直径,∴∠BAD=90°,∵AB=3,∴AD=\\frac{AB}{tan30°}=\\frac{3}{\\frac{√{3}}{3}}=3√{3}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "5.196152422706632", "org_choices": ["6", "3√{5}", "5", "3√{3}"], "choices": [6.0, 6.708, 5.0, 5.196], "label": 3}
-{"prob_id": 8505, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8505.png", "question": "如图,在⊙O中,∠ABC=130°,则∠AOC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∠1=2∠ABC=2×130°=260°,则∠AOC=360°-∠1=360°-260°=100°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["50°", "80°", "90°", "100°"], "choices": [50.0, 80.0, 90.0, 100.0], "label": 3}
-{"prob_id": 8522, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8522.png", "question": "如图,AC、BC是两个半圆的直径,∠ACP=30°,若AB=20cm,则PQ的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BQ,AP,如图,∵AC,BC为直径,∴∠APC=90°,∠BQC=90°,∵∠ACP=30°,∴PC=\\frac{√{3}}{2}AC,CQ=\\frac{√{3}}{2}BC,∴PQ=PC-CQ=\\frac{√{3}}{2}(AC-BC)=\\frac{√{3}}{2}AB=\\frac{√{3}}{2}×20=10√{3}(cm)．故选:B．", "dataset_name": "Geoqa", "ground_truth": "17.320508075688775", "org_choices": ["10cm", "10√{3}cm", "12cm", "16cm"], "choices": [10.0, 17.321, 12.0, 16.0], "label": 1}
-{"prob_id": 8523, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8523.png", "question": "如图,四边形ABCD中,AB=AC=AD,∠CBD=23°,则∠CAD为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD中,AB=AC=AD,∴B、C、D三点在以A为圆心,AD为半径的圆上．∵∠CBD=23°,∴∠CAD=2∠CBD=46°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "46.0", "org_choices": ["47°", "46°", "45°", "44°"], "choices": [47.0, 46.0, 45.0, 44.0], "label": 1}
-{"prob_id": 8524, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8524.png", "question": "如图,⊙O是△ABC的外接圆,∠BCO=40°,则∠A的度数等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OC=OB,∠BCO=40°,∴∠OBC=40°,∴∠BOC=180°-40°-40°=100°,∴∠A=100°×\\frac{1}{2}=$50°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["60°", "50°", "45°", "40°"], "choices": [60.0, 50.0, 45.0, 40.0], "label": 1}
-{"prob_id": 8528, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8528.png", "question": "如图,A、B、C是⊙O上的三个点,∠ABC=25°,则∠AOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ABC=25°,∠AOC=2∠ABC,∴∠AOC=50°,故选:D．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["25°", "30°", "40°", "50°"], "choices": [25.0, 30.0, 40.0, 50.0], "label": 3}
-{"prob_id": 8535, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8535.png", "question": "如图,A、B、C是⊙O上的点,∠ACB=32°,则∠AOB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠AOB与∠ACB都对⁀{AB},∠ACB=32°,∴∠AOB=2∠ACB=64°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "64.0", "org_choices": ["16°", "64°", "148°", "32°"], "choices": [16.0, 64.0, 148.0, 32.0], "label": 1}
-{"prob_id": 8538, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8538.png", "question": "如图,点A、B、C在⊙O上,若∠ABC=35°,则∠AOC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵点A、B、C在⊙O上,∠ABC=35°,∴∠AOC=2∠ABC=70°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["20°", "40°", "60°", "70°"], "choices": [20.0, 40.0, 60.0, 70.0], "label": 3}
-{"prob_id": 8579, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8579.png", "question": "如图,点A,B,C在⊙O上,连接AB,AC,若∠BOC=100°,则∠B+∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作直径AD,如图所示,∵OA=OB=OC,∴∠B=∠BAO,∠C=∠CAO,∵∠BOD=∠B+∠BAO∴∠BOD=2∠B,∵∠COD=∠C+∠CAO∴∠COD=2∠C,∵∠BOD+∠COD=∠BOC=100°,即2∠B+2∠C=100°,∴∠B+∠C=50°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["25°", "50°", "100°", "无法计算"], "choices": [25.0, 50.0, 100.0], "label": 1}
-{"prob_id": 8589, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8589.png", "question": "如图,将直角三角板45°角的顶点放在圆心O上,斜边和一直角边分别与⊙O相交于A、B两点,C是优弧AB上任意一点(与A、B不重合),则∠ACB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠AOB=45°,∴∠ACB=\\frac{1}{2}∠AOB=22.5°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "22.5", "org_choices": ["30°", "22.5°", "90°", "15°"], "choices": [30.0, 22.5, 90.0, 15.0], "label": 1}
-{"prob_id": 8590, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8590.png", "question": "如图,线段AB是⊙O的直径,弦CD丄AB,∠CAB=20°,则∠AOD等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵线段AB是⊙O的直径,弦CD丄AB,∴⁀{CB}=⁀{BD},∵∠CAB=20°,∴∠BOD=40°,∴∠AOD=140°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["160°", "150°", "140°", "120°"], "choices": [160.0, 150.0, 140.0, 120.0], "label": 2}
-{"prob_id": 8596, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8596.png", "question": "如图,▱ABCD的顶点A、B、D在⊙O上,顶点C在⊙O的直径BE上,连接AE,∠E=36°,则∠ADC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BE是直径,∴∠BAE=90°,∵四边形ABCD是平行四边形,∠E=36°,∴∠BEA=∠DAE=36°,∴∠BAD=126°,∴∠ADC=54°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "54.0", "org_choices": ["44°", "54°", "72°", "53°"], "choices": [44.0, 54.0, 72.0, 53.0], "label": 1}
-{"prob_id": 8625, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8625.png", "question": "量角器的直径与直角三角板ABC的斜边AB重合,其中量角器O刻度线的端点N与点A重合,射线CP从CA处出发沿顺时针方向以每秒3度的速度旋转,CP与量角器的半圆弧交于点E,当第20秒时,点E在量角器上对应的读数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OE,∵射线CP从CA处出发沿顺时针方向以每秒3度的速度旋转,∴第20秒时,∠ACE=3°×20=60°,∵∠ACB=90°,∴点C在以AB为直径的圆上,即点C在⊙O上,∴∠EOA=2∠ECA=2×60°=120°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["150°", "120°", "75°", "60°"], "choices": [150.0, 120.0, 75.0, 60.0], "label": 1}
-{"prob_id": 8627, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8627.png", "question": "如图,A、B、C三点在⊙O上,且∠ABO=50°,则∠ACB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA=OB,∴∠BAO=∠ABO=50°,∴∠AOB=180°-50°-50°=80°,∴∠ACB=\\frac{1}{2}∠AOB=40°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["100°", "80°", "50°", "40°"], "choices": [100.0, 80.0, 50.0, 40.0], "label": 3}
-{"prob_id": 8640, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8640.png", "question": "AB为⊙O的直径,点C在⊙O上,若∠C=15°,则∠BOC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA=OC,∴∠A=∠C=15°；∴∠BOC=2∠A=30°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["60°", "45°", "30°", "15°"], "choices": [60.0, 45.0, 30.0, 15.0], "label": 2}
-{"prob_id": 8650, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8650.png", "question": "如图,圆内的两条弦AB、CD相交于E,∠D=35°,∠AEC=105°,则∠C=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠D=35°,∠AEC=105°,∴∠A=∠AEC-∠D=70°,∴∠C=∠A=70°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["60°", "70°", "80°", "85°"], "choices": [60.0, 70.0, 80.0, 85.0], "label": 1}
-{"prob_id": 8651, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8651.png", "question": "如图,AB、CD是⊙O的两条弦,连结AD、BC．若∠BCD=70°,则∠BAD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BCD=70°,∴∠BAD=∠BCD=70°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["40°", "50°", "60°", "70°"], "choices": [40.0, 50.0, 60.0, 70.0], "label": 3}
-{"prob_id": 8652, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8652.png", "question": "如图,A、B、C在⊙O上,若∠BAC=24°,则∠BOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BAC=24°,∴∠BOC的=2∠BAC=48°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "48.0", "org_choices": ["12°", "24°", "48°", "84°"], "choices": [12.0, 24.0, 48.0, 84.0], "label": 2}
-{"prob_id": 8653, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8653.png", "question": "如图,点A,B,C都在⊙O上,若∠C=34°,则∠AOB为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠C=34°,∴∠AOB=2∠C=68°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "68.0", "org_choices": ["34°", "56°", "60°", "68°"], "choices": [34.0, 56.0, 60.0, 68.0], "label": 3}
-{"prob_id": 8658, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8658.png", "question": "如图,直径为10的⊙A经过点C(0,5)和点O(0,0),B是y轴右侧⊙A优弧上一点,则∠OBC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设⊙A与x轴交于另一点D,连接CD,∵∠COD=90°,∴CD是⊙A的直径,且CD=10,∵点C(0,5)和点O(0,0),∴OC=5,∴sin∠ODC=\\frac{OC}{CD}=\\frac{1}{2},∴∠ODC=30°,∴∠OBC=∠ODC=30°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["30°", "40°", "50°", "60°"], "choices": [30.0, 40.0, 50.0, 60.0], "label": 0}
-{"prob_id": 8662, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8662.png", "question": "如图,△ABC内接于⊙O,∠A=15°,连接OB,则∠OBC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵连接OC,∵△ABC内接于⊙O,∠A=15°,∴∠BOC=2∠A=30°,∵OB=OC,∴∠OBC=∠OCB=\\frac{180°-∠BOC}{2}=75°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "75.0", "org_choices": ["30°", "60°", "65°", "75°"], "choices": [30.0, 60.0, 65.0, 75.0], "label": 3}
-{"prob_id": 8685, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8685.png", "question": "如图,在⊙O中,∠ABC=40°,则∠AOC=()度．. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在⊙O中,∠ABC=40°,∴∠AOC=2∠ABC=80°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["40", "20", "80", "50"], "choices": [40.0, 20.0, 80.0, 50.0], "label": 2}
-{"prob_id": 8686, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8686.png", "question": "如图,A、B、C、是⊙O上的三点,且∠CAO=25°,∠BCO=35°,则∠AOB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:延长CO交⊙O于点D,∵∠BCO=35°,∴∠BOD=70°．∵∠CAO=25°,CO=OA,∴∠ACO=∠CAO=25°,∴∠AOD=2∠ACO=50°,∴∠AOB=50°+70°=120°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["100°", "110°", "120°", "130°"], "choices": [100.0, 110.0, 120.0, 130.0], "label": 2}
-{"prob_id": 8688, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8688.png", "question": "如图,AB为⊙O的直径,弦CD⊥AB,E为⁀{BC}上一点,若∠CEA=28°,则∠ABD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB为直径,弦CD⊥AB,∴⁀{AC}=⁀{AD},∴∠ABD=∠CEA=28°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "28.0", "org_choices": ["14°", "28°", "56°", "无法确定"], "choices": [14.0, 28.0, 56.0], "label": 1}
-{"prob_id": 8692, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8692.png", "question": "如图所示,⊙O是△ABC的外接圆,已知∠B=70°,则∠CAO的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:延长AO交圆于点D,连接CD,如图所示,∵AD是直径,∴∠ACD=90°,∵∠D=∠B,∠B=70°,∴∠D=70°,∵∠ACD+∠D+∠CAO=180°,∴∠CAO=180°-70°-90°=20°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["20°", "30°", "35°", "40°"], "choices": [20.0, 30.0, 35.0, 40.0], "label": 0}
-{"prob_id": 8706, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8706.png", "question": "如图,⊙O是△ABC的外接圆,∠OCB=30°,则∠A的度数等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OB=OC,∴∠OBC=∠OCB=30°,∴∠BOC=180°-30°-30°=120°,∴∠A=\\frac{1}{2}∠BOC=60°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["60°", "50°", "40°", "30°"], "choices": [60.0, 50.0, 40.0, 30.0], "label": 0}
-{"prob_id": 8711, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8711.png", "question": "如图,⊙O是△ABC的外接圆,AB是直径,若∠BOC=70°,则∠A等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB是直径,∠BOC=70°,∴∠A=\\frac{1}{2}∠BOC=35°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["35°", "45°", "40°", "30°"], "choices": [35.0, 45.0, 40.0, 30.0], "label": 0}
-{"prob_id": 8712, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8712.png", "question": "如图,在⊙O中,直径AB=5cm,弦AC=4cm,则点O到直线AC的距离为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,过点C作CD⊥AB于点D,连接BC．则AD=CD,即点D是AC的中点．∵AB是⊙O的直径,∴∠ACB=90°．∴BC=√{AB^{2}-AC^{2}}∵AB=5cm,弦AC=4cm,∴BC=3cm．∵点O是AB的中点,∴OD=\\frac{1}{2}BC=1.5cm．故选:A．", "dataset_name": "Geoqa", "ground_truth": "1.5", "org_choices": ["1.5cm", "2cm", "2.5cm", "3cm"], "choices": [1.5, 2.0, 2.5, 3.0], "label": 0}
-{"prob_id": 8718, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8718.png", "question": "如图,AB是⊙O的直径,若∠BAC=35°,则∠ADC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB为⊙O直径,∴∠ACB=90°,∵∠BAC=35°,∴∠B=90°-35°=55°,∴∠D=∠B=55°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["110°", "70°", "55°", "35°"], "choices": [110.0, 70.0, 55.0, 35.0], "label": 2}
-{"prob_id": 8724, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8724.png", "question": "一副直角三角板如图放置(∠ACB=∠ADB=90°),∠CAB=30°,∠BAD=45°,AB交CD于E,则∠CEB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ADB=90°,∠DAB=45°,∴△DAB是等腰直角三角形,∴∠DAB=∠ABD=45°；由于∠ACB=∠ADB=90°,所以A、C、B、D四点共圆,且直径为AB；由圆周角定理知:∠ACD=∠ABD=45°；△ACE中,外角∠CEB=∠CAB+∠ACD=30°+45°=75°；故选:D．", "dataset_name": "Geoqa", "ground_truth": "75.0", "org_choices": ["30°", "45°", "60°", "75°"], "choices": [30.0, 45.0, 60.0, 75.0], "label": 3}
-{"prob_id": 8727, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8727.png", "question": "如下图,点C在以AB为直径的半圆O上,∠BAC=20°,则∠BOC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:根据圆周角定理,得∠BOC=2∠BAC=40°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["20°", "30°", "40°", "50°"], "choices": [20.0, 30.0, 40.0, 50.0], "label": 2}
-{"prob_id": 8738, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8738.png", "question": "如图,AB为⊙O直径,∠ABC=25°,则∠D的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB为⊙O直径,∴∠ACB=90°,∵∠ABC=25°,∴∠CAB=90°-25°=65°,∴∠D=∠CAB=65°．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["70°", "75°", "60°", "65°"], "choices": [70.0, 75.0, 60.0, 65.0], "label": 3}
-{"prob_id": 8742, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8742.png", "question": "如图,△ABC是⊙O的内接三角形,BD为直径,若∠DBC=18°,则∠A的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接OC．∵OB=OC,∴∠DBC=∠OCB=18°,∴∠BOC=180°-2∠DBC=144°,∴∠A=\\frac{1}{2}∠BOC=72°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "72.0", "org_choices": ["36°", "72°", "60°", "无法确定"], "choices": [36.0, 72.0, 60.0], "label": 1}
-{"prob_id": 8753, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8753.png", "question": "如图,AB、CD是⊙O的弦,且AB∥CD,若∠BAD=36°,则∠AOC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB∥CD,∴∠ADC=∠BAD=36°,∴∠AOC=2∠ADC=2×36°=72°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "72.0", "org_choices": ["36°", "54°", "72°", "90°"], "choices": [36.0, 54.0, 72.0, 90.0], "label": 2}
-{"prob_id": 8754, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8754.png", "question": "如图,A、B、C是⊙O上的三个点,若∠C=35°,则∠OAB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠AOB与∠C是同弧所对的圆心角与圆周角,∴∠AOB=2∠C=2×35°=70°,∵OA=OB,∴∠OAB=∠OBA=\\frac{180{^°}-∠AOB}{2}=\\frac{180{^°}-70{^°}}{2}=55°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["35°", "55°", "65°", "70°"], "choices": [35.0, 55.0, 65.0, 70.0], "label": 1}
-{"prob_id": 8779, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8779.png", "question": "如图,▱ABCD的顶点A、B、D在⊙O上,顶点C在⊙O的直径BE上,∠ADC=54°,连接AE,则∠AEB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∠ADC=54°,∴∠B=∠ADC=54°,∵BE为⊙O的直径,∴∠BAE=90°,∴∠AEB=90°-∠B=90°-54°=36°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "36.0", "org_choices": ["36°", "46°", "27°", "63°"], "choices": [36.0, 46.0, 27.0, 63.0], "label": 0}
-{"prob_id": 8781, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8781.png", "question": "如图,CD是⊙O的直径,弦DE∥OA,若∠D的度数是50°,则∠A的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥OA,∠D=50°,∴∠AOD=∠D=50°,∴∠C=\\frac{1}{2}∠AOD=25°,∵OA=OC,∴∠A=∠C=25°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["25°", "30°", "40°", "50°"], "choices": [25.0, 30.0, 40.0, 50.0], "label": 0}
-{"prob_id": 8789, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8789.png", "question": "如图,已知⊙O是△ABC的外接圆,∠AOB=110°,则∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵⊙O是△ABC的外接圆,∠AOB=110°,∴∠C=\\frac{1}{2}∠AOB=\\frac{1}{2}×110°=55°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["55°", "70°", "60°", "45°"], "choices": [55.0, 70.0, 60.0, 45.0], "label": 0}
-{"prob_id": 8812, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8812.png", "question": "如图,AB是⊙O的直径,点C在⊙O上,若∠A=40°,则∠B的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB是⊙O的直径,∴∠C=90°,∵∠A=40°,∴∠B=90°-∠A=50°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["80°", "60°", "50°", "40°"], "choices": [80.0, 60.0, 50.0, 40.0], "label": 2}
-{"prob_id": 8814, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8814.png", "question": "如图,若AB是⊙O的直径,CD是⊙O的弦,∠ABD=55°,则∠BCD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接AD,∵AB是⊙O的直径,∴∠ADB=90°,∵∠ABD=55°,∴∠A=90°-∠ABD=35°,∴∠BCD=∠A=35°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["35°", "45°", "55°", "75°"], "choices": [35.0, 45.0, 55.0, 75.0], "label": 0}
-{"prob_id": 8830, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8830.png", "question": "如图,点A、B、C是⊙O上的三点,∠BAC=40°,则∠BOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BAC=40°,∴∠BOC=2∠BAC=80°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["80°", "40°", "50°", "20°"], "choices": [80.0, 40.0, 50.0, 20.0], "label": 0}
-{"prob_id": 8839, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8839.png", "question": "如图,在半径为5的⊙O中,如果弦AB的长为8,那么它的弦心距OC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OA,在Rt△OAC中,OA=5,AC=4,根据勾股定理可得,OC=√{OA²-AC²}=√{5²-4²}=3．故选:B．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["2", "3", "4", "6"], "choices": [2.0, 3.0, 4.0, 6.0], "label": 1}
-{"prob_id": 8841, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8841.png", "question": "如图,点O是⊙O的圆心,点A、B、C在⊙O上,AO∥BC,∠AOB=40°,则∠OAC的度数等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠C=\\frac{1}{2}∠AOB=\\frac{1}{2}×40°=20°,又∵AO∥BC,∴∠OAC=∠C=20°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["40°", "60°", "50°", "20°"], "choices": [40.0, 60.0, 50.0, 20.0], "label": 3}
-{"prob_id": 8847, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8847.png", "question": "已知:如图,⊙O中直径AB垂直于弦CD,垂足为E,若AB=10,CD=6,则BE的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接OC,∵AB=10,∴半径OC=10÷2=5,∵CD=6,∴CE=6÷2=3,根据勾股定理OE=√{OC²-CE²}=√{5²-3²}=4,∴BE=5-4=1．故选:A．", "dataset_name": "Geoqa", "ground_truth": "1.0", "org_choices": ["1", "2", "3", "4"], "choices": [1.0, 2.0, 3.0, 4.0], "label": 0}
-{"prob_id": 8867, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8867.png", "question": "如图,⊙O的半径为10,AB为弦,OC⊥AB,垂足为E．如果CE=4,那么AB的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OA,∵半径OC⊥AB,∴AE=BE=\\frac{1}{2}AB,∵OC=10,CE=4,∴OE=6,在Rt△AOE中,AE=√{OA²-OE²}=√{10²-6²}=8,∴AB=2AE=16,故选:C．", "dataset_name": "Geoqa", "ground_truth": "16.0", "org_choices": ["8", "12", "16", "20"], "choices": [8.0, 12.0, 16.0, 20.0], "label": 2}
-{"prob_id": 8883, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8883.png", "question": "如图,正方形ABCD的边长为3,以CD为一边向CD两侧作等边三角形PCD和等边三角形QCD,那么PQ的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:根据题意可知△PDQ是等腰三角形,且DC垂直平分PQ,易得DE=1.5,DQ=3；在Rt△DEQ中QE=√{9-\\frac{9}{4}}=\\frac{3√{3}}{2},所以PQ=2QE=3√{3}；故选:C．", "dataset_name": "Geoqa", "ground_truth": "5.196152422706632", "org_choices": ["\\frac{3√{3}}{2}", "\\frac{2√{3}}{3}", "3√{3}", "6√{3}"], "choices": [2.598, 1.155, 5.196, 10.392], "label": 2}
-{"prob_id": 8893, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8893.png", "question": "如图,在正方形ABCD中,E是DC上一点,F为BC延长线上一点,∠BEC=70°,且△BCE≌△DCF．连接EF,则∠EFD的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是正方形,∴∠BCE=∠DCF=90°；由旋转的性质知:CE=CF,∠BEC=∠DFC=70°；则△ECF是等腰直角三角形,得∠EFC=45°,∴∠EFD=∠DFC-∠EFC=25°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["10°", "15°", "20°", "25°"], "choices": [10.0, 15.0, 20.0, 25.0], "label": 3}
-{"prob_id": 8923, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8923.png", "question": "如图,已知⊙O的半径为5mm,弦AB=8mm,则圆心O到AB的距离是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过O作OC⊥AB于C,∵OC过O,∴AC=BC=\\frac{1}{2}AB=4cm,在Rt△AOC中,由勾股定理得:OC=√{5²-4²}=3(cm),故选:C．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["1mm", "2mm", "3mm", "4mm"], "choices": [1.0, 2.0, 3.0, 4.0], "label": 2}
-{"prob_id": 8932, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8932.png", "question": "如图,MN切⊙O于点A,∠AOB=60°,那么∠BAM等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵MN切⊙O于点A,∴∠MAO=90°．∵∠AOB=60°,OB=OA,∴∠OAB=60°,∴∠BAM=30°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["120°", "90°", "60°", "30°"], "choices": [120.0, 90.0, 60.0, 30.0], "label": 3}
-{"prob_id": 8938, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8938.png", "question": "如图,从⊙O外一点P引圆的切线PA和PB,切点分别是A和B,如果∠APB=70°,那么这两条切线所夹劣弧AB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA和PB是切线,∴∠A=∠B=90°,∵∠APB=70°,∴∠AOB=180°-∠P=110°,∴劣弧AB的度数是110°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "110.0", "org_choices": ["110°", "70°", "55°", "35°"], "choices": [110.0, 70.0, 55.0, 35.0], "label": 0}
-{"prob_id": 8947, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8947.png", "question": "如图,PB切⊙O于点B,PO交⊙O于点E,延长PO交⊙O于点A,连结AB,⊙O的半径OD⊥AB于点C,BP=6,∠P=30°,则CD的长度是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接OB,∵PB切⊙O于点B,∴∠OBP=90°,∵BP=6,∠P=30°,∴∠POB=60°,OD=OB=BPtan30°=6×\\frac{√{3}}{3}=2√{3},∵OA=OB,∴∠OAB=∠OBA=30°,∵OD⊥AB,∴∠OCB=90°,∴∠OBC=30°,则OC=\\frac{1}{2}OB=√{3},∴CD=√{3},故选:C．", "dataset_name": "Geoqa", "ground_truth": "1.7320508075688772", "org_choices": ["\\frac{√{3}}{3}", "\\frac{√{3}}{2}", "√{3}", "2√{3}"], "choices": [0.577, 0.866, 1.732, 3.464], "label": 2}
-{"prob_id": 8950, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8950.png", "question": "如图,PA、PB分别切⊙O于A、B,点C和点D分别是线段PA、PB上的动点,并且CD始终保持与圆O相切,若PA=8cm,则△PCD的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA、PB分别切⊙O于A、B,∴PB=PA=8,∵CD切⊙O于E,∴CA=CE,DE=DB,∴△PCD的周长=PC+PD+CD=PC+PD+CE+DE=PA+PB=8+8=16(cm)．故选:C．", "dataset_name": "Geoqa", "ground_truth": "16.0", "org_choices": ["8", "12", "16", "不能确定"], "choices": [8.0, 12.0, 16.0], "label": 2}
-{"prob_id": 8952, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8952.png", "question": "如图,两个同心圆中,大圆的弦AB切小圆于点C,若AB=6,则圆环的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC,OA∵AB切小⊙O于C,∴OC⊥AB,∴AC=BC=\\frac{1}{2}AB=3,∠OCA=90°,由勾股定理得:OA²-OC²=AC²=9,∴圆环的面积是πOB²-πOC²=π(OA²-OC²)=9π,故选:A．", "dataset_name": "Geoqa", "ground_truth": "28.274333882308138", "org_choices": ["9π", "6π", "3π", "π"], "choices": [28.274, 18.85, 9.425, 3.142], "label": 0}
-{"prob_id": 8978, "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/Geoqa/image/8978.png", "question": "如图,正方形P、Q夹在ABCD框架中,正方形P下边一条边与AB夹角为15°,正方形P、Q有两个相邻边夹角为150°,则∠1为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,延长正方形P、Q的边相交于点E,过E作BC的平行线,过E作EM∥AB,则∠AED=360°-150°-90°-90°=30°,∵∠AED=∠1+∠EAG,∴∠1=∠AED-∠EAG=30°-15°=15°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "15.0", "org_choices": ["55°", "15°", "50°", "70°"], "choices": [55.0, 15.0, 50.0, 70.0], "label": 1}
+{"prob_id": 0, "image_path": "images/0.png", "question": "如图,在△ABC中,已知∠A=80°,∠B=60°,DE∥BC,那么∠CED的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠A+∠B+∠C=180°(三角形内角和定理),∠A=80°,∠B=60°,∴∠C=180°-∠A-∠B=180°-80°-60°=40°,又∵DE//BC,∴∠CED+∠C=180°(两直线平行,同旁内角互补).∴∠CED=180°-40°=140°.故选D.", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["40°", "60°", "120°", "140°"], "choices": [40.0, 60.0, 120.0, 140.0], "label": 3}
+{"prob_id": 1, "image_path": "images/1.png", "question": "如图,AB∥CD,直线EF交AB于点E,交CD于点F,EG平分∠BEF,交CD于点G,∠1=50°,则∠2等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵ABIICD,∴∠BEF+∠1=180°(两直线平行,同旁内角互补)∵∠1=50°,∴∠BEF=130°∵EG平分∠BEF,∴∠BEG=\\frac{1}{2}∠BEF=65°(角平分线的定义)5°(角平分线的定义)∴∠2=∠BEG=65°(两直线平行1内错角相等),故选C", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["50°", "60°", "65°", "90°"], "choices": [50.0, 60.0, 65.0, 90.0], "label": 2}
+{"prob_id": 101, "image_path": "images/101.png", "question": "如图,BD平分∠ABC,CD∥AB,若∠BCD=70°,则∠CDB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵CD//AB,∴∠BCD+CBA=180^{°},∴∠CBA=180°-70°=110°,∵BD平分∠ABC,∴∠ABD=\\frac{1}{2}∠CBA=55^{°},而AB//CD∴∠CDB=∠ABD=55^{°}.故选A.", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["55°", "50°", "45°", "30°"], "choices": [55.0, 50.0, 45.0, 30.0], "label": 0}
+{"prob_id": 103, "image_path": "images/103.png", "question": "如图,AB与⊙O相切于点B,AO的延长线交⊙O于点C,连接BC,若∠A=36°,则∠C等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB与⊙O相切于点B,∴∠ABO=90°,∵∠A=36°,∴∠BOA=54°∴由圆周角定理得:∠C=\\frac{1}{2}∠BOA=27^{°},故选D.", "dataset_name": "Geoqa", "ground_truth": "27.0", "org_choices": ["36°", "54°", "60°", "27°"], "choices": [36.0, 54.0, 60.0, 27.0], "label": 3}
+{"prob_id": 110, "image_path": "images/110.png", "question": "如图所示,直线a,b相交于点O,若∠1等于50°,则∠2等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵∠2与∠1是对顶角,∴∠2=∠1=50^{°}.故选A.", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["50°", "40°", "140°", "130°"], "choices": [50.0, 40.0, 140.0, 130.0], "label": 0}
+{"prob_id": 112, "image_path": "images/112.png", "question": "如图,AB//CD,EF分别为交AB,CD于点E,F,∠1=50°,则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:如答图,∵AB//C,∠1=50^{°}.∴∠3=∠1=50^{°}.∴∠2=180°-∠3=130°故选C.", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["50°", "120°", "130°", "150°"], "choices": [50.0, 120.0, 130.0, 150.0], "label": 2}
+{"prob_id": 120, "image_path": "images/120.png", "question": "如图,△ABC≌△ADE,若∠B=70°,∠C=30°,∠DAC=35°,则∠EAC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:∵∠B=70°,∠C=30°,∴∠BAC=180°-∠B-∠C=180^{°}-70^{°}-30^{°}=80^{°},∵△ABC≌△ADE,∴∠EAD=∠BAC=80°,∴∠EAC=∠EAD-∠DAC=80°-35°=45°,故选B.", "dataset_name": "Geoqa", "ground_truth": "45.0", "org_choices": ["40°", "45°", "35°", "25°"], "choices": [40.0, 45.0, 35.0, 25.0], "label": 1}
+{"prob_id": 121, "image_path": "images/121.png", "question": "如图,△ABC≌△DEF,点A与D,B与E分别是对应顶点,且测得BC=5cm,BF=7cm,则EC长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵△ABC≌△BAD∴EF=BC=5cm,∵BF=7cm,BC=5cm∴CF=EF-CF=3cm,故选C.", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["1cm", "2cm", "3cm", "4cm"], "choices": [1.0, 2.0, 3.0, 4.0], "label": 2}
+{"prob_id": 123, "image_path": "images/123.png", "question": "如图,在△ABC中,∠C=90°,AC=BC,AD平分∠CAB交BC于D,DE⊥AB于E,若AB=6cm,则△DBE的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AD平分∠CAB,AC⊥BC于点C,DE⊥AB于E,∴CD=DE.又∵AD=AD∴Rt△ACD≌Rt△AED,∴AC=AE.又∵AC=BC,∴△DBE的周长为DE+BD+EB=CD+BD+EB=BC+EB=AC+EB=AE+EB=AB=6故选A", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["6cm", "7cm", "8cm", "9cm"], "choices": [6.0, 7.0, 8.0, 9.0], "label": 0}
+{"prob_id": 150, "image_path": "images/150.png", "question": "如图,△ABC中,AB=AC,∠A=36°,AB的垂直平分线DE交AC于D,交AB于E,则∠BDC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵AB=AC,∠A=36°,∴∠ABC=∠C=\\frac{180^{°}-∠A}}{2}=\\frac{180^{°}-36^{°}}{2}=72^{°}∵DE垂直平分AB,∴∠A=∠ABD=36°,∴∠BDC=∠A+∠ABD=36^{°}+36^{°}=72^{°}.故选A.", "dataset_name": "Geoqa", "ground_truth": "72.0", "org_choices": ["72°", "36°", "60°", "82°"], "choices": [72.0, 36.0, 60.0, 82.0], "label": 0}
+{"prob_id": 159, "image_path": "images/159.png", "question": "如图,在△ABC中,∠C=36°,将△ABC绕点A逆时针旋转60°得到△AED,AD与BC交于点F,则∠AFC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:根据旋转图形可得∠FAC=60°,根据△AFC的内角和定理可得∠AFC=180°-36°-60°=84°.", "dataset_name": "Geoqa", "ground_truth": "84.0", "org_choices": ["84°", "80°", "60°", "90°"], "choices": [84.0, 80.0, 60.0, 90.0], "label": 0}
+{"prob_id": 165, "image_path": "images/165.png", "question": "如图,直线AB∥CD,Rt△DEF如图放置,∠EDF=90°,若∠1+∠F=70°,则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:根据∠1+∠F=70°以及三角形的外角的性质可得∠ABD=70°,根据AB//CD可得∠ABD+∠BDC=180°,则∠BDC=110°,根据∠EDF=90°可得∠2=110°-90°=20°.", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["20°", "25°", "30°", "40°"], "choices": [20.0, 25.0, 30.0, 40.0], "label": 0}
+{"prob_id": 167, "image_path": "images/167.png", "question": "如图,AB∥EF,CD⊥EF,∠BAC=50°,则∠ACD=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:如图,延长AC交EF于点G;∵AB//EF,∴∠DGC=∠BAC=50°;∵CD⊥EF,∴∠CDG=90°,∴∠ACD=90°+50°=140°,故选C.", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["120°", "130°", "140°", "150°"], "choices": [120.0, 130.0, 140.0, 150.0], "label": 2}
+{"prob_id": 186, "image_path": "images/186.png", "question": "如图,△ABC是⊙O的内接三角形,∠OAB=35°,则∠ACB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:根据OA=OB可得∠OBA=∠OAB=35°,则∠AOB=110°,根据圆的基本性质可得,∠ACB=\\frac{1}{2}∠AOB=55^{°}", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["35°", "55°", "60°", "70°"], "choices": [35.0, 55.0, 60.0, 70.0], "label": 1}
+{"prob_id": 188, "image_path": "images/188.png", "question": "将直尺和直角三角板按如图方式摆放(∠ACB为直角),已知∠1=30°,则∠2的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:先根据两角互余的性质求出∠3的度数,再由平行线的性质即可得出结论.∵∠1+∠3=90°,∠1=30°,∴∠3=60°.∵直尺的两边互相平行,∴∠2=∠3=60°.", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["30°", "45°", "60°", "65°"], "choices": [30.0, 45.0, 60.0, 65.0], "label": 2}
+{"prob_id": 194, "image_path": "images/194.png", "question": "如图,直线a与直线b被直线c所截,b⊥c,垂足为点A,∠1=70°．若使直线b与直线a平行,则可将直线b绕着点A顺时针旋转(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:∵b⊥c,∴∠2=90°.∵∠1=70°,a//b,∴直线b绕着点A顺时针旋转的度数=90°-70°=20°.故选D.", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["70°", "50°", "30°", "20°"], "choices": [70.0, 50.0, 30.0, 20.0], "label": 3}
+{"prob_id": 196, "image_path": "images/196.png", "question": "如图,在⊙O中,弦AC∥半径OB,∠BOC=50°,则∠OAB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图,∵∠BOC=50^{°},∴∠BAC=25^{°},∵AC//OB,∴∠OBA=∠BAC=25^{°},∵OA=OB∴∠OAB=∠OBA=25^{°}.故选A.", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["25°", "50°", "60°", "30°"], "choices": [25.0, 50.0, 60.0, 30.0], "label": 0}
+{"prob_id": 199, "image_path": "images/199.png", "question": "□ABCD中,对角线AC与BD交于点O,∠DAC=42°,∠CBD=23°,则∠COD是()．. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵AD//BC,∴∠BCA=∠DAC=42°,根据三角形的外角等于和它不相邻的内角和,∠COD=∠BCO+∠CBO=42°+23°=65°,故选", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["61°", "63°", "65°", "67°"], "choices": [61.0, 63.0, 65.0, 67.0], "label": 2}
+{"prob_id": 200, "image_path": "images/200.png", "question": "直线a、b、c、d的位置如图所示,如果∠1=58°,∠2=58°,∠3=70°,那么∠4等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:根据同位角相等,两直线平行这一定理可知a//b,再根据两直线平行,同旁内角互补可得∠3+∠5=180°,即∠5=180°-∠3=180°-70°=110°,因此可求得∠4=∠5=110°.故选C", "dataset_name": "Geoqa", "ground_truth": "110.0", "org_choices": ["58°", "70°", "110°", "116°"], "choices": [58.0, 70.0, 110.0, 116.0], "label": 2}
+{"prob_id": 202, "image_path": "images/202.png", "question": "如图所示,a∥b,∠1=158°,∠2=42°,∠4=50°．那么∠3=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:作BC//a,BE//b,∵a//b,∴a//b//BC//DE,∵∠1=158°,∠2=42°,∠4=50°∴∠ABC=180°-158°=22°∴∠CBD=∠BDE=42°-22°=20°,∠EDF=∠4=50°∴∠3=∠BDE+∠EDF=20°+50°=70°.故选C.", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["50°", "60°", "70°", "80°"], "choices": [50.0, 60.0, 70.0, 80.0], "label": 2}
+{"prob_id": 218, "image_path": "images/218.png", "question": "如图,AB是⊙O的直径,C、D是⊙O上的两点,分别连结AC、BC、CD、OD.若∠DOB=140°,则∠ACD=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵∠DOB=140°,∴∠AOD=40^{°},∴∠ACD=\\frac{1}{2}∠AOD=20^{°},故选A.", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["20°", "30°", "40°", ".70°A70°"], "choices": [20.0, 30.0, 40.0, 70.0], "label": 0}
+{"prob_id": 22, "image_path": "images/22.png", "question": "如图,已知∠1=∠2=∠3=55°,则∠4的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵∠1=∠2,∠5=∠1(对顶角相等),∴∠2=∠5,∴a//b(同位角相等,得两直线平行);∴∠3=∠6=55°(两直线平行,内错角相等),故∠4=180°-55°=125°(邻补角互补).故选D.", "dataset_name": "Geoqa", "ground_truth": "125.0", "org_choices": ["110°", "115°", "120°", "125°"], "choices": [110.0, 115.0, 120.0, 125.0], "label": 3}
+{"prob_id": 222, "image_path": "images/222.png", "question": "如图,在菱形ABCD中,M,N分别为AB、CD上,且AM=CN,MN与AC交于点O,连接BO.若∠DAC=28°,则∠OBC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵四边形ABCD为菱形,∴AB//CD,AB=BC,∴∠MAO=∠NCO,∠AMO=∠CNO,在△AMO和△CNO中,∴△AMO≌△CNO(ASA),∴AO=CO,∵AB=BC,∴BO⊥AC,∴∠BOC=90°,∵∠DAC=28°,BC//AD,∴∠BCA=∠DAC=28°,∴∠OBC=90°-28°=62°,故选C.", "dataset_name": "Geoqa", "ground_truth": "62.0", "org_choices": ["28°", "52°", "62°", "72°"], "choices": [28.0, 52.0, 62.0, 72.0], "label": 2}
+{"prob_id": 234, "image_path": "images/234.png", "question": "如图,PA,PB分别与⊙O相切于A,B两点,若∠C=65°,则∠P的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵PA、PB是⊙O的切线,∴OA⊥AP,OB⊥BP,∴∠OAP=∠OBP=90°,又∵∠AOB=2∠C=130°,则∠P=360°-(90°+90°+130°)=50°.故选C.", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["65°", "130°", "50°", "100°"], "choices": [65.0, 130.0, 50.0, 100.0], "label": 2}
+{"prob_id": 235, "image_path": "images/235.png", "question": "(4分)如图,直线a∥b,直线c分别与a,b相交,∠1=50°,则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:如图所示,∵a//b,∠1=50°,∴∠3=∠1=50°,∵∠2+∠3=180°,∴∠2=130°.故选B.", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["150°", "130°", "100°", "50°"], "choices": [150.0, 130.0, 100.0, 50.0], "label": 1}
+{"prob_id": 244, "image_path": "images/244.png", "question": "(3分)如图,EF∥BC,AC平分∠BAF,∠B=50°,则∠C的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵EF//BC,∴∠EAB=∠B=50°,∠C=∠CAF,∴∠BAF=180°-50°=130°,又∵AC平分∠BAF,∴∠CAF=130°÷2=65°,∴∠C=65°.故选D.", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["50°", "55°", "60°", "65°"], "choices": [50.0, 55.0, 60.0, 65.0], "label": 3}
+{"prob_id": 249, "image_path": "images/249.png", "question": "如图,为测量学校旗杆的高度,小东用长为3.2米的竹竿作测量工具,移动竹竿,使竹竿顶端与旗杆顶端的影子恰好落在地面的同一点,此时,竹竿与这一点相距8米,与旗杆相距22米,则旗杆的高度为()米.. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "若设旗杆高x米,则\\frac{3.2}{x}=\\frac{8}{8+22}∴x=12.故选C.", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["8.8", "10", "12", "14"], "choices": [8.8, 10.0, 12.0, 14.0], "label": 2}
+{"prob_id": 26, "image_path": "images/26.png", "question": "如图,在平地上种植树木时,要求株距(相邻两树间的水平距离)为4m．如果在坡度为0.75的山坡上种树,也要求株距为4m,那么相邻两树间的坡面距离为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "tan\\alpha=0.5=\\frac{铅直高度}{水平距离}=\\frac{AC}{AB}∵AB=4m,∴AC=0.75×4=3m由勾股定理知:面相邻两株数间的坡面距离BC=√{AB²+AC²}=√{4²+3²}=5m故选A.", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["5m", "6m", "7m", "8m"], "choices": [5.0, 6.0, 7.0, 8.0], "label": 0}
+{"prob_id": 269, "image_path": "images/269.png", "question": "如图,以线段AB为边分别作直角三角形ABC和等边三角形ABD,其中∠ACB=90°.连接CD,当CD的长度最大时,此时∠CAB的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图所示:∵AB长一定,∴只有C点距离AB距离最大,则CD的长度最大.∴只有C点在C′位置,即C′在半圆的中点时,此时当CD的长度最大故此时AC′=BC′,∴∠C′AB的大小是45°.故选B.", "dataset_name": "Geoqa", "ground_truth": "45.0", "org_choices": ["75°", "45°", "30°", "15°"], "choices": [75.0, 45.0, 30.0, 15.0], "label": 1}
+{"prob_id": 291, "image_path": "images/291.png", "question": "如图所示,D是△ABC的角平分线BD和CD的交点,若∠A=50°,则∠D=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵∠A=50°,∴∠ABC+∠ACB=180°-∠A=180°-50°=130°,∵D是△ABC的角平分线BD和CD的交点,∴∠DBC+∠DCB=\\frac{1}{2}(∠ABC+∠ACB)=\\frac{1}{2}×130^{°}=65^{°},在△BCD中,∠D=180°-(∠DBC+∠DCB)=180°-65°=115°.故选C.", "dataset_name": "Geoqa", "ground_truth": "115.0", "org_choices": ["120°", "130°", "115°", "110°"], "choices": [120.0, 130.0, 115.0, 110.0], "label": 2}
+{"prob_id": 3, "image_path": "images/3.png", "question": "如图,已知OA=OB=OC且∠ACB=30°,则∠AOB的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵OA=OB=OC,∴A、B、C在以O为圆心OA为半径的圆上.作⊙O.∵∠ACB和∠AOB是同弧AB所对的圆周角和圆心角,且∠ACB=30°,∴根据同弧所对的圆周角是圆心角的一半的性质,得∠AOB=60°.故选C.", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["40°", "50°", "60°", "70°"], "choices": [40.0, 50.0, 60.0, 70.0], "label": 2}
+{"prob_id": 30, "image_path": "images/30.png", "question": "如图,直线a∥b,点B在直线b上,且AB⊥BC,∠2=65°,则∠1的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:直线a//b,可得∠3=∠2=65°,根据AB⊥BC,可得∠1=25°.", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["65°", "25°", "35°", "45°"], "choices": [65.0, 25.0, 35.0, 45.0], "label": 1}
+{"prob_id": 314, "image_path": "images/314.png", "question": "圆I是三角形ABC的内切圆,D,E,F为3个切点,若∠DEF=52°,则∠A的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:连接DI,FI,∵∠DEF=52^{°},∴∠DIF=104°,∵⊙I是△ABC的内切圆,D,E,F为三个切点,∴∠IDA=∠IFA=90°,∴∠A=360^{°}-90^{°}-90^{°}-104^{°}=76^{°}.故选C.", "dataset_name": "Geoqa", "ground_truth": "76.0", "org_choices": ["68°", "52°", "76°", "38°"], "choices": [68.0, 52.0, 76.0, 38.0], "label": 2}
+{"prob_id": 323, "image_path": "images/323.png", "question": "如图,直线AB∥CD,∠1=136°,∠E为直角,则∠C等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:∵∠1=136^{°},∴∠BAE=180^{°}-∠1=44^{°},过E作EF//AB,∴AB//CD,∴AB//EF//CD,∴∠BAE=∠AEF,∠CEF=∠C,∵∠BAE=44°,∠E为直角,∴∠AEF=44°,∴∠C=∠CEF=90^{°}-44^{°}=46^{°},故选C.", "dataset_name": "Geoqa", "ground_truth": "46.0", "org_choices": ["42°", "44°", "46°", "48°"], "choices": [42.0, 44.0, 46.0, 48.0], "label": 2}
+{"prob_id": 332, "image_path": "images/332.png", "question": "如图所示,直线AB、CD被直线EF所截,若AB∥CD,∠1=100°,则∠2的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵AB//CD,∠3=∠1=100°,∴∠2=180°-∠3=80°,故选C.", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["10°", "50°", "80°", "100°"], "choices": [10.0, 50.0, 80.0, 100.0], "label": 2}
+{"prob_id": 359, "image_path": "images/359.png", "question": "如图:AB∥DE,∠B=30°,∠C=110°,∠D的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:过点C作CF//AB,∵AB//DE,∴AB//DE//CF,∵∠B=30°,∴∠1=30°,∵∠C=110°,∴∠2=80°,∴∠D=180°∠2=180°-80°=100°.故选C.", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["115°", "120°", "100°", "80°"], "choices": [115.0, 120.0, 100.0, 80.0], "label": 2}
+{"prob_id": 361, "image_path": "images/361.png", "question": "如图,AB是⊙O的直径,点C在⊙O上,过点C作⊙O的切线交AB的延长线于点D,连接AC．若∠D=50°,则∠A的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:∵CD切⊙O于C,∴OC⊥CD,∴∠OCD=90°,∵∠D=50^{°},∴∠COD=180^{°}-90^{°}-50^{°}=40^{°},∵OA=OC,∴∠A=∠OCA,∵∠A+∠OCA=∠COD=40^{°},∴∠A=20°故选A.", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["20°", "25°", ".40°", "50°"], "choices": [20.0, 25.0, 0.4, 50.0], "label": 0}
+{"prob_id": 377, "image_path": "images/377.png", "question": "如图,AB∥CD,CP交AB于O,AO=PO,若∠C=50°,则∠A的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:∵AB//CD,CP交AB于O,∴∠POB=∠C,∵∠C=50°,∴∠POB=50°,∵AO=PO,∴∠A=∠P,∴∠A=25°故选A.", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["25°", "35°", "15°", "50°"], "choices": [25.0, 35.0, 15.0, 50.0], "label": 0}
+{"prob_id": 385, "image_path": "images/385.png", "question": "如图,在△ABC中,AB=AC,过点A作AD∥BC.若∠1=70°,则∠BAC的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:根据AD//BC可得出∠C=∠1=70°/再根据AB=AC即可得出∠B=∠C=70°,结合三角形的内角和为180°,即可算出C=180°-∠B-∠C=40°.故选A.", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "30°", ".70°", "50°"], "choices": [40.0, 30.0, 0.7, 50.0], "label": 0}
+{"prob_id": 399, "image_path": "images/399.png", "question": "将一张宽度相等的长方形纸条按如图所示的方式折叠一下,如果∠1=140°,那么∠2的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:根据平行线的性质可得∠3+∠4=∠1=140°,根据折叠图形的性质可得:∠3=∠4=70°,根据平行线的性质可得:∠2=180°-70°=110°.", "dataset_name": "Geoqa", "ground_truth": "110.0", "org_choices": ["100°", "110°", "120°", "140°"], "choices": [100.0, 110.0, 120.0, 140.0], "label": 1}
+{"prob_id": 402, "image_path": "images/402.png", "question": "如图,已知直线a、b被直线c所截,a∥b,∠1=50°,则∠2=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:先利用平行线的性质可得∠3=∠1,又由对顶角相等推出∠2=∠3,故∠2的度数可求.如图,∵a//b,∠1=50°,∴∠3=∠1=50°,∵∠2=∠3,∴∠2=∠1=50°", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["50°", "130°", "40°", "60°"], "choices": [50.0, 130.0, 40.0, 60.0], "label": 0}
+{"prob_id": 413, "image_path": "images/413.png", "question": "直线a、b、c、d的位置如图,如果∠1=100°,∠2=100°,∠3=125°,那么∠4等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠1=100°,∠2=100°,∴∠1=∠2,∴a//b,∴∠4=∠5,∵∠3+∠5=180°,∴∠5=180^{°}-∠3=180^{°}-125^{°}=55^{°},∴∠4=55°故选D.", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["80°", "65°", "60°", "55°"], "choices": [80.0, 65.0, 60.0, 55.0], "label": 3}
+{"prob_id": 417, "image_path": "images/417.png", "question": "如图是小刘做的一个风筝支架示意图,已知BC∥PQ,AB:AP=2:5,AQ=20cm,则CQ的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "[解析]试题解析:∵BC//PQ,∴△ABC\\sim△APQ,∴\\frac{AB}{AP}=\\frac{AC}{AQ},∵AB:AP=2:5,AQ=20cm,∴\\frac{Ac}{20}=\\frac{2}{5}解得:AC=8cm,∴CQ=AQ-AC=20-8=12(cm),故选B.", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["8cm", "12cm", "30cm", "50cm"], "choices": [8.0, 12.0, 30.0, 50.0], "label": 1}
+{"prob_id": 419, "image_path": "images/419.png", "question": "如图,△ODC是由△OAB绕点O顺时针旋转30°后得到的图形,若点D恰好落在AB上,且∠AOC的度数为100°,则∠DOB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意得,∠AOD=30°,∠BOC=30°,又∠AOC=100°,∴∠DOB=100°-30°-30°=40°.故选A.", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "30°", "38°", "15°"], "choices": [40.0, 30.0, 38.0, 15.0], "label": 0}
+{"prob_id": 422, "image_path": "images/422.png", "question": "如图,甲、乙两盏路灯相距30米,一天晚上,当小刚从路灯甲底部向路灯乙底部直行25米时,发现自己的身影顶部正好接触到路灯乙的底部,已知小刚的身高为1.5米,那么路灯甲的高为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:如图∵AB⊥OB,CD⊥OB,∴△ABO~△CDOr∴\\frac{CD}{AB}=\\frac{DO}{BO},\\frac{1.5}{AB}=\\frac{30-25}{30},解得AB=9,故选A.", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["9米", "8米", "7米", "6米"], "choices": [9.0, 8.0, 7.0, 6.0], "label": 0}
+{"prob_id": 430, "image_path": "images/430.png", "question": "如图,C是⊙O上一点,O是圆心,若∠C=35°,则∠AOB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:同弧所对的圆心角的度数等于圆周角度数的两倍,则∠AOB=2∠C=70°.", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["35°", "70°", "105°", "150°"], "choices": [35.0, 70.0, 105.0, 150.0], "label": 1}
+{"prob_id": 435, "image_path": "images/435.png", "question": "如图,若AB∥CD,∠A=70°,则∠1的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "[解析]试题解析:如图,∵AB//CD,∠A=70°∴∠2=∠A=70°∴∠1=180^{°}-∠2=180^{°}-70^{°}=110°故选D.", "dataset_name": "Geoqa", "ground_truth": "110.0", "org_choices": ["20°", "30°", "70°", "110°"], "choices": [20.0, 30.0, 70.0, 110.0], "label": 3}
+{"prob_id": 448, "image_path": "images/448.png", "question": "如图,直线AB∥CD,∠C=44°,∠E为直角,则∠1等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过E作EF//AB,∵AB//CD,∴AB//CD//EF,∴∠C=∠FEC,∠BAE=∠FEA,∵∠C=44°,∠AEC为直角,∴∠FEC=44°,∠BAE=∠AEF=90°-44°=46°∴∠1=180°-∠BAE=180°-46°=134°故选B.", "dataset_name": "Geoqa", "ground_truth": "134.0", "org_choices": ["132°", "134°", "136°", "138°"], "choices": [132.0, 134.0, 136.0, 138.0], "label": 1}
+{"prob_id": 449, "image_path": "images/449.png", "question": "如图,A、B、C为⊙O上的任意三点,若∠BOC=100°,则∠BAC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "取⊙O上的一点D,连接BD,CD,∵∠BOC=100°,△∠D=50°,∴∠BAC=180°50°=130°,故选D.", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["50°", "80°", "100°", "130°"], "choices": [50.0, 80.0, 100.0, 130.0], "label": 3}
+{"prob_id": 458, "image_path": "images/458.png", "question": "如图,在⊙O的内接五边形ABCDE中,∠CAD=35°,∠AED=115°,则∠B的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:∵四边形ACDE是圆内接四边形,∴∠AED+∠ACD=180^{°},∵∠AED=115°∴∠ACD=65°∵∠CAD=35°,∴∠ADC=80°,∵四边形ABCD是圆内接四边形,∴∠B+∠ADC=180°,∴∠B=100°,故选D.", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["50°", "75°", "80°", "100°"], "choices": [50.0, 75.0, 80.0, 100.0], "label": 3}
+{"prob_id": 462, "image_path": "images/462.png", "question": "如图,△ABC中,∠C=90°,AD是∠BAC的平分线,DE⊥AB于E,若DE=8cm,DB=10cm则BC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "已知△ABC中,∠C=90°,AD是∠BAC的平分线,DE⊥AB于E,根据角平分线的性质可得CD=DE=8cm,所以BC=CD+BD=18cm,故选C.", "dataset_name": "Geoqa", "ground_truth": "18.0", "org_choices": ["14cm", "16cm", "18cm", "20cm"], "choices": [14.0, 16.0, 18.0, 20.0], "label": 2}
+{"prob_id": 467, "image_path": "images/467.png", "question": "如图,直线AB,CD相交于点O,EO⊥AB,垂直为点O,∠BOD=50°,则∠COE=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:EO⊥AB,∴∠AOE=90^{°},∵∠AOC=∠BOD=50^{°},∴∠COE=∠AOC+∠AOE=50^{°}+90^{°}=140°故选B.", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["30°", "140°", "50°", "60°"], "choices": [30.0, 140.0, 50.0, 60.0], "label": 1}
+{"prob_id": 472, "image_path": "images/472.png", "question": "如图,点B,E,C,F在同一条直线上,△ABC≌△DEF,∠B=45°,∠F=65°,则∠COE的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵△ABC≌△DEF,∠B=45°∠F=65°∴∠DEF=∠B=45°,∠ACB=∠F=65°在△OEC中,∠COE=180°-∠DEF-∠ACB=180^{°}-45^{°}-65^{°}=70°故选C.", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["40°", "60°", "70°", "100°"], "choices": [40.0, 60.0, 70.0, 100.0], "label": 2}
+{"prob_id": 476, "image_path": "images/476.png", "question": "如图,把一块含有45°角的直角三角板的两个顶点放在直尺的对边上,如果∠1=27.5°,那么∠2等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB//CD,∴∠1=∠AEC,又∠1=27.5,∠FEC=45°,∴∠2=∠FEC-∠1=17.5°.故选D.", "dataset_name": "Geoqa", "ground_truth": "17.5", "org_choices": ["32.5°", "22.5°", "20.5°", "17.5°"], "choices": [32.5, 22.5, 20.5, 17.5], "label": 3}
+{"prob_id": 479, "image_path": "images/479.png", "question": "如图,直线a∥b,点B在直线b上,且AB⊥BC,∠1=55°,则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵a//b,∴BC与b所夹锐角等于∠1=55°,又AB⊥BC,∴∠2=180°-90°-55°=35°.故选B.", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["25°", "35°", "45°", "55°"], "choices": [25.0, 35.0, 45.0, 55.0], "label": 1}
+{"prob_id": 48, "image_path": "images/48.png", "question": "如图,直线a∥b,直线c与a,b相交,∠1=55°,则∠2=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图,a//b,,∠1=55^{°},∴∠3=∠1=55^{°}.∵∠2和∠3是对顶角,∴∠2=∠3=55°故选A.", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["55°", "35°", "125°", "65°"], "choices": [55.0, 35.0, 125.0, 65.0], "label": 0}
+{"prob_id": 484, "image_path": "images/484.png", "question": "把一尺与三角板如图放置,∠1=40°则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:如图,∵∠3=∠1+90^{°},而∠1=40°,∴∠3=130^{°},∵a//b,∴∠2=∠3=130^{°}.故选A.", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["130°", "140°", "120°", "125°"], "choices": [130.0, 140.0, 120.0, 125.0], "label": 0}
+{"prob_id": 489, "image_path": "images/489.png", "question": "如图,直线AB,CD相交于点O,射线OM平分∠AOC,ON⊥OM．若∠AOC=70°,则∠CON的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵ON⊥OM,∴∠MON=90°.OM平分∠AOC,∠AOC=70°∴∠MOC=\\frac{1}{2}∠AOC=35^{°},∴∠CON=90^{°}-35^{°}=55^{°}故选B.", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["65°", "55°", "45°", "35°"], "choices": [65.0, 55.0, 45.0, 35.0], "label": 1}
+{"prob_id": 50, "image_path": "images/50.png", "question": "如图,⊙O的直径CD过弦EF的中点G,∠DCF=20°,则∠EOD等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵⊙O的直径CD过弦EF的中点G,∠DCF=20°DF=DE,且弧的度数是40°.∴∠DOE=40°.故选C", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["10°", "20°", "40°", "80°"], "choices": [10.0, 20.0, 40.0, 80.0], "label": 2}
+{"prob_id": 51, "image_path": "images/51.png", "question": "如图,AB平行CD,如果∠B=20°,那么∠C为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB//CD,,∠B=20^{°}∴∠C=∠B=20^{°}故选B.", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["40°", "20°", "60°", "70°"], "choices": [40.0, 20.0, 60.0, 70.0], "label": 1}
+{"prob_id": 56, "image_path": "images/56.png", "question": "如图,AB∥CD,∠CED=90°,∠AEC=35°,则∠D的大小(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB//CD,∴∠D=∠BED.∵∠CED=90°,∠AEC=35°∴∠BED=180°-90°-35°=55°.故选B.", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["65°", "55°", "45°", "35°"], "choices": [65.0, 55.0, 45.0, 35.0], "label": 1}
+{"prob_id": 57, "image_path": "images/57.png", "question": "如图,AB∥CD,AD平分∠BAC,且∠C=80°,则∠D的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AD平分∠BAC,∴∠BAD=∠CAD.∵AB//CD,∴∠BAD=∠D.∴∠CAD=∠D.∵在△ACD中,∠C+∠D+∠CAD=180°,即80^{°}+∠D+∠D=180^{°}解得∠D=50°,故选A.", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["50°", "60°", "70°", "100°"], "choices": [50.0, 60.0, 70.0, 100.0], "label": 0}
+{"prob_id": 6, "image_path": "images/6.png", "question": "如图,AB∥CD,若∠2=135°,那么∠1的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "由AB1ICD,知∠1的对顶角与∠2互补,所以∠1=45°", "dataset_name": "Geoqa", "ground_truth": "45.0", "org_choices": ["30°", "45°", "60°", "75°"], "choices": [30.0, 45.0, 60.0, 75.0], "label": 1}
+{"prob_id": 81, "image_path": "images/81.png", "question": "如图,AB∥CD,点E在BC上,且CD=CE,∠D=74°,则∠B的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵CD=CE,∠D=74°∴∠C=32°又∵AB//CD故选B", "dataset_name": "Geoqa", "ground_truth": "32.0", "org_choices": ["74°", "32°", "22°", "16°"], "choices": [74.0, 32.0, 22.0, 16.0], "label": 1}
+{"prob_id": 86, "image_path": "images/86.png", "question": "如图,AB∥CD,点E在CA的延长线上.若∠BAE=40°,则∠ACD的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:如图,延长DC到F,则∵AB//CD,∠BAE=40°,∴∠ECF=∠BAE=40°∴∠ACD=180^{°}-∠ECF=140^{°}.故选B.", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["150°", "140°", "130°", "120°"], "choices": [150.0, 140.0, 130.0, 120.0], "label": 1}
+{"prob_id": 9, "image_path": "images/9.png", "question": "如图,利用标杆BE测量树CD的高度,如果标杆BE长为2米,测得AB=3米,AC=9米,且点A、E、D在一条直线上,则树CD是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "本题考查的三角形的相似.由题意得三角形ABE~三角形ACD所以有\\frac{AB}{AC}=\\frac{BE}{CD}即\\frac{3}{9}=\\frac{2}{CD}解得CD=6故A正确.", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["6米", "7.5米", "8米", "8.5米"], "choices": [6.0, 7.5, 8.0, 8.5], "label": 0}
+{"prob_id": 95, "image_path": "images/95.png", "question": "在直径为200cm的圆柱形油槽内装入一些油以后,截面如图．若油面的宽AB=160cm,则油的最大深度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:连接OA,过点O作OE⊥AB,交AB于点M,由垂径定理求出AM的长,再根据勾股定理求出OM的长,进而可得出ME的长.", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40cm", "60cm", "80cm", "100cm"], "choices": [40.0, 60.0, 80.0, 100.0], "label": 0}
+{"prob_id": 1506, "image_path": "images/1506.png", "question": "如图,∠1=∠2,∠3=30°,则∠4等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠1=∠2,∴allb,∴∠5=∠3=30°,∴∠4=180°-∠5,=150°,故选D", "dataset_name": "Geoqa", "ground_truth": "150.0", "org_choices": ["120°", "130°", "145°", "150°"], "choices": [120.0, 130.0, 145.0, 150.0], "label": 3}
+{"prob_id": 1518, "image_path": "images/1518.png", "question": "如图,AB∥CD,∠B=20°,∠D=60°,则∠BED的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图:过点E做EF||AB,则CD||EF∴∠BEF=∠B=20°,∠DEF=∠D=60°∴∠BED=∠BEF+∠DEF=80°", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["40°", "80°", "90°", "l00°"], "choices": [40.0, 80.0, 90.0, 0.0], "label": 1}
+{"prob_id": 1524, "image_path": "images/1524.png", "question": "如图,直线AB∥CD,AE平分∠CAB,∠ACD=40°,则∠AEC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵ABIICD,∴∠ACD+∠BAC=180°,∵∠ACD=40°,∴∠BAC=180°-40°=140°,∵AE平分∠CAB,∴∠BAE=\\frac{1}{2}∠BAC=\\frac{1}{2}×140^{°}=70^{°},∴∠AEC=∠BAE=70°,故选:B.", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["40°", "70°", "80°", "140°"], "choices": [40.0, 70.0, 80.0, 140.0], "label": 1}
+{"prob_id": 1525, "image_path": "images/1525.png", "question": "轩轩和凯凯在同一个数学学习小组,在一次数学活动课上,他们各自用一张边长为12cm的正方形纸片制作了一副七巧板,并合作设计了如图所示的作品请你帮他们计算图中圈出来的三块图形的面积之和为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "根据七巧板的特点可知:圈出来的图形面积是正方形面积的四分之一,所以面积是12×12÷4=36故选:C", "dataset_name": "Geoqa", "ground_truth": "36.0", "org_choices": ["12cm", "24cm", "36cm", "48cm"], "choices": [12.0, 24.0, 36.0, 48.0], "label": 2}
+{"prob_id": 1528, "image_path": "images/1528.png", "question": "如图,直线a∥b,∠2=35°,∠3=40°,则∠1的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵a||b,∴∠1=∠4,又∵∠2=35°,∠3=40°∴∠4=180°-35°-40°=105°,∴∠1=105°,故选:B.", "dataset_name": "Geoqa", "ground_truth": "105.0", "org_choices": ["75°", "105°", "140°", "145°"], "choices": [75.0, 105.0, 140.0, 145.0], "label": 1}
+{"prob_id": 1533, "image_path": "images/1533.png", "question": "如图,BD是△ABC的角平分线,AE⊥BD,垂足为F,若∠ABC=35°,∠C=50°,则∠CDE的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵BD是△ABC的角平分线,AE⊥BD,∴∠ABD=∠EBD=\\frac{1}{2}∠ABC=\\frac{35^{°}}{2}\\quad∠AFB=∠EFB=90°,∴∠BAF=∠BEF=90°-17.5°∴AB=BE,∴AF=EF,∴AD=ED,∴∠DAF=∠DEF,∵∠BAC=180°-∠ABC-∠C=95°∴∠BED=∠BAD=95°∴∠CDE=95°-50°=45°,故选C.", "dataset_name": "Geoqa", "ground_truth": "45.0", "org_choices": ["35°", "40°", "45°", "50°"], "choices": [35.0, 40.0, 45.0, 50.0], "label": 2}
+{"prob_id": 1547, "image_path": "images/1547.png", "question": "如图,直线AD∥BC,若∠1=42°,∠BAC=78°,则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠1=42^{°},∠BAC=78°,∴∠ABC=180°-∠1-∠BAC=60°,又∵AD||BC,∴∠2=∠ABC=60°,故选C.", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["42°", "50°", "60°", "68°"], "choices": [42.0, 50.0, 60.0, 68.0], "label": 2}
+{"prob_id": 1548, "image_path": "images/1548.png", "question": "如图,□ABCD的周长为16cm,AC、BD相交于点O,OE⊥AC交AD于点E,则△DCE的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵平行四边形ABCD,∴AD=BC,AB=CD,OA=OC∵EO⊥AC∴AE=BC∵AB+BC+CD+AD=16cm∴AD+DC=8cm∴△DCE的周长是:CD+DE+CE-AE+DE+CD=AD+CD=8(cm)故选:B", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["10cm", "8cm", "6cm", "4cm"], "choices": [10.0, 8.0, 6.0, 4.0], "label": 1}
+{"prob_id": 1549, "image_path": "images/1549.png", "question": "如图所示,△ABC是⊙O的内接三角形.若∠ABC=70°,则∠AOC的度数等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "因为∠ABC和∠AOC是同一条弧AC所对的圆周角和圆心角,所以∠AOC=2∠ABC×70°=140°", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["140°", "130°", "120°", "110°"], "choices": [140.0, 130.0, 120.0, 110.0], "label": 0}
+{"prob_id": 1559, "image_path": "images/1559.png", "question": "如图,AB∥CD,射线AE交CD于点F,若∠1=115°,则∠2的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB||CD,∴∠1+∠AFD=180°,∵∠1=115°,∴∠AFD=65°,∵∠2和∠AFD是对顶角,∴∠2=∠AFD=65°故选B.", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["55°", "65°", "75°", "85°"], "choices": [55.0, 65.0, 75.0, 85.0], "label": 1}
+{"prob_id": 1561, "image_path": "images/1561.png", "question": "如图,a//b,将一块三角板的直角顶点放在直线a上,∠1=42°,则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠1=42°∴∠3=90^{°}-42^{°}=48^{°},∵a||b,∴∠2=∠3,∴∠2=48°故选:B", "dataset_name": "Geoqa", "ground_truth": "48.0", "org_choices": ["46°", "48°", "56°", "72°"], "choices": [46.0, 48.0, 56.0, 72.0], "label": 1}
+{"prob_id": 1566, "image_path": "images/1566.png", "question": "如图,a∥b,点B在直线b上,且AB⊥BC,∠1=36°,那么∠2=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "由题意可知:如下图所示∵AB⊥BC,∠1=36°,∴∠3=90°-∠1=54°∵a||b∴∠3=∠2=54°故选A", "dataset_name": "Geoqa", "ground_truth": "54.0", "org_choices": ["54°", "56°", "44°", "46°"], "choices": [54.0, 56.0, 44.0, 46.0], "label": 0}
+{"prob_id": 1579, "image_path": "images/1579.png", "question": "如图,如果∠1=∠3,∠2=60°,那么∠4的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠1=∠3,∴a||b,∴∠5=∠2=60^{°},∴∠4=18O-60°=120°故选:C.", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["60°", "100°", "120°", "130°"], "choices": [60.0, 100.0, 120.0, 130.0], "label": 2}
+{"prob_id": 1593, "image_path": "images/1593.png", "question": "如图,AB∥CD,AE平分∠CAB交CD于点E,若∠C=70°,则∠AED度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB||CD,∴∠BAC+∠C=180°,∵∠C=70°∴∠CAB=180°-70°=110°,又∵AE平分∠BAC,∴∠CAE=55°,∴∠AED=∠C+∠CAE=125°,故选B.", "dataset_name": "Geoqa", "ground_truth": "125.0", "org_choices": ["110°", "125°", "135°", "140°"], "choices": [110.0, 125.0, 135.0, 140.0], "label": 1}
+{"prob_id": 1594, "image_path": "images/1594.png", "question": "如图,▱ABCD的周长为32cm,AC,BD相交于点O,OE⊥AC交AD于点E,则△DCE的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵平行四边形ABCD,∴AD=BC,AB=CD,OA=OC,∵EO⊥AC,∴AE=EC,∵AB+BC+CD+AD=32cm,∴AD+DC=16cm,∴△DCE的周长是:CD+DE+CE=AE+DE+CD=AD+CD=16cm,故选D.", "dataset_name": "Geoqa", "ground_truth": "16.0", "org_choices": ["8cm", "24cm", "10cm", "16cm"], "choices": [8.0, 24.0, 10.0, 16.0], "label": 3}
+{"prob_id": 1612, "image_path": "images/1612.png", "question": "如图,一个底面圆周长为24m,高为5m的圆柱体,一只蚂蚁沿表面从点A到点B所经过的最短路线长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "将圆柱体的侧面展开,连接AB.如图所示:由于圆柱体的底面周长为24m,AD=24×\\frac{1}{2}=12m.又因为AC=5m,所以AB=√{12²+5²}=13m.即蚂蚁沿表面从点A到点B所经过的最短路线长为13m.故选C.", "dataset_name": "Geoqa", "ground_truth": "13.0", "org_choices": ["12m", "15m", "13m", "14m"], "choices": [12.0, 15.0, 13.0, 14.0], "label": 2}
+{"prob_id": 1626, "image_path": "images/1626.png", "question": "如图,在△ABC中,∠BAC=90°,AD⊥BC于点D,AE平分∠DAC,∠B=50°,求∠DAE的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "在△ABC中,∵∠BAC=90°,∠B=50°,∴∠C=90°-∠B=40°∵AD⊥BC于点D,∴∠BAD=90°-∠B=40°;在△ADC中∵∠ADC=90°∠C=40°∴∠DAC=90°-∠C=50°,∵AE平分∠DAC,∴∠DAE=\\frac{1}{2}∠DAC=25^{°},故选:D", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["45°", "20°", "30°", "25°"], "choices": [45.0, 20.0, 30.0, 25.0], "label": 3}
+{"prob_id": 1632, "image_path": "images/1632.png", "question": "如图,直线l∥m∥n,三角形ABC的顶点B,C分别在直线n和m上,边BC与直线n所夹的角为25°,且∠ACB=60°,则∠a的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图,∵I||m||n,∴∠a=∠1,∠2=25°∵∠ACB=∠a+∠2=60°∴∠a=60°-25°=35°故选C.", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["25°", "30°", "35°", "45°"], "choices": [25.0, 30.0, 35.0, 45.0], "label": 2}
+{"prob_id": 1638, "image_path": "images/1638.png", "question": "如图,已知⊙O中,圆心角∠AOB=100°,则圆周角∠ACB等于().. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图:设点E是优弧AB上的一-点,连接EA,EB∵∠AOB=100^{°}∴∠E=\\frac{1}{2}∠AOB=50^{°}∴∠ACB=180^{°}-∠E=130^{°}", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["130°", "120°", "110°", "100°"], "choices": [130.0, 120.0, 110.0, 100.0], "label": 0}
+{"prob_id": 1656, "image_path": "images/1656.png", "question": "如图,△ABC内接于半径为1的⊙O中,若∠BAC=60°,则BC的长度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作直径BD,连接CD,\n则∠BCD=90°,\n由圆周角定理得,∠D=∠BAC=60°,∴BC=BD×sin∠D=√{3},\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "1.7320508075688772", "org_choices": ["2", "2√{3}", "√{3}", "2√{2}"], "choices": [2.0, 3.464, 1.732, 2.828], "label": 2}
+{"prob_id": 1657, "image_path": "images/1657.png", "question": "如图,圆O是△ABC的外接圆,∠BAC与∠ABC的平分线相交于点I,延长AI交圆O于点D,连结BD、DC．若圆O的半径为8,∠BAC=120°,则DI的长度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AI平分∠BAC,∴∠BAD=∠DAC,∴⁀{BD}=⁀{CD},∴BD=DC．∵BI平分∠ABC,∴∠ABI=∠CBI．∵∠BAD=∠DAC,∠DBC=∠DAC,∴∠BAD=∠DBC．\n又∵∠DBI=∠DBC+∠CBI,∠DIB=∠ABI+∠BAD,∴∠DBI=∠DIB,∴△BDI为等腰三角形,∴BD=ID,∴BD=DC=DI．∵∠BAC=120°,△ABC为钝角三角形,∴圆心O在△ABC外．\n连接OB、OD、OC．∵BD=CD,∴⁀{BD}=⁀{CD},∴∠DOC=∠BOD=2∠BAD=120°,∴∠DBC=∠DCB=60°,∴△BDC为正三角形．\n延长CO交BD于点E,则OE⊥BD,∴BE=\\frac{1}{2}BD,\n又∵OB=18,∴BD=2OB\\cos30°=2×8×\\frac{√{3}}{2}=√{3}8,∴DI=BD=8√{3},\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "13.856406460551018", "org_choices": ["4√{3}+2", "4√{3}+3", "8√{3}+1", "8√{3}"], "choices": [8.928, 9.928, 14.856, 13.856], "label": 3}
+{"prob_id": 1662, "image_path": "images/1662.png", "question": "如图,⊙O是△ABC的外接圆,连接OB、OC,若⊙O的半径为2,∠BAC=60°,则BC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": ":延长BO交圆于D,连接CD．则∠BCD=90°,∠BDC=∠BAC=60°,∵⊙O的半径为2,∴BD=4,∴BC=2√{3},\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "3.4641016151377544", "org_choices": ["√{3}", "2√{3}", "4", "4√{3}"], "choices": [1.732, 3.464, 4.0, 6.928], "label": 1}
+{"prob_id": 1680, "image_path": "images/1680.png", "question": "如图,AB和CD是⊙O的两条直径,弦DE∥AB,弧DE为50°的弧,那么∠BOC为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OE,∵弧DE为50°,∴∠EOD=50°,∴∠OED+∠ODE=130°∵OE=OD,∴∠OED=∠ODE=65°,∵DE∥AB,∴∠AOE=∠OED=65°,∴∠AOD=∠AOE+∠EOD=65°+50°=115°,∴∠BOC=∠AOD=115°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "115.0", "org_choices": ["115°", "100°", "80°", "50°"], "choices": [115.0, 100.0, 80.0, 50.0], "label": 0}
+{"prob_id": 1714, "image_path": "images/1714.png", "question": "如图,点A、B、C在⊙O上,∠ABO=22°,∠ACO=42°,则∠BOC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过A作⊙O的直径,交⊙O于D；在△OAB中,OA=OB,则∠BOD=∠ABO+∠OAB=2×22°=44°,同理可得:∠COD=∠ACO+∠OAC=2×42°=84°,故∠BOC=∠BOD+∠COD=128°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "128.0", "org_choices": ["128°", "108°", "86°", "64°"], "choices": [128.0, 108.0, 86.0, 64.0], "label": 0}
+{"prob_id": 1716, "image_path": "images/1716.png", "question": "如图,A,B,C是⊙O上三点,∠ACB=25°,则∠BAO的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB,∵∠ACB=25°,,∴∠AOB=2∠ACB=50°,,∵OA=OB,,∴∠OAB=∠OBA=\\frac{180^{°}-∠AOB}{2}=65°．,故选:D．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["50°", "55°", "60°", "65°"], "choices": [50.0, 55.0, 60.0, 65.0], "label": 3}
+{"prob_id": 1748, "image_path": "images/1748.png", "question": "如图,已知⊙O中,∠AOB=50°,则圆周角∠ACB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠AOB=50°,∴∠ACB=\\frac{1}{2}∠AOB=25°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["50°", "25°", "100°", "30°"], "choices": [50.0, 25.0, 100.0, 30.0], "label": 1}
+{"prob_id": 1750, "image_path": "images/1750.png", "question": "如图,AB为⊙O的直径,C、D是⊙O上的两点,∠BAC=30°,⁀{AD}=⁀{CD}．则∠DAC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB为⊙O的直径,∴∠ACB=90°,∴∠B=90°-∠BAC=90°-30°=60°,∴∠D=180°-∠B=120°,∵⁀{AD}=⁀{CD},∴AD=CD,∴∠DAC=∠DCA=\\frac{1}{2}(180°-120°)=30°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["70°", "45°", "30°", "25°"], "choices": [70.0, 45.0, 30.0, 25.0], "label": 2}
+{"prob_id": 1764, "image_path": "images/1764.png", "question": "如图,AB是⊙O的直径,C、D为圆上两点,∠D=34°,则∠BOC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BC,∵∠D=34°,∴由圆周角定理得:∠B=∠D=34°,∵OC=OB,∴∠OCB=∠B=34°,∴∠BOC=180°-∠B-∠OCB=112°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "112.0", "org_choices": ["102°", "112°", "122°", "132°"], "choices": [102.0, 112.0, 122.0, 132.0], "label": 1}
+{"prob_id": 1781, "image_path": "images/1781.png", "question": "如图,点A,B,C均在⊙O上,当∠OBC=40°时,∠A的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OB=OC,∴∠OCB=∠OBC=40°,∴∠BOC=180°-40°-40°=100°,∴∠A=\\frac{1}{2}∠BOC=50°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["50°", "55°", "60°", "65°"], "choices": [50.0, 55.0, 60.0, 65.0], "label": 0}
+{"prob_id": 1782, "image_path": "images/1782.png", "question": "如图,⊙O的直径AB垂直于弦CD,垂足是点E,∠CAO=22.5°,OC=6,则CD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵CD⊥AB,∴CE=DE,∵∠BOC=2∠A=2×22.5°=45°,∴△OCE为等腰直角三角形,∴CE=\\frac{√{2}}{2}OC=\\frac{√{2}}{2}×6=3√{2},∴CD=2CE=6√{2}．故选:A．", "dataset_name": "Geoqa", "ground_truth": "8.48528137423857", "org_choices": ["6√{2}", "3√{2}", "6", "12"], "choices": [8.485, 4.243, 6.0, 12.0], "label": 0}
+{"prob_id": 1795, "image_path": "images/1795.png", "question": "如图,⊙O中,弦BC与半径OA相交于点D,连接AB,OC．若∠A=60°,∠ADC=90°,则∠C的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ADC=∠A+∠B,∠A=60°,∠ADC=90°,∴∠B=30°,∴∠AOC=2∠B=60°,∵∠ADC=∠AOC+∠C,∴∠C=90°-60°=30°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["25°", "27.5°", "30°", "35°"], "choices": [25.0, 27.5, 30.0, 35.0], "label": 2}
+{"prob_id": 1805, "image_path": "images/1805.png", "question": "如图,点A,B,P是⊙O上的三点,若∠AOB=40°,则∠APB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∠APB=\\frac{1}{2}∠AOB=\\frac{1}{2}×40°=20°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["80°", "140°", "20°", "50°"], "choices": [80.0, 140.0, 20.0, 50.0], "label": 2}
+{"prob_id": 1809, "image_path": "images/1809.png", "question": "如图,AB是⊙O的弦,OC⊥AB,交⊙O于点C,连接OA,OB,BC,若∠ABC=25°,则∠AOB的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OC⊥AB,∴⁀{AC}=⁀{BC},∴∠AOC=∠BOC,∵∠AOC=2∠ABC=2×25°=50°,∴∠AOB=2∠AOC=100°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["80°", "90°", "100°", "120°"], "choices": [80.0, 90.0, 100.0, 120.0], "label": 2}
+{"prob_id": 1812, "image_path": "images/1812.png", "question": "如图,已知圆周角∠A=50°,则∠OBC的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠A=50°,∴∠BOC=2∠A=100°．在△BOC中,OB=OC,∠BOC=100°,∴∠OBC=∠OCB=\\frac{1}{2}(180°-∠BOC)=40°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["50°", "40°", "130°", "80°"], "choices": [50.0, 40.0, 130.0, 80.0], "label": 1}
+{"prob_id": 1815, "image_path": "images/1815.png", "question": "如图,AB为⊙O的直径,CD是⊙O的弦,∠ADC=26°,则∠CAB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由圆周角定理得,∠ABC=∠ADC=26°,∵AB为⊙O的直径,∴∠ACB=90°,∴∠CAB=90°-∠ABC=64°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "64.0", "org_choices": ["26°", "74°", "64°", "54°"], "choices": [26.0, 74.0, 64.0, 54.0], "label": 2}
+{"prob_id": 1822, "image_path": "images/1822.png", "question": "如图,在⊙O中,AB是直径,CD是弦,AB⊥CD,垂足为点E,连接CO,AD,若∠BOC=30°,则∠BAD的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB⊥CD,∴⁀{BC}=⁀{BD},CE=DE,∴∠BAD=\\frac{1}{2}∠BOC=15°,故选:D．", "dataset_name": "Geoqa", "ground_truth": "15.0", "org_choices": ["30°", "25°", "20°", "15°"], "choices": [30.0, 25.0, 20.0, 15.0], "label": 3}
+{"prob_id": 1832, "image_path": "images/1832.png", "question": "如图,AB是⊙O的直径,点C、D是圆上两点,且∠AOC=126°,则∠CDB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠AOC=126°,∴∠BOC=180°-∠AOC=54°,∵∠CDB=\\frac{1}{2}∠BOC=27°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "27.0", "org_choices": ["54°", "64°", "27°", "37°"], "choices": [54.0, 64.0, 27.0, 37.0], "label": 2}
+{"prob_id": 1848, "image_path": "images/1848.png", "question": "如图,AB是⊙O的直径,点C、D在⊙O上,且点C是弧BD的中点,过点C作AD的垂线EF交直线AD于点E,若⊙O的半径为2.5,AC长为4,则CE的长度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BC,∵点C是弧BD的中点,∴∠EAC=∠CAB,又∵AB为直径,AE⊥EF,∴∠AEC=∠ACB=90°,∴△EAC∽△CAB,∴\\frac{AC}{AB}=\\frac{EC}{BC},∴EC=\\frac{AC\\cdotBC}{AB}=\\frac{4×√{5^{2}-4^{2}}}{5}=\\frac{12}{5}．故选:C．", "dataset_name": "Geoqa", "ground_truth": "2.4", "org_choices": ["3", "\\frac{20}{3}", "\\frac{12}{5}", "\\frac{16}{5}"], "choices": [3.0, 6.667, 2.4, 3.2], "label": 2}
+{"prob_id": 1849, "image_path": "images/1849.png", "question": "如图,点A,B,C在⊙O上,已知∠ABC=130°,则∠AOC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在优弧AC上取点D,连接AD,CD,∵四边形ABCD是圆内接四边形,∠ABC=130°,∴∠D=180°-10°=50°．∵∠D与∠AOC是同弧所对的圆周角与圆心角,∴∠AOC=2∠D=100°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["100°", "110°", "120°", "130°"], "choices": [100.0, 110.0, 120.0, 130.0], "label": 0}
+{"prob_id": 1858, "image_path": "images/1858.png", "question": "如图,已知⊙O的半径为5,弦AB、CD所对的圆心角分别是∠AOB,∠COD,且∠AOB与∠COD互补,弦CD=8,则弦AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:解:如图,延长AO交⊙O于点E,连接BE,则∠AOB+∠BOE=180°,又∵∠AOB+∠COD=180°,∴∠BOE=∠COD,∴BE=CD,∵AE为⊙O的直径,∴∠ABE=90°,∴AB=√{AE^{2}-BE^{2}}=√{10^{2}-8^{2}}=6,故选:A．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["6", "8", "5√{2}", "5√{3}"], "choices": [6.0, 8.0, 7.071, 8.66], "label": 0}
+{"prob_id": 1860, "image_path": "images/1860.png", "question": "如图,AB是圆O的直径,CD是圆O的弦,AB、CD的延长线交于点E,已知AB=2DE,∠E=16°,则∠ABC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OD,∵AB是圆O的直径,∴AB=2OD,∵AB=2DE,∴OD=DE,∴∠EOD=∠E=16°∴∠C=\\frac{1}{2}∠BOD=8°,∴∠ABC=∠C+∠E=8°+16°=24°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "24.0", "org_choices": ["32°", "24°", "16°", "48°"], "choices": [32.0, 24.0, 16.0, 48.0], "label": 1}
+{"prob_id": 1903, "image_path": "images/1903.png", "question": "本题考查了圆周角定理,关键是根据同弦所对圆心角与圆周角的关系解答．\n4．如图,AB是⊙O的直径,C是⊙O上一点(A、B除外),∠AOD=136°,则∠C的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解,∵∠AOD=136°,∴∠BOD=44°,∴∠C=22°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "22.0", "org_choices": ["44°", "22°", "46°", "36°"], "choices": [44.0, 22.0, 46.0, 36.0], "label": 1}
+{"prob_id": 1916, "image_path": "images/1916.png", "question": "如图,AB是⊙O的直径,点C、D在⊙O上．若∠BOD=130°,则∠ACD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BOD=130°,∴∠AOD=50°,∴∠ACD=\\frac{1}{2}∠AOD=25°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["50°", "30°", "25°", "20°"], "choices": [50.0, 30.0, 25.0, 20.0], "label": 2}
+{"prob_id": 1929, "image_path": "images/1929.png", "question": "绍兴是著名的桥乡．如图,圆拱桥的桥顶到水面的距离CD为8m,桥拱半径OC为5m,则水面宽AB为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OA,如图所示．∵CD⊥AB,∴AD=BD=\\frac{1}{2}AB．在Rt△ADO中,OA=OC=5m,OD=CD-OC=3m,∠ADO=90°,∴AD=√{0A^{2}-0D^{2}}=4m,∴AB=2AD=8m．故选:D．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["4m", "5m", "6m", "8m"], "choices": [4.0, 5.0, 6.0, 8.0], "label": 3}
+{"prob_id": 1933, "image_path": "images/1933.png", "question": "如图,已知∠α=130°,则∠β=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠α=130°,∴∠1=130°-90°=40°,∴∠β=∠1=40°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["30°", "40°", "50°", "65°"], "choices": [30.0, 40.0, 50.0, 65.0], "label": 1}
+{"prob_id": 1937, "image_path": "images/1937.png", "question": "如图,当圆形桥孔中的水面宽度AB为8米时,弧ACB恰为半圆．当水面上涨1米时,桥孔中的水面宽度A′B′为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设圆的圆心是O,作弦A′B′的弦心距OE,连接OA′．根据题意,得在直角三角形OA′E中,OA′=4,OE=1．根据勾股定理得A′E=√{15}m．再根据垂径定理得A′B′=2A′E=2√{15}m．故选:B．", "dataset_name": "Geoqa", "ground_truth": "7.745966692414834", "org_choices": ["√{15}米", "2√{15}米", "2√{17}米", "不能计算"], "choices": [3.873, 7.746, 8.246], "label": 1}
+{"prob_id": 1957, "image_path": "images/1957.png", "question": "在直角三角形ABC中,∠CAB=90°,∠ABC=72°,AD是∠CAB的角平分线,交边BC于点D,过点C作△ACD中AD边上的高线CE,则∠ECD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠CAB=90°,AD是∠CAB的角平分线,∴∠CAD=\\frac{1}{2}×90°=45°,∵CE⊥AD,∴∠ACE=90°-45°=45°,又∵∠CAB=90°,∠ABC=72°,∴∠ACB=90°-72°=18°,∴∠ECD=∠ACE-∠ACB=45°-18°=27°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "27.0", "org_choices": ["63°", "45°", "27°", "18°"], "choices": [63.0, 45.0, 27.0, 18.0], "label": 2}
+{"prob_id": 1977, "image_path": "images/1977.png", "question": "如图,AO是圆锥的高,圆锥的底面半径OB=0.7,AB的长为2.5,则AO的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由勾股定理得,AO=√{AB^{2}-0B^{2}}=2.4,故选:A．", "dataset_name": "Geoqa", "ground_truth": "2.4", "org_choices": ["2.4", "2.2", "1.8", "1.6"], "choices": [2.4, 2.2, 1.8, 1.6], "label": 0}
+{"prob_id": 1981, "image_path": "images/1981.png", "question": "如图,在⊙O中,弦AC和BD相交于点E,⁀{AB}=⁀{BC}=⁀{CD},若∠BEC=110°,则∠BDC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵⁀{AB}=⁀{BC}=⁀{CD},∴∠BDC=∠ACB=∠DBC,∵∠BEC=110°,∴∠ACB=∠DBC=35°．∴∠BDC=35°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["35°", "45°", "55°", "70°"], "choices": [35.0, 45.0, 55.0, 70.0], "label": 0}
+{"prob_id": 1988, "image_path": "images/1988.png", "question": "如图,半径为1cm,圆心角为90°的扇形OAB中,分别以OA,OB为直径作半圆,则图中阴影部分的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过点C作CD⊥OB,CE⊥OA,∵OB=OA,∠AOB=90°,∴△AOB是等腰直角三角形,∵OA是直径,∴∠ACO=90°,∴△AOC是等腰直角三角形,∵CE⊥OA,∴OE=AE,OC=AC,在Rt△OCE与Rt△ACE中,∵≥ft\\lbrace\\begin{array}{l}{OC=AC}\\\\{OE=AE}\\end{array}\\right.,∴Rt△OCE≌Rt△ACE,∵S扇形OEC=S扇形AEC,∴➝{0C}与弦OC围成的弓形的面积等于⌒{AC}与弦AC所围成的弓形面积,同理可得,➝{0C}与弦OC围成的弓形的面积等于⌒{BC}与弦BC所围成的弓形面积,∴S阴影=S△AOB=\\frac{1}{2}×1×1=\\frac{1}{2}cm²．故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.5", "org_choices": ["πcm²", "\\frac{2}{3}πcm²", "\\frac{1}{2}cm²", "\\frac{2}{3}cm²"], "choices": [3.142, 2.094, 0.5, 0.667], "label": 2}
+{"prob_id": 1991, "image_path": "images/1991.png", "question": "用圆心角为120°,半径为6cm的扇形纸片卷成一个圆锥形无底纸帽(如图所示),则这个纸帽的底面周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:这个纸帽的底面周长=\\frac{120\\cdotπ\\cdot6}{180}=4π(cm)．故选:C．", "dataset_name": "Geoqa", "ground_truth": "12.566370614359172", "org_choices": ["2πcm", "3πcm", "4πcm", "5πcm"], "choices": [6.283, 9.425, 12.566, 15.708], "label": 2}
+{"prob_id": 2020, "image_path": "images/2020.png", "question": "如图是一顶圆锥形烟囱小纸帽,它的母线长l是13cm,高h为12cm,则制作这顶纸帽所需纸张的面积是(接缝忽略不计)(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵圆锥的母线长l是13cm,高h为12cm,∴圆锥的底面半径为r=√{13^{2}-12^{2}}=5cm,∴这张扇形纸板的面积=\\frac{1}{2}×2π×5×13=65π(cm^{2})．故选:B．", "dataset_name": "Geoqa", "ground_truth": "204.20352248333657", "org_choices": ["60π", "65π", "78π", "156π"], "choices": [188.496, 204.204, 245.044, 490.088], "label": 1}
+{"prob_id": 2045, "image_path": "images/2045.png", "question": "用圆心角为120°,半径为3cm的扇形纸片卷成一个圆锥形无底纸冒(如图所示),则这个纸冒的高是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设圆锥的底面半径长为xcm,根据题意得2πx=\\frac{120\\cdotπ\\cdot3}{180}解得x=1,所以这个纸冒的高=√{3^{2}-1^{2}}=2√{2}(cm)．故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.8284271247461903", "org_choices": ["3cm", "2√{2}cm", "3√{2}cm", "4√{2}cm"], "choices": [3.0, 2.828, 4.243, 5.657], "label": 1}
+{"prob_id": 2053, "image_path": "images/2053.png", "question": "如图,一个圆锥的侧面展开图是半径为10的半圆,则它的底面半径是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设圆锥的底面半径为r,根据题意得\\frac{1}{2}•2π•r•10=\\frac{180\\cdotπ\\cdot10^{2}}{360},解得r=5,即圆锥的底面半径为5．故选:C．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["3", "4", "5", "6"], "choices": [3.0, 4.0, 5.0, 6.0], "label": 2}
+{"prob_id": 2069, "image_path": "images/2069.png", "question": "如图,用一张半径为24cm的扇形纸板制作一顶圆锥形帽子(接缝忽略不计),如果圆锥形帽子的底面半径为10cm,那么这张扇形纸板的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:这张扇形纸板的面积=\\frac{1}{2}×2π×10×24=240π(cm^{2})．故选:A．", "dataset_name": "Geoqa", "ground_truth": "753.9822368615504", "org_choices": ["240πcm^{2}", "480πcm^{2}", "1200πcm^{2}", "2400πcm^{2}"], "choices": [753.982, 1507.964, 3769.911, 7539.822], "label": 0}
+{"prob_id": 2088, "image_path": "images/2088.png", "question": "如图,圆锥的母线长为5cm,高线长为4cm,则圆锥的底面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:圆锥的底面圆的半径=√{5^{2}-4^{2}}=3,所以圆锥的底面积=π•3^{2}=9π(cm^{2})．故选:B．", "dataset_name": "Geoqa", "ground_truth": "28.274333882308138", "org_choices": ["3πcm^{2}", "9πcm^{2}", "16πcm^{2}", "25πcm^{2}"], "choices": [9.425, 28.274, 50.265, 78.54], "label": 1}
+{"prob_id": 2093, "image_path": "images/2093.png", "question": "我国纸伞的制作工艺十分巧妙．如图,伞不管是张开还是收拢,伞柄AP始终平分同一平面内两条伞骨所成的角∠BAC,且AE=AF,DE=DF,从而保证伞圈能沿着伞柄滑动．有一种玩具伞张开时,BDC在同一直线上,若AB=50cm,AD=14cm,则制作一把这样的纸伞需要油纸的面积是(不记接缝)(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB=50cm,AD=14cm,∴BD=√{AB^{2}-AD^{2}}=√{50^{2}-14^{2}}=48cm,S侧=\\frac{1}{2}lR=\\frac{1}{2}•48π×2×50=2400π,故选:C．", "dataset_name": "Geoqa", "ground_truth": "7539.822368615503", "org_choices": ["48cm^{2}", "70πcm^{2}", "2400πcm^{2}", "2500πcm^{2}"], "choices": [48.0, 219.911, 7539.822, 7853.982], "label": 2}
+{"prob_id": 2099, "image_path": "images/2099.png", "question": "如图用圆心角为120°,半径为6的扇形围成一个圆锥的侧面(接缝忽略不计),则这个圆锥的高是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设圆锥的底面圆的半径为r,根据题意得2πr=\\frac{120\\cdotπ\\cdot6}{180},解得r=2,所以圆锥的高=√{6^{2}-2^{2}}=4√{2}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "5.656854249492381", "org_choices": ["6", "8", "3√{3}", "4√{2}"], "choices": [6.0, 8.0, 5.196, 5.657], "label": 3}
+{"prob_id": 2110, "image_path": "images/2110.png", "question": "如图,在Rt△ABC中,∠ACB=90°,AC=4,BC=3,将△ABC绕AC所在的直线旋转一周得到一个旋转体,则该旋转体的侧面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由勾股定理得AB=5,BC=3,则圆锥的底面周长=6π,旋转体的侧面积=\\frac{1}{2}×6π×5=15π,故选:B．", "dataset_name": "Geoqa", "ground_truth": "47.1238898038469", "org_choices": ["12π", "15π", "30π", "60π"], "choices": [37.699, 47.124, 94.248, 188.496], "label": 1}
+{"prob_id": 2142, "image_path": "images/2142.png", "question": "如图,在纸上剪下一个圆形和一个扇形的纸片,使之恰好能围成一个圆锥模型．若圆的半径为1,扇形的圆心角等于90°,则扇形的半径是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:扇形的弧长等于底面圆的周长得出2π．设扇形的半径是r,则\\frac{90πr}{180}=2π,解得:r=4．故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["2", "4", "6", "8"], "choices": [2.0, 4.0, 6.0, 8.0], "label": 1}
+{"prob_id": 2161, "image_path": "images/2161.png", "question": "如图一个扇形铁皮OAB,已知OA=30cm,∠AOB=120°,工人师傅将OA、OB合拢制成了一个圆锥形的烟囱帽(接缝忽略不计),则烟囱帽的底面圆的半径为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:扇形的弧长是:\\frac{120π×30}{180}=20πcm,设底面半径是r,则2πr=20π,解得:r=10．故选:C．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["5cm", "12cm", "10cm", "15cm"], "choices": [5.0, 12.0, 10.0, 15.0], "label": 2}
+{"prob_id": 2177, "image_path": "images/2177.png", "question": "如图,已知圆锥的底面半径为6,母线长为10,则此圆锥的侧面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:底面周长是:2×6π=12π,则圆锥的侧面积是:\\frac{1}{2}×12π×10=60π．故选:A．", "dataset_name": "Geoqa", "ground_truth": "188.4955592153876", "org_choices": ["60π", "80π", "10π", "96π"], "choices": [188.496, 251.327, 31.416, 301.593], "label": 0}
+{"prob_id": 2201, "image_path": "images/2201.png", "question": "露露从纸上剪下一个圆形和一个扇形的纸片(如图),用它们恰好能围成一个圆锥模型,若圆的半径为1．扇形的圆心角等于120°,则此扇形的半径为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:扇形的弧长是2π．设扇形的半径是r,则\\frac{120πr}{180}=2π,解得:r=3．故选:C．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["√{3}", "√{6}", "3", "6"], "choices": [1.732, 2.449, 3.0, 6.0], "label": 2}
+{"prob_id": 2203, "image_path": "images/2203.png", "question": "如图,有一圆心角为120°、半径长为6cm的扇形,若将OA、OB重合后围成一圆锥侧面,那么圆锥底面的直径是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:扇形的弧长是:\\frac{120π×6}{180}=4π,即底面周长是4π．设底面半径是r,则2πr=4π,解得:2r=4cm．故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["2cm", "4cm", "3cm", "5cm"], "choices": [2.0, 4.0, 3.0, 5.0], "label": 1}
+{"prob_id": 2231, "image_path": "images/2231.png", "question": "如图所示,圆锥形帐篷顶的母线长AB=10cm,底面半径长BO=5m,这个圆锥形帐篷顶的侧面积(不计接缝)是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意得,l=10cm,故可得S圆锥形帐篷顶的侧面积=πrl=50πcm^{2}．故选:C．", "dataset_name": "Geoqa", "ground_truth": "157.07963267948966", "org_choices": ["15πm^{2}", "30πm^{2}", "50πm^{2}", "75πm^{2}"], "choices": [47.124, 94.248, 157.08, 235.619], "label": 2}
+{"prob_id": 2237, "image_path": "images/2237.png", "question": "如图,在⊙O中,弦AB的长为10,圆周角∠ACB=45°,则这个圆的直径AD为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BD,∵∠ACB=45°,∴∠ADB=45°,∵直径AD,∴∠ABD=90°,∵AB=10,∴AD=10√{2}．故选B．", "dataset_name": "Geoqa", "ground_truth": "14.142135623730951", "org_choices": ["5√{2}", "10√{2}", "15√{2}", "20√{2}"], "choices": [7.071, 14.142, 21.213, 28.284], "label": 1}
+{"prob_id": 2257, "image_path": "images/2257.png", "question": "如图,△ABC中．∠C=90°,点D是边BC上一个动点(点D不与点C重合)．以CD为直径的圆交AD于点P．若AC=6．线段BP长度的最小值是2．则AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵CD为直径,∴∠CPD=90°,∵∠APC=90°,∴点P在以AC为直径的⊙O上,如图,连接OB交⊙O于P′,∵线段BP长度的最小值是2,∴BP′=2,∴OB=2+3=5,在Rt△OBC中,BC=√{5^{2}-3^{2}}=4,在Rt△ABC中,AB=√{4^{2}+6^{2}}=2√{13}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "7.211102550927978", "org_choices": ["8", "2√{10}", "4√{3}", "2√{13}"], "choices": [8.0, 6.325, 6.928, 7.211], "label": 3}
+{"prob_id": 2284, "image_path": "images/2284.png", "question": "如图,小明为了测量一凉亭的高度AB(顶端A到水平地面BD的距离),在凉亭的旁边放置一个与凉亭台阶BC等高的台阶DE(DE=BC=0.6米,求A、B、C三点共线),把一面镜子水平放置在平台上的点G处,测得CG=12米,然后沿直线CG后退到点E处,这时恰好在镜子里看到凉亭的顶端A,测得GE=2米,小明身高EF=1.6米,则凉亭的高度AB约为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意∠AGC=∠FGE,∵∠ACG=∠FEG=90°,∴△ACG∽△FEG,∴AC:EF=CG:GE,∴\\frac{AC}{1.6}=\\frac{12}{2},∴AC=9.6米,∴AB=AC+BC=9.6+0.6=10.2米．故选:D．", "dataset_name": "Geoqa", "ground_truth": "10.2", "org_choices": ["9米", "9.6米", "10米", "10.2米"], "choices": [9.0, 9.6, 10.0, 10.2], "label": 3}
+{"prob_id": 2287, "image_path": "images/2287.png", "question": "如图,为了估计荆河的宽度,在荆河的对岸选定一个目标点P,在近岸取点Q和S,使点P、Q、S在一条直线上,且直线PS与河垂直,在过点S且与PS垂直的直线a上选择适当的点T,PT与过点Q且与PS垂直的直线b的交点为R,如果QS=60m,ST=120m,QR=80m,则荆河的宽度PQ为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意可知:QR∥ST,∴△PQR∽△PST,∴\\frac{PQ}{PS}=\\frac{QR}{ST}设PQ=x,∴\\frac{x}{x+60}=\\frac{80}{120}解得:x=120故PQ=120m故选:B．", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["40m", "120m", "60m", "180m"], "choices": [40.0, 120.0, 60.0, 180.0], "label": 1}
+{"prob_id": 2303, "image_path": "images/2303.png", "question": "如图是小莹设计用手电来测量某古城墙高度的示意图．在点P处放一水平的平面镜,光线从点A出发经平面镜反射后,刚好射到古城墙CD的顶端C处．已知AB⊥BD,CD⊥BD．且测得AB=1.4米,BP=2.1米,PD=12米．那么该古城墙CD的高度是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠APB=∠CPD,∠ABP=∠CDP,∴△ABP∽△CDP∴\\frac{AB}{CD}=\\frac{BP}{PD}即\\frac{1.4}{CD}=\\frac{2.1}{12}解得:CD=8米．故选:B．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["6米", "8米", "10米", "12米"], "choices": [6.0, 8.0, 10.0, 12.0], "label": 1}
+{"prob_id": 2312, "image_path": "images/2312.png", "question": "如图,在⊙O中,点M是⁀{AB}的中点,连结MO并延长,交⊙O于点N,连结BN,若∠AOB=140°,则∠N的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵点M是⁀{AB}的中点,∴⁀{AM}=⁀{BM},∵∠AOB=140°,∴∠BOM=\\frac{1}{2}∠AOB=70°,∴∠N=\\frac{1}{2}∠BOM=35°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["70°", "40°", "35°", "20°"], "choices": [70.0, 40.0, 35.0, 20.0], "label": 2}
+{"prob_id": 2317, "image_path": "images/2317.png", "question": "如图,某数学学习兴趣小组为了测量树AB的度数,他们测得此树在阳光下的影子BC的长为9m,在相同时刻,他们还测得小亮在阳光下的影长为1.5m,已知小亮的身高为1.8m,则树AB的高为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵同一时刻物高与影长成正比例．∴1.8:1.5=树AB的高:9,∴树AB的高是10.8米．故选:A．", "dataset_name": "Geoqa", "ground_truth": "10.8", "org_choices": ["10.8m", "9m", "7.5m", "0.3m"], "choices": [10.8, 9.0, 7.5, 0.3], "label": 0}
+{"prob_id": 2319, "image_path": "images/2319.png", "question": "如图所示为农村一古老的捣碎器,已知支撑柱AB的高为0.3米,踏板DE长为1米,支撑点A到踏脚D的距离为0.6米,原来捣头点E着地,现在踏脚D着地,则捣头点E上升了(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图:∵AB∥EF,∴△DAB∽△DEF,∴AD:DE=AB:EF,∴0.6:1=0.3:EF,∴EF=0.5(米)．∴捣头点E上升了0.5米．故选:A．", "dataset_name": "Geoqa", "ground_truth": "0.5", "org_choices": ["0.5米", "0.6米", "0.3米", "0.9米"], "choices": [0.5, 0.6, 0.3, 0.9], "label": 0}
+{"prob_id": 2356, "image_path": "images/2356.png", "question": "如图,光源P在横杆AB的正上方,AB在灯光下的影子为CD,AB∥CD,AB=2m,CD=5m,点P到CD的距离是3m,则AB与CD的距离是()m．. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设点P到AB的距离为xm,∵AB∥CD,∴△PAB∽△PCD,∴\\frac{x}{3}=\\frac{AB}{CD}=\\frac{2}{5},解得x=\\frac{6}{5}m．3-\\frac{6}{5}=\\frac{9}{5}m,故选:C．", "dataset_name": "Geoqa", "ground_truth": "1.8", "org_choices": ["\\frac{6}{5}", "\\frac{7}{6}", "\\frac{9}{5}", "\\frac{15}{2}"], "choices": [1.2, 1.167, 1.8, 7.5], "label": 2}
+{"prob_id": 2358, "image_path": "images/2358.png", "question": "如图,小强自制了一个小孔成像装置,其中纸筒的长度为15cm,他准备了一支长为20cm的蜡烛,想要得到高度为4cm的像,蜡烛与纸筒的距离应该为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,AB=20cm,OF=15cm,CD=4cm,∵AB∥CD,EF⊥AB∴EF⊥CD,∴△OAB∽△ODC,∴\\frac{CD}{AB}=\\frac{0F}{OE},即\\frac{4}{20}=\\frac{15}{OE},解得OE=75cm．故选:D．", "dataset_name": "Geoqa", "ground_truth": "75.0", "org_choices": ["60cm", "65cm", "70cm", "75cm"], "choices": [60.0, 65.0, 70.0, 75.0], "label": 3}
+{"prob_id": 2375, "image_path": "images/2375.png", "question": "如图,在一场羽毛球比赛中,站在场内M处的运动员林丹把求从N点击到了对方内的B点,已知网高OA=1.52m,OB=4m,OM=5m,则林丹起跳后击球点离地面的距离NM=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:根据题意得:AO⊥BM,NM⊥BM,∴AO∥NM,∴△ABO∽△NBM,∴\\frac{0A}{NM}=\\frac{OB}{BM},∵OA=1.52米,OB=4米,OM=5米,∴BM=OB+OM=4+5=9(米),∴\\frac{1.52}{NM}=\\frac{4}{9},解得:NM=3.42(米),∴林丹起跳后击球点N离地面的距离NM为3.42米．故选:A．", "dataset_name": "Geoqa", "ground_truth": "3.42", "org_choices": ["3.42m", "1.9m", "3m", "3.24m"], "choices": [3.42, 1.9, 3.0, 3.24], "label": 0}
+{"prob_id": 2377, "image_path": "images/2377.png", "question": "小明在测量楼高时,先测出楼房落在地面上的影长BA为15米(如图),然后在A处树立一根高2米的标杆,测得标杆的影长AC为3米,则楼高为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵\\frac{标杆的高}{标杆的影长}=\\frac{楼高}{楼影长}即\\frac{2}{3}=\\frac{楼高}{15},∴楼高=10米．故选:A．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["10米", "12米", "15米", "22.5米"], "choices": [10.0, 12.0, 15.0, 22.5], "label": 0}
+{"prob_id": 2383, "image_path": "images/2383.png", "question": "如图所示:两根竖直的电线杆AB长为6,CD长为3,AD交于BC于点E点,则E到地面的距离EF的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵两根电线杆AB、CD都竖直,EF垂直于地面,∴△ABD∽△EFD,△BCD∽△BEF,∴\\frac{DF}{BD}=\\frac{EF}{AB},\\frac{BF}{BD}=\\frac{EF}{CD},∴\\frac{DF}{BD}+\\frac{BF}{BD}=\\frac{EF}{CD}+\\frac{EF}{AB},即\\frac{EF}{6}+\\frac{EF}{3}=1,解得EF=2．故选:A．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["2", "2.2", "2.4", "2.5"], "choices": [2.0, 2.2, 2.4, 2.5], "label": 0}
+{"prob_id": 2420, "image_path": "images/2420.png", "question": "如图,要在一块△ABC的纸片上截取正方形DEFG模型．其中,G、F在BC边上,D、E分别在AB、AC边上,AH⊥BC交DE于M,若BC=12cm,AH=8cm,则正方形DEFG的边长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:假设正方形边长为x厘米,\n在△ABC中可得:\\frac{DE}{BC}=\\frac{AM}{AH},∵BC=12cm,BC边上的高为8cm,∴AH=8cm,DE=xcm,AM=(8-x)cm代入上式得:\\frac{x}{12}=\\frac{8-x}{8},\n解得:x=4.8cm．∴正方形的边长是4.8cm．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "4.8", "org_choices": ["\\frac{24}{5}cm", "4cm", "\\frac{24}{7}cm", "5cm"], "choices": [4.8, 4.0, 3.429, 5.0], "label": 0}
+{"prob_id": 2431, "image_path": "images/2431.png", "question": "2009年l0月27日,上海队小将吴迪在全运会赛场上脱颖而出,以2:0的比分战胜了男子单打头号种子选手曾少眩,勇夺全运会网球男子单打冠军．下图是吴迪在决赛中打的一个球,已知网高0.8米,击球点到网的水平距离为4米,打球时使球恰好能打过网,且落点恰好在离网6米的位置上,则球拍击球的高度h为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图:∵AB∥CD∴△ABE∽△CDE,∴\\frac{CE}{AE}=\\frac{CD}{AB},∴\\frac{6}{10}=\\frac{0.8}{AB},∴h=AB=\\frac{4}{3}(米)．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "1.3333333333333333", "org_choices": ["\\frac{8}{5}米", "\\frac{4}{3}米", "1米", "\\frac{8}{15}米"], "choices": [1.6, 1.333, 1.0, 0.533], "label": 1}
+{"prob_id": 2432, "image_path": "images/2432.png", "question": "如图,点A、B、C在⊙O上,∠ABO=40°,∠ACO=30°,则∠BOC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过A作⊙O的直径,交⊙O于D；在△OAB中,OA=OB,即∠OBA=∠OAB,则∠BOD=∠ABO+∠OAB=2×40°=80°,同理可得:∠COD=∠ACO+∠OAC=2×30°=60°,故∠BOC=∠BOD+∠COD=140°,故选:D．", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["60°", "70°", "120°", "140°"], "choices": [60.0, 70.0, 120.0, 140.0], "label": 3}
+{"prob_id": 2434, "image_path": "images/2434.png", "question": "如图,AB是斜靠在墙上的梯子,梯脚距墙2米,梯子上的D点距墙1.8米,BD长0.6米,则梯子的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE⊥AC,BC⊥AC,∴DE∥BC,∴△ADE∽△ABC,∴\\frac{AB}{AD}=\\frac{BC}{DE},∴AB=6．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["5.60米", "6.00米", "6.10米", "6.20米"], "choices": [5.6, 6.0, 6.1, 6.2], "label": 1}
+{"prob_id": 2436, "image_path": "images/2436.png", "question": "某校数学兴趣小组为测量学校旗杆AC的高度,在点F处竖立一根长为1.5米的标杆DF,如图所示,量出DF的影子EF的长度为1米,再量出旗杆AC的影子BC的长度为6米,那么旗杆AC的高度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵\\frac{标杆的高}{标杆的影长}=\\frac{旗杆的高}{旗杆的影长}\n即\\frac{1.5}{1}=\\frac{AC}{6},∴AC=6×1.5=9米．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["6米", "7米", "8.5米", "9米"], "choices": [6.0, 7.0, 8.5, 9.0], "label": 3}
+{"prob_id": 2438, "image_path": "images/2438.png", "question": "如图,小东用长3.2m的竹竿做测量工具测量学校旗杆的高度,移动竹竿,使竹竿、旗杆顶端的影子恰好落在地面的同一点．此时,竹竿与这一点相距8m,与旗杆相距22m,则旗杆的高为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:因为BE∥CD,所以△AEB∽△ADC,\n于是\\frac{AE}{AD}=\\frac{BE}{CD},即\\frac{8}{22+8}=\\frac{3.2}{CD},\n解得:CD=12．\n旗杆的高为12m．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["12m", "10m", "8m", "7m"], "choices": [12.0, 10.0, 8.0, 7.0], "label": 0}
+{"prob_id": 2445, "image_path": "images/2445.png", "question": "如图,CD是平面镜子,光线从A点射出,经CD上一点E反射后照射到B点,若入射角为α,AC⊥CD,BD⊥CD,垂足分别为C、D,且AC=3,BD=6,CD=10,则线段ED的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,∵CD是平面镜,α为入射角,∠1为反射角∴α=∠1．∵α+∠AEC=90°,∠1+∠BED=90°∴∠AEC=BED,∵AC⊥CD,BD⊥CD∴∠ACE=∠BDE=90°∴Rt△ACE∽Rt△BDE,∴\\frac{AC}{BD}=\\frac{CE}{ED},∵AC=3,BD=6,CD=10∴\\frac{3}{6}=\\frac{10-ED}{ED},\n解得ED=\\frac{20}{3}．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "6.666666666666667", "org_choices": ["\\frac{20}{3}", "\\frac{10}{3}", "7", "\\frac{14}{3}"], "choices": [6.667, 3.333, 7.0, 4.667], "label": 0}
+{"prob_id": 2446, "image_path": "images/2446.png", "question": "如图,小明设计两个直角,来测量河宽BC,他量得AB=2米,BD=\\frac{7}{3}米,CE=9米,则河宽BC为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BD∥CE∴△ABD∽△ACE∴,∵AB=2,BD=\\frac{7}{3},CE=9∴AC=\\frac{AB\\cdotCE}{BD}=\\frac{2×9}{\\frac{7}{3}}=\\frac{54}{7},∴BC=AC-AB=\\frac{54}{7}-2=\\frac{40}{7}米．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "5.714285714285714", "org_choices": ["\\frac{7}{2}米", "\\frac{17}{2}米", "\\frac{40}{7}米", "11米"], "choices": [3.5, 8.5, 5.714, 11.0], "label": 2}
+{"prob_id": 2451, "image_path": "images/2451.png", "question": "如图,一同学在湖边看到一棵树,他目测出自己与树的距离为20m,树的顶端在水中的倒影距自己5m远,该同学的身高为1.7m,则树高为()m．. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由相似三角形的性质,设树高x米,\n则\\frac{5}{20-5}=\\frac{1.7}{x},∴x=5.1m．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "5.1", "org_choices": ["3.4", "5.1", "6.8", "8.5"], "choices": [3.4, 5.1, 6.8, 8.5], "label": 1}
+{"prob_id": 2466, "image_path": "images/2466.png", "question": "如图,AB是斜靠在墙壁上的固定爬梯,梯脚B到墙脚C的距离1.6m,梯上一点D到墙面的距离1.4m,BD长0.5m,则梯子的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:因为梯子每一条踏板均和地面平行,所以构成一组相似三角形,\n即△ABC∽△ADE,则\\frac{DE}{BC}=\\frac{AD}{AB},\n设梯子长为x米,则\\frac{x-0.5}{x}=\\frac{1.4}{1.6},\n解得,x=4(m)．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["3.5m", "4m", "4.5m", "5m"], "choices": [3.5, 4.0, 4.5, 5.0], "label": 1}
+{"prob_id": 2472, "image_path": "images/2472.png", "question": "如图,阳光从教室的窗户射入室内,窗户框AB在地面上的影长DE=1.8m,窗户下檐到地面的距离BC=1m,EC=1.2m,那么窗户的高AB为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BE∥AD,∴△BCE∽△ACD,∴\\frac{CB}{AC}=\\frac{CE}{CD}即\\frac{BC}{AB+BC}=\\frac{EC}{DE+EC}\n且BC=1,DE=1.8,EC=1.2∴\\frac{1}{AB+1}=\\frac{1.2}{1.8+1.2}∴1.2AB=1.8,∴AB=1.5m．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "1.5", "org_choices": ["1.5m", "1.6m", "1.86m", "2.16m"], "choices": [1.5, 1.6, 1.86, 2.16], "label": 0}
+{"prob_id": 2484, "image_path": "images/2484.png", "question": "如图,AB是斜靠在墙壁上的长梯,梯脚B距墙1.6米,梯上点D距墙1.4米,BD长0.55米,则梯子长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:因为梯子每一条踏板均和地面平行,所以构成一组相似三角形,\n即△ABC∽△ADE,则\\frac{DE}{BC}=\\frac{AD}{AB}\n设梯子长为x米,则\\frac{x-0.55}{x}=\\frac{1.4}{1.6},\n解得,x=4.40．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "4.4", "org_choices": ["3.85米", "4.00米", "4.40米", "4.50米"], "choices": [3.85, 4.0, 4.4, 4.5], "label": 2}
+{"prob_id": 2496, "image_path": "images/2496.png", "question": "如图,身高1.6米的学生小李想测量学校的旗杆的高度,当他站在C处时,他头顶端的影子正好与旗杆顶端的影子重合,并测得AC=2米,BC=8米,则旗杆的高度是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设旗杆高度为h,\n由题意得\\frac{1.6}{h}=\\frac{2}{2+8},h=8米．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["6.4米", "7米", "8米", "9米"], "choices": [6.4, 7.0, 8.0, 9.0], "label": 2}
+{"prob_id": 2500, "image_path": "images/2500.png", "question": "如图,四边形ABCD和A′B′C′D′是以点O为位似中心的位似图形,若OA′:A′A=2:1,四边形A′B′C′D′的面积为12cm^{2},则四边形ABCD的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD和A′B′C′D′是以点O为位似中心的位似图形,OA′:A′A=2:1,∴OA′:OA=2:3,∴四边形ABCD与四边形A′B′C′D′的面积比为:9:4,∵四边形A′B′C′D′的面积为12cm^{2},∴四边形ABCD的面积为:27cm^{2}．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "27.0", "org_choices": ["24cm^{2}", "27cm^{2}", "36cm^{2}", "54cm^{2}"], "choices": [24.0, 27.0, 36.0, 54.0], "label": 1}
+{"prob_id": 2542, "image_path": "images/2542.png", "question": "如图,△ABC中,∠C=90°,若AC=4,BC=3,则\\cosB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由勾股定理,得\nAB=√{AC^{2}+BC^{2}}=5,\n\\cosB=\\frac{BC}{AB}=\\frac{3}{5},\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "0.6", "org_choices": ["\\frac{3}{5}", "\\frac{3}{4}", "\\frac{4}{5}", "\\frac{4}{3}"], "choices": [0.6, 0.75, 0.8, 1.333], "label": 0}
+{"prob_id": 2545, "image_path": "images/2545.png", "question": "如图,在Rt△ABC中,∠C=90°,AC=4,BC=3,则sinB的值等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在Rt△ABC中,由勾股定理,得\nAB=√{AC^{2}+BC^{2}}=5．\nsinB=\\frac{AC}{AB}=\\frac{4}{5},\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.8", "org_choices": ["\\frac{4}{3}", "\\frac{3}{4}", "\\frac{4}{5}", "\\frac{3}{5}"], "choices": [1.333, 0.75, 0.8, 0.6], "label": 2}
+{"prob_id": 2546, "image_path": "images/2546.png", "question": "如图,在Rt△ABC中,∠C=90°,AC=3,BC=4,则\\cosA的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在Rt△ABC中,∠C=90°,AC=3,BC=4,\n由勾股定理,得\nAB=√{AC^{2}+BC^{2}}=5．\n\\cosA=\\frac{AC}{AB}=\\frac{3}{5},\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "0.6", "org_choices": ["\\frac{3}{5}", "\\frac{5}{3}", "\\frac{4}{5}", "\\frac{3}{4}"], "choices": [0.6, 1.667, 0.8, 0.75], "label": 0}
+{"prob_id": 2554, "image_path": "images/2554.png", "question": "如图,已知Rt△ABC中,∠C=90°,AB=10,AC=8,则tanB的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在Rt△ABC中,由勾股定理,得\nBC=√{AB^{2}-AC^{2}}=√{10^{2}-8^{2}}=6,\n由正切函数的意义,得\ntanB=\\frac{AC}{BC}=\\frac{8}{6}=\\frac{4}{3},\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "1.3333333333333333", "org_choices": ["\\frac{3}{5}", "\\frac{3}{4}", "\\frac{4}{5}", "\\frac{4}{3}"], "choices": [0.6, 0.75, 0.8, 1.333], "label": 3}
+{"prob_id": 2572, "image_path": "images/2572.png", "question": "如图,位似图形由三角尺与其灯光照射下的中心投影组成,若灯泡到三角尺一顶点的距离与灯泡到三角尺投影的对应顶点距离比为2:5,且三角尺的一边长为8cm,则投影三角形的对应边长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵位似图形由三角尺与其灯光照射下的中心投影组成,相似比为2:5,三角尺的一边长为8cm,∴投影三角形的对应边长为:8÷\\frac{24}{5}=20cm．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["8cm", "20cm", "3.2cm", "10cm"], "choices": [8.0, 20.0, 3.2, 10.0], "label": 1}
+{"prob_id": 2592, "image_path": "images/2592.png", "question": "如图,已知圆周角∠BAC=40°,那么圆心角∠BOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BOC=2∠BAC,∠BAC=40°,∴∠BOC=80°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["40°", "60°", "80°", "100°"], "choices": [40.0, 60.0, 80.0, 100.0], "label": 2}
+{"prob_id": 2601, "image_path": "images/2601.png", "question": "如图,在Rt△ABC中,∠C=90°,AC=4,AB=5,则\\cosA的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在Rt△ABC中,\\cosA=\\frac{AC}{AB}=\\frac{4}{5},\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.8", "org_choices": ["\\frac{3}{5}", "\\frac{4}{5}", "\\frac{3}{4}", "\\frac{4}{3}"], "choices": [0.6, 0.8, 0.75, 1.333], "label": 1}
+{"prob_id": 2632, "image_path": "images/2632.png", "question": "如图,在△ABC中,∠C=Rt∠,AB=5,AC=4,则sinA的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由勾股定理得,BC=√{AB^{2}-AC^{2}}=√{5^{2}-4^{2}}=3,\n所以,sinA=\\frac{BC}{AB}=\\frac{3}{5}．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.6", "org_choices": ["\\frac{3}{4}", "\\frac{4}{5}", "\\frac{3}{5}", "\\frac{5}{3}"], "choices": [0.75, 0.8, 0.6, 1.667], "label": 2}
+{"prob_id": 2657, "image_path": "images/2657.png", "question": "在Rt△ABC中,∠C=90°,AB=2,BC=1,则sinB的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:根据勾股定理可得:AC=√{AB^{2}-BC^{2}}=√{3},∴sinB=\\frac{AC}{AB}=\\frac{√{3}}{2}．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.8660254037844386", "org_choices": ["\\frac{1}{2}", "\\frac{√{2}}{2}", "\\frac{√{3}}{2}", "2"], "choices": [0.5, 0.707, 0.866, 2.0], "label": 2}
+{"prob_id": 2662, "image_path": "images/2662.png", "question": "如图,在Rt△ABC中,已知∠A=90°,AC=3,AB=4,则sinB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由勾股定理得,BC=√{AC^{2}+AB^{2}}=√{3^{2}+4^{2}}=5,\n所以,sinB=\\frac{AC}{BC}=\\frac{3}{5}．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.6", "org_choices": ["\\frac{3}{4}", "\\frac{3}{5}", "\\frac{4}{5}", "\\frac{5}{4}"], "choices": [0.75, 0.6, 0.8, 1.25], "label": 1}
+{"prob_id": 2664, "image_path": "images/2664.png", "question": "在Rt△ACB中,∠C=90°,BC=5,AC=12,则sinA=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:AB=√{AC^{2}+BC^{2}}=13,\n则sinA=\\frac{BC}{AB}=\\frac{5}{13}．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.38461538461538464", "org_choices": ["\\frac{5}{12}", "\\frac{12}{5}", "\\frac{5}{13}", "\\frac{12}{13}"], "choices": [0.417, 2.4, 0.385, 0.923], "label": 2}
+{"prob_id": 2707, "image_path": "images/2707.png", "question": "如图,在直角坐标系中,P是第一象限内的点,其坐标是(4,m),且OP与x轴正半轴的夹角α的余弦值是\\frac{3}{5},则tan∠α的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图所示:过点P作PA⊥x轴于点A,∵P是第一象限内的点,其坐标是(4,m),∴AO=4,∵OP与x轴正半轴的夹角α的余弦值是\\frac{3}{5},∴OP=\\frac{20}{3},∴PA=√{0P^{2}-A0^{2}}=\\frac{16}{3},∴tan∠α的值是:\\frac{16}{\\frac{3}{4}}=image_018080.png\\frac{4}{3}．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "1.3333333333333333", "org_choices": ["\\frac{4}{5}", "\\frac{5}{4}", "\\frac{3}{4}", "\\frac{4}{3}"], "choices": [0.8, 1.25, 0.75, 1.333], "label": 3}
+{"prob_id": 2730, "image_path": "images/2730.png", "question": "如图,已知Rt△ABC中,∠C=90°,AC=6,BC=8,则tanA的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在Rt△ABC中,∠C=90°,AC=6,BC=8,∴tanA=\\frac{BC}{AC}=\\frac{8}{6}=\\frac{4}{3}．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "1.3333333333333333", "org_choices": ["\\frac{3}{5}", "\\frac{4}{5}", "\\frac{3}{4}", "\\frac{4}{3}"], "choices": [0.6, 0.8, 0.75, 1.333], "label": 3}
+{"prob_id": 2738, "image_path": "images/2738.png", "question": "如图:在Rt△ABC中,∠C=90°,AC=8,AB=10,则sinB的值等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:sinB=\\frac{AC}{AB}=\\frac{4}{5}．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.8", "org_choices": ["\\frac{3}{5}", "\\frac{4}{5}", "\\frac{3}{4}", "\\frac{4}{3}"], "choices": [0.6, 0.8, 0.75, 1.333], "label": 1}
+{"prob_id": 2747, "image_path": "images/2747.png", "question": "如图,在Rt△ABC中,∠C=90°,AC=1,BC=2,则\\cosB的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在Rt△ABC中,∠C=90°,AC=1,BC=2,由勾股定理,得\nAB=√{AC^{2}+BC^{2}}=√{5}．\n由锐角的余弦,得\\cosB=\\frac{BC}{AB}=\\frac{2}{√{5}}=\\frac{2√{5}}{5},\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.8944271909999159", "org_choices": ["\\frac{√{5}}{5}", "\\frac{2√{5}}{5}", "\\frac{1}{2}", "2"], "choices": [0.447, 0.894, 0.5, 2.0], "label": 1}
+{"prob_id": 2750, "image_path": "images/2750.png", "question": "如图,在直角坐标系中,点A的坐标是(2,3),则tanα的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,过点A作AB⊥x轴于B,∵A(2,3),∴OB=2,AB=3,∴tanα=\\frac{AB}{OB}=\\frac{3}{2}．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "1.5", "org_choices": ["\\frac{2}{3}", "\\frac{3}{2}", "\\frac{2√{13}}{13}", "\\frac{3√{13}}{13}"], "choices": [0.667, 1.5, 0.555, 0.832], "label": 1}
+{"prob_id": 2760, "image_path": "images/2760.png", "question": "如图,已知Rt△ABC中,∠C=90°,AC=4,tanA=\\frac{1}{2},则BC的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵tanA=\\frac{1}{2}=\\frac{BC}{AC},AC=4,∴BC=2,\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["2", "8", "2√{5}", "4√{5}"], "choices": [2.0, 8.0, 4.472, 8.944], "label": 0}
+{"prob_id": 2785, "image_path": "images/2785.png", "question": "如图,ABC中,AB=AC=4cm,BC=6cm,则\\cosB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作AD⊥BC于点D．∵AB=AC,∴BD=\\frac{1}{2}BC=3cm,∴\\cosB=\\frac{BD}{AB}=\\frac{3}{4}．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "0.75", "org_choices": ["\\frac{3}{4}", "\\frac{4}{3}", "\\frac{3}{5}", "\\frac{4}{5}"], "choices": [0.75, 1.333, 0.6, 0.8], "label": 0}
+{"prob_id": 2801, "image_path": "images/2801.png", "question": "如图,在Rt△ABC中,∠C=90°,AC=4,AB=5,则sinB的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在△ABC中,∠C=90°,AC=4,AB=5,∴sin∠B=\\frac{AC}{AB}=\\frac{4}{5},\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "0.8", "org_choices": ["\\frac{2}{3}", "\\frac{3}{5}", "\\frac{3}{4}", "\\frac{4}{5}"], "choices": [0.667, 0.6, 0.75, 0.8], "label": 3}
+{"prob_id": 2803, "image_path": "images/2803.png", "question": "如图,四个边长为1的小正方形拼成一个大正方形,A、B、O是小正方形顶点,⊙O的半径为1,P是⊙O上的点,且位于右上方的小正方形内,则sin∠APB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接AB,BC．∵AC是直径．∴∠ABC=90°,则△ABC是等腰直角三角形．∴∠C=45°∴sin∠APB=sinC=sin45°=\\frac{√{2}}{2}．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.7071067811865476", "org_choices": ["\\frac{√{3}}{2}", "\\frac{√{2}}{2}", "\\frac{1}{2}", "1"], "choices": [0.866, 0.707, 0.5, 1.0], "label": 1}
+{"prob_id": 2820, "image_path": "images/2820.png", "question": "如图,Rt△ABC的斜边AB=10cm,\\cosA=\\frac{3}{5},则BC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵\\cosA=\\frac{CA}{BA}=\\frac{3}{5},∵AB=10,∴AC=6．∴BC=8,\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["5cm", "6cm", "3cm", "8cm"], "choices": [5.0, 6.0, 3.0, 8.0], "label": 3}
+{"prob_id": 2836, "image_path": "images/2836.png", "question": "如图,在四边形ABCD中,E、F分別是AB、AD的中点,若EF=2,BC=5,CD=3,则tanC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BD．∵E、F分別是AB、AD的中点．∴BD=2EF=4∵BC=5,CD=3∴△BCD是直角三角形．∴tanC=\\frac{BD}{CD}=\\frac{4}{3}\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "1.3333333333333333", "org_choices": ["\\frac{3}{4}", "\\frac{4}{3}", "\\frac{3}{5}", "\\frac{4}{5}"], "choices": [0.75, 1.333, 0.6, 0.8], "label": 1}
+{"prob_id": 2867, "image_path": "images/2867.png", "question": "在Rt△ABC中,∠ACB=90°,CD⊥AB于点D,若AC=3,BC=4,则tanα等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ACB=90°,∴∠ACD+∠DCB=90°,∵CD⊥AB于点D,∴∠AB+∠DCB=90°,∴∠ACD=∠B,∴tanα=tanB=\\frac{AC}{CB}=\\frac{3}{4},\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.75", "org_choices": ["\\frac{4}{5}", "\\frac{3}{5}", "\\frac{3}{4}", "\\frac{4}{3}"], "choices": [0.8, 0.6, 0.75, 1.333], "label": 2}
+{"prob_id": 2882, "image_path": "images/2882.png", "question": "如图,在Rt△ABC中,∠C=90°,sinA=\\frac{1}{3},则\\cosB的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠C=90°,∴∠A+∠B=90°,∴\\cosB=sinA,\n而sinA=\\frac{1}{3},∴\\cosB=\\frac{1}{3}．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "0.3333333333333333", "org_choices": ["\\frac{1}{3}", "\\frac{2}{3}", "\\frac{√{2}}{3}", "\\frac{2√{2}}{3}"], "choices": [0.333, 0.667, 0.471, 0.943], "label": 0}
+{"prob_id": 2883, "image_path": "images/2883.png", "question": "我们知道,如果两个锐角的和等于一直角,那么这两个角互为余角,简称互余．如图,∠A与∠B互余,且有:sinA=\\frac{∠A的对边}{斜边}=\\frac{a}{c},\\cosB=\\frac{∠B的邻边}{斜边}=\\frac{a}{c},因此知sinA=\\cosB,注意到在△ABC中,∠A+∠B=90°,即∠B=90°-∠A,∠A=90°-∠B,于是有:sin(90°-A)=\\cosA,\\cos(90°-A)=sinA．试完成下列选择题:如果α是锐角,且\\cosα=\\frac{4}{5},那么sin(90°-α)的值等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵\\cosα=\\frac{4}{5},∴sin(90°-α)=\\cosα=\\frac{4}{5}．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.8", "org_choices": ["\\frac{9}{25}", "\\frac{4}{5}", "\\frac{3}{5}", "\\frac{16}{25}"], "choices": [0.36, 0.8, 0.6, 0.64], "label": 1}
+{"prob_id": 2970, "image_path": "images/2970.png", "question": "如图,已知AB、AD是⊙O的弦,∠BOD=50°,则∠BAD的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BOD=50°,∴∠BAD=25°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["50°", "40°", "25°", "35°"], "choices": [50.0, 40.0, 25.0, 35.0], "label": 2}
+{"prob_id": 2999, "image_path": "images/2999.png", "question": "如图,在△ABC中,∠ABC和∠ACB的外角平分线交于点O,且∠BOC=40°,则∠A=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∠BOC=40°∴∠OBC+∠OCB=140°∴∠ABC+∠ACB=180°×2-140°×2=80°∴∠A=180°-(∠ABC+∠ACB)=180°-80°=100°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["10°", "70°", "100°", "160°"], "choices": [10.0, 70.0, 100.0, 160.0], "label": 2}
+{"prob_id": 3001, "image_path": "images/3001.png", "question": "如图,已知CD为圆O的直径,过点D的弦DE平行于半径OA,若角D=50°,则角C的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA∥DE,∴∠AOD=∠D=50°,∴∠C=\\frac{1}{2}∠AOD=25°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["50°", "25°", "30°", "40°"], "choices": [50.0, 25.0, 30.0, 40.0], "label": 1}
+{"prob_id": 3022, "image_path": "images/3022.png", "question": "如图,点B在⊙O上,弦AC∥OB,∠BOC=50°,则∠OAB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BOC=2∠BAC,∠BOC=50°,∴∠BAC=25°,∵AC∥OB,∴∠BAC=∠B=25°,∵OA=OB,∴∠OBA=∠BAO=25°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["25°", "50°", "60°", "30°"], "choices": [25.0, 50.0, 60.0, 30.0], "label": 0}
+{"prob_id": 3039, "image_path": "images/3039.png", "question": "如图,点A、B、C是⊙O上的三点,若∠A=40°,则∠BOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∠BOC=2∠A=2×40°=80°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["100°", "80°", "60°", "40°"], "choices": [100.0, 80.0, 60.0, 40.0], "label": 1}
+{"prob_id": 3055, "image_path": "images/3055.png", "question": "在⊙O中,AB是直径,CD是弦,∠ABD=28°,则∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接AD．∵AB是直径,∴∠ADB=90°,∵∠ABD=28°,∴∠DAB=90°-28°=62°,∴∠C=∠DAB=62°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "62.0", "org_choices": ["28°", "56°", "62°", "72°"], "choices": [28.0, 56.0, 62.0, 72.0], "label": 2}
+{"prob_id": 3059, "image_path": "images/3059.png", "question": "如图,点A、B、C是⊙O上的三点,若∠BOC=80°,则∠A的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BOC与∠A是同弧所对的圆心角与圆周角,∠BOC=80°,∴∠A=\\frac{1}{2}∠BOC=40°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "60°", "80°", "100°"], "choices": [40.0, 60.0, 80.0, 100.0], "label": 0}
+{"prob_id": 3071, "image_path": "images/3071.png", "question": "已知如图,AB是⊙O的直径,CD是⊙O的弦,∠CDB=40°,则∠CBA的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接AC,∵AB是⊙O的直径,∴∠ACB=90°,∵∠A=∠CDB=40°,∴∠CBA=90°-∠A=50°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["60°", "50°", "40°", "30°"], "choices": [60.0, 50.0, 40.0, 30.0], "label": 1}
+{"prob_id": 3116, "image_path": "images/3116.png", "question": "如图,已知O是四边形ABCD内一点,OA=OB=OC,∠ABC=∠ADC=65°,则∠DAO+∠DCO=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA=OB=OC,∴∠ABO=∠BAO,∠OBC=∠OCB,∵∠ABC=65°=∠ABO+∠OBC,∴∠BAO+∠BCO=65°,∵∠ADC=65°,∴∠DAO+∠DCO=360°-(∠ADC+∠BAO+∠BCO+∠ABC)=360°-(65°+65°+65°)=165°,\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "165.0", "org_choices": ["90°", "110°", "120°", "165°"], "choices": [90.0, 110.0, 120.0, 165.0], "label": 3}
+{"prob_id": 3153, "image_path": "images/3153.png", "question": "如图,AB是⊙O直径,∠D=33°,则∠AOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BOC=2∠BDC=66°,\n又∵∠AOC=180°-∠BOC,∴∠AOC=114°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "114.0", "org_choices": ["99°", "108°", "114°", "127°"], "choices": [99.0, 108.0, 114.0, 127.0], "label": 2}
+{"prob_id": 3164, "image_path": "images/3164.png", "question": "如图,在⊙O中,OA⊥BC,∠AOB=48°,D为⊙O上一点,则∠ADC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA⊥BC,∴⁀{AC}=⁀{AB},∴∠ADC=\\frac{1}{2}∠AOB=\\frac{1}{2}×48°=24°．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "24.0", "org_choices": ["24°", "42°", "48°", "12°"], "choices": [24.0, 42.0, 48.0, 12.0], "label": 0}
+{"prob_id": 3171, "image_path": "images/3171.png", "question": "如图,A、B、C三点都在⊙O上,∠ABO=50°,则∠ACB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA=OB∴∠OAB=∠OBA=50°∴∠AOB=80°∴∠ACB=40°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["50°", "40°", "30°", "25°"], "choices": [50.0, 40.0, 30.0, 25.0], "label": 1}
+{"prob_id": 3176, "image_path": "images/3176.png", "question": "如图,点AC是⊙O的直径,若∠OBC=40°,则∠AOB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OC=OB,∴∠OBC=∠C,∵弧AB所对的圆周角是∠C,所对的圆心角是∠AOB,∴∠AOB=2∠OCB=80°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["40°", "50°", "80°", "100°"], "choices": [40.0, 50.0, 80.0, 100.0], "label": 2}
+{"prob_id": 3180, "image_path": "images/3180.png", "question": "如图,在⊙A中,已知弦BC=8,DE=6,∠BAC+∠EAD=180°,则⊙A的半径长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作直径CF,连结BF,如图,∵∠BAC+∠EAD=180°,\n而∠BAC+∠BAF=180°,∴∠DAE=∠BAF,∴⁀{DE}=⁀{BF},∴DE=BF=6,∵CF是直径,∴∠CBF=90°,∴CF=√{BC^{2}+BF^{2}}=√{8^{2}+6^{2}}=10．∴⊙A的半径为5．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["10", "6", "5", "8"], "choices": [10.0, 6.0, 5.0, 8.0], "label": 2}
+{"prob_id": 3191, "image_path": "images/3191.png", "question": "将量角器按如图所示的方式放在一个残缺的玻璃碎片上,使点A在半圆上,点B、C的读数分别为105°、155°,则∠BAC的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设半圆的圆心为O,连接OB,OC,\n由题意得:∠COB=50°,∵∠BAC与∠COB都对⁀{BC},∴∠BAC=\\frac{1}{2}∠COB=25°,\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["55°", "50°", "27.5°", "25°"], "choices": [55.0, 50.0, 27.5, 25.0], "label": 3}
+{"prob_id": 3198, "image_path": "images/3198.png", "question": "如图,点A、B、是⊙O上三点且AB=AC,连接BO、CO,若∠ABC=65°,则∠BOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意可得:AB=AC,∵∠ABC=65°,∴∠ACB=65°,∴∠A=50°,∴∠BOC=100°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["50°", "65°", "100°", "130°"], "choices": [50.0, 65.0, 100.0, 130.0], "label": 2}
+{"prob_id": 3208, "image_path": "images/3208.png", "question": "如图,已知圆心角∠AOB的度数为110°,则圆周角∠ACB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设点E是优弧AB上的一点,连接EA,EB∵∠AOB=110°∴∠E=\\frac{1}{2}∠AOB=55°∴∠ACB=180°-∠E=125°．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "125.0", "org_choices": ["110°", "70°", "55°", "125°"], "choices": [110.0, 70.0, 55.0, 125.0], "label": 3}
+{"prob_id": 3225, "image_path": "images/3225.png", "question": "如图,某隧道的截面是一个半径为3.4m的半圆形,一辆宽3.2m的卡车恰好能通过该隧道,连车带货一起最高为多少米(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过O作OE⊥AB于E,则∠OEB=90°,AB=DC=3.2m,由垂径定理得:AE=BE=\\frac{1}{2}×3.2m=1.6m,在Rt△BEO中,∠BEO=90°,BE=1.6m,OB=3.4m,由勾股定理得:OE=√{3.4^{2}-1.6^{2}}=3(m),即连车带货一起最高为3m,故选:A．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["3m", "3.4m", "4m", "2.8m"], "choices": [3.0, 3.4, 4.0, 2.8], "label": 0}
+{"prob_id": 3232, "image_path": "images/3232.png", "question": "如图,AB和CD是⊙O的两条直径,弦DE∥AB,若弧DE为40°的弧,则∠BOC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OE,∵弧DE为40°的弧,∴∠DOE=40°．∵OD=OE,∴∠ODE=\\frac{180^{°}-40^{°}}{2}=70°．∵弦DE∥AB,∴∠AOC=∠ODE=70°,∴∠BOC=180°-∠AOC=180°-70°=110°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "110.0", "org_choices": ["110°", "80°", "40°", "70°"], "choices": [110.0, 80.0, 40.0, 70.0], "label": 0}
+{"prob_id": 3234, "image_path": "images/3234.png", "question": "如图,在⊙O中,若点C是⁀{AB}的中点,∠A=50°,则∠BOC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠A=50°,OA=OB,∴∠OBA=∠OAB=50°,∴∠AOB=180°-50°-50°=80°,∵点C是⁀{AB}的中点,∴∠BOC=\\frac{1}{2}∠AOB=40°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "45°", "50°", "60°"], "choices": [40.0, 45.0, 50.0, 60.0], "label": 0}
+{"prob_id": 3255, "image_path": "images/3255.png", "question": "若AB∥CD,∠C=60°,则∠A+∠E等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB∥CD,∴∠C=∠EFB=60°,∵∠EFB是△AEF的一个外角,∴∠EFB=∠A+∠E=60°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["20°", "30°", "40°", "60°"], "choices": [20.0, 30.0, 40.0, 60.0], "label": 3}
+{"prob_id": 3275, "image_path": "images/3275.png", "question": "已知:如图,在⊙O中,OA⊥BC,∠AOB=70°,则∠ADC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA⊥BC,∠AOB=70°,∴⁀{AB}=⁀{AC},∴∠ADC=\\frac{1}{2}∠AOB=35°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["30°", "35°", "45°", "70°"], "choices": [30.0, 35.0, 45.0, 70.0], "label": 1}
+{"prob_id": 3280, "image_path": "images/3280.png", "question": "如图,CD是⊙O的弦,O是圆心,把⊙O的劣弧沿着CD对折,A是对折后劣弧上的一点,∠CAD=110°,则∠B的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,翻折△ACD,点A落在A'处,∴∠A'=∠A=110°,∵四边形A'CBD是⊙O的内接四边形,∴∠A'+∠B=180°,∴∠B=70°,\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["110°", "70°", "60°", "55°"], "choices": [110.0, 70.0, 60.0, 55.0], "label": 1}
+{"prob_id": 3287, "image_path": "images/3287.png", "question": "如图,AB是⊙O直径,点C为⊙O上一点,∠C=20°,则∠BOC度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA=OC,∴∠A=∠C=20°,\n由圆周角定理得,∠BOC=2∠A=40°\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["20°", "30°", "40°", "60°"], "choices": [20.0, 30.0, 40.0, 60.0], "label": 2}
+{"prob_id": 3292, "image_path": "images/3292.png", "question": "如图,⊙O是△ABC的外接圆,若∠AOB=130°,则∠ACB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,在优弧AB上取一点D,连接AD,BD,\n则∠ADB=\\frac{1}{2}AOB=65°,∴∠ACB=180°-∠ADB=115°．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "115.0", "org_choices": ["115°", "120°", "125°", "130°"], "choices": [115.0, 120.0, 125.0, 130.0], "label": 0}
+{"prob_id": 3306, "image_path": "images/3306.png", "question": "如图,在⊙O中,弦AB与CD交于点E,BE=DE,∠B=40°,则∠A的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BE=DE,∠B=40°,∴∠D=∠B=40°,∴∠A=∠D=40°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["20°", "30°", "40°", "80°"], "choices": [20.0, 30.0, 40.0, 80.0], "label": 2}
+{"prob_id": 3308, "image_path": "images/3308.png", "question": "如图,点A、B、C、D在⊙O上,DE⊥OA,DF⊥OB,垂足分别为E,F,若∠EDF=50°,则∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE⊥OA,DF⊥OB,∴∠OED=∠OFD=90°,∴∠AOB=360°-90°-90°-50°=130°,\n由圆周角定理得,∠C=\\frac{1}{2}∠AOB=65°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["40°", "50°", "65°", "130°"], "choices": [40.0, 50.0, 65.0, 130.0], "label": 2}
+{"prob_id": 3316, "image_path": "images/3316.png", "question": "如图,CD为⊙O的直径,弦AB交CD于点M,M是AB的中点,点P在⁀{AD}上,PC与AB交于点N,∠PNA=60°,则∠PDC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵CD为⊙O的直径,∴∠P=90°．∵M是AB的中点,∴CM⊥AB．∵∠PNA=60°,∴∠C=90°-60°=30°,∴∠PDC=90°-∠C=90°-30°=60°．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["40°", "50°", "60°", "70°"], "choices": [40.0, 50.0, 60.0, 70.0], "label": 2}
+{"prob_id": 3317, "image_path": "images/3317.png", "question": "如图,AB是⊙O的直径,弦CD⊥AB于E,连结OC、AD,且∠A=35°,则∠AOC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OD,∵∠A=35°,∴∠BOD=70°．∵AB是⊙0的直径,弦CD⊥AB于E,∴∠BOC=∠BOD=70°,∴∠AOC=180°-70°=110°．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "110.0", "org_choices": ["70°", "105°", "110°", "140°"], "choices": [70.0, 105.0, 110.0, 140.0], "label": 2}
+{"prob_id": 3321, "image_path": "images/3321.png", "question": "如图,在△ABC中,AB=AC,以BC为直径画半圆交AB于E,交AC于D,⁀{CD}的度数为40°,则∠A的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BC为圆的直径,∴∠BDC=90°,∵⁀{CD}的度数为40°,∴∠DBC=20°,∴∠C=70°,∵AB=AC,∴∠ABC=∠C=70°,∴∠A=40°,\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "70°", "50°", "20°"], "choices": [40.0, 70.0, 50.0, 20.0], "label": 0}
+{"prob_id": 3324, "image_path": "images/3324.png", "question": "如图,点A,B,C,P在⊙O上,CD⊥OA,CE⊥OB,垂足分别为D,E,∠DCE=36°,则∠P的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵CD⊥OA,CE⊥OB,垂足分别为D,E,∠DCE=36°,∴∠DOE=180°-36°=144°,∴∠P=\\frac{1}{2}∠DOE=72°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "72.0", "org_choices": ["144°", "72°", "60°", "36°"], "choices": [144.0, 72.0, 60.0, 36.0], "label": 1}
+{"prob_id": 3328, "image_path": "images/3328.png", "question": "如图,点A、B、C、P在⊙O上,CD⊥OA,CE⊥OB,垂足分别为D,E,∠DCE=40°,则∠P的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵CD⊥OA,CE⊥OB,垂足分别为D,E,∠DCE=40°,∴∠DOE=180°-40°=140°,∴∠P=\\frac{1}{2}∠DOE=70°．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["70°", "60°", "40°", "35°"], "choices": [70.0, 60.0, 40.0, 35.0], "label": 0}
+{"prob_id": 3333, "image_path": "images/3333.png", "question": "如图,A、B、C三点在圆上,在△ABC中,∠ABC=70°,∠ACB=30°,D是弧BAC的中点,连结DB,DC,则∠DBC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在△ABC中,∠ABC=70°,∠ACB=30°,∴∠A=180°-∠ABC-∠ACB=80°,∴∠D=∠A=80°,∵D是弧BAC的中点,∴⁀{BD}=⁀{CD},∴∠DBC=∠DCB,∴∠DBC=\\frac{1}{2}(180°-∠D)=50°,\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["70°", "50°", "45°", "30°"], "choices": [70.0, 50.0, 45.0, 30.0], "label": 1}
+{"prob_id": 3345, "image_path": "images/3345.png", "question": "如图,AB,CD是⊙O的两条弦,连接AD,BC,若∠BCD=50°,则∠BAD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BCD=70°,∴∠BAD=∠BCD=70°．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["70°", "60°", "50°", "40°"], "choices": [70.0, 60.0, 50.0, 40.0], "label": 2}
+{"prob_id": 3357, "image_path": "images/3357.png", "question": "如图,△ABC内接于⊙O,若∠OAB=26°,则∠C的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB,\n在△OAB中,∵OA=OB,∴∠OAB=∠OBA,\n又∵∠OAB=26°,∴∠OBA=26°；∴∠AOB=180°-2×26°=128°；∴∠C=\\frac{1}{2}∠AOB=64°．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "64.0", "org_choices": ["26°", "52°", "60°", "64°"], "choices": [26.0, 52.0, 60.0, 64.0], "label": 3}
+{"prob_id": 3358, "image_path": "images/3358.png", "question": "如图,⊙O是△ABC的外接圆,∠A=70°,则∠BOC的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵⊙O是△ABC的外接圆,∠A=70°,∴∠BOC=2∠A=140°．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["30°", "35°", "70°", "140°"], "choices": [30.0, 35.0, 70.0, 140.0], "label": 3}
+{"prob_id": 3382, "image_path": "images/3382.png", "question": "如图,在⊙O中,弦AC∥半径OB,∠BOC=50°,则∠OBA的度数(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BOC=2∠BAC,∠BOC=50°,∴∠BAC=25°,∵AC∥OB,∴∠BAC=∠B=25°,∵OA=OB,∴∠OBA=∠BAO=25°,\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["25°", "50°", "60°", "30°"], "choices": [25.0, 50.0, 60.0, 30.0], "label": 0}
+{"prob_id": 3384, "image_path": "images/3384.png", "question": "如图,若∠ABC=30°,则∠AOC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠AOC=2∠ABC,∴∠AOC=2×30°=60°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["30°", "45°", "60°", "70°"], "choices": [30.0, 45.0, 60.0, 70.0], "label": 2}
+{"prob_id": 3385, "image_path": "images/3385.png", "question": "如图,在⊙O中,CD是直径,点A,点B在⊙O上,连接OA、OB、AC、AB,若∠AOB=40°,CD∥AB,则∠BAC的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA=OB,∴∠OAB=∠OBA=\\frac{180^{°}-∠AOB}{2}=\\frac{180^{°}-40^{°}}{2}=70°,\n又∵CD∥AB,∴∠COB=∠OBA=70°,∴∠BAC=\\frac{1}{2}∠COB=35°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["30°", "35°", "40°", "70°"], "choices": [30.0, 35.0, 40.0, 70.0], "label": 1}
+{"prob_id": 3389, "image_path": "images/3389.png", "question": "如图,是一个圆形展厅,为了监控整个展厅,在其圆形边缘上安装了甲、乙两台监视器,若甲监视器的监控角度为65°,则乙监控器的监控角度至少为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∠D=180°-∠B=180°-65°=115°．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "115.0", "org_choices": ["25°", "65°", "115°", "130°"], "choices": [25.0, 65.0, 115.0, 130.0], "label": 2}
+{"prob_id": 3394, "image_path": "images/3394.png", "question": "如图,⊙O是△ABC的外接圆,连接OA、OB,∠AOB=50°,则∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵⊙O是△ABC的外接圆,∠AOB=50°,∴∠ACB\\frac{1}{2}∠AOB=\\frac{1}{2}×50°=25°．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["25°", "40°", "50°", "80°"], "choices": [25.0, 40.0, 50.0, 80.0], "label": 0}
+{"prob_id": 3397, "image_path": "images/3397.png", "question": "已知:如图,AB是圆O的直径,CD为弦,连AD、AC,∠CAB=55°,则∠D=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB为⊙O的直径,∴∠ACB=90°,∵∠CAB=55°,∴∠B=90°-∠CAB=35°,∴∠ADC=∠B=35°．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["55°", "50°", "35°", "45°"], "choices": [55.0, 50.0, 35.0, 45.0], "label": 2}
+{"prob_id": 3440, "image_path": "images/3440.png", "question": "如图,点A,B,C在⊙O上,若∠C=35°,则∠AOB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由圆周角定理可得:∠AOB=2∠ACB=70°．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["17.5°", "35°", "60°", "70°"], "choices": [17.5, 35.0, 60.0, 70.0], "label": 3}
+{"prob_id": 3442, "image_path": "images/3442.png", "question": "如图,AB是⊙O的直径,∠ADC的度数是35°,则∠BOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠D=35°,∴∠AOC=2∠D=35°×2=70°,∵∠AOC+∠BOC=180°,∴∠BOC=180°-70°=110°,\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "110.0", "org_choices": ["120°", "110°", "100°", "70°"], "choices": [120.0, 110.0, 100.0, 70.0], "label": 1}
+{"prob_id": 3448, "image_path": "images/3448.png", "question": "如图,四边形ABCD内接于⊙O,AB为⊙O的直径,点C为⁀{BD}的中点,若∠DAB=50°,则∠ABC的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC,∵点C为⁀{BD}的中点,∴∠BOC=∠DAB=50°,∵OC=OB,∴∠ABC=∠OCB=65°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["55°", "60°", "65°", "70°"], "choices": [55.0, 60.0, 65.0, 70.0], "label": 2}
+{"prob_id": 3481, "image_path": "images/3481.png", "question": "如图,四边形ABCD是⊙O的内接四边形,AB为⊙O的直径,连结BD．若∠BCD=120°,则∠ABD的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是⊙O的内接四边形,∴∠BAD+∠BCD=180°,∵∠BCD=120°,∴∠BAD=60°,∵AB为⊙O的直径,∴∠ADB=90°,∴∠ABD=90°-60°=30°,\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["60°", "50°", "40°", "30°"], "choices": [60.0, 50.0, 40.0, 30.0], "label": 3}
+{"prob_id": 3519, "image_path": "images/3519.png", "question": "如图,点A、B、C、D在圆O上,点E在AD的延长线上,若∠ABC=60°,则∠CDE的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD为圆O的内接四边形,∴∠ABC+∠ADC=180°,∵∠CDE+∠ADC=180°,∠B=60°,∴∠CDE=∠B=60°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["30°", "45°", "60°", "70°"], "choices": [30.0, 45.0, 60.0, 70.0], "label": 2}
+{"prob_id": 3520, "image_path": "images/3520.png", "question": "如图,四边形ABCD内接于半圆O,已知∠ADC=140°,则∠AOC的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是圆内接四边形,∴∠ADC+∠B=180°,又∠ADC=140°,∴∠B=40°,∴∠AOC=2∠B=80°,\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["40°", "60°", "70°", "80°"], "choices": [40.0, 60.0, 70.0, 80.0], "label": 3}
+{"prob_id": 3524, "image_path": "images/3524.png", "question": "如图,四边形ABCD内接于圆O,若∠BOD=138°,则它的一个外角∠DCE的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由圆周角定理得,∠A=\\frac{1}{2}∠BOD=69°,∴∠DCE=,∠A=69°,\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "69.0", "org_choices": ["138°", "69°", "52°", "42°"], "choices": [138.0, 69.0, 52.0, 42.0], "label": 1}
+{"prob_id": 3528, "image_path": "images/3528.png", "question": "如图,四边形ABCD内接于⊙O,E为BC延长线上一点,∠A=50°,则∠DCE的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB,OD,∵∠DOB与∠A都对⁀{BD},∠DOB(大于平角的角)与∠BCD都对⁀{DAB},∴∠DOB=2∠A,∠DOB(大于平角的角)=2∠BCD,∵∠DOB+∠DOB(大于平角的角)=360°,∴∠A+∠BCD=180°,∵∠DCE+∠BCD=180°,∴∠DCE=∠A=50°,\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["40°", "50°", "60°", "130°"], "choices": [40.0, 50.0, 60.0, 130.0], "label": 1}
+{"prob_id": 3533, "image_path": "images/3533.png", "question": "如图,四边形ABCD内接于⊙O,F是⁀{CD}上一点,且⁀{DF}=⁀{BC},连接CF并延长交AD的延长线于点E,连接AC．若∠ABC=105°,∠BAC=25°,则∠E的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD内接于⊙O,∠ABC=105°,∴∠ADC=180°-∠ABC=180°-105°=75°．∵⁀{DF}=⁀{BC},∠BAC=25°,∴∠DCE=∠BAC=25°,∴∠E=∠ADC-∠DCE=75°-25°=50°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["45°", "50°", "55°", "60°"], "choices": [45.0, 50.0, 55.0, 60.0], "label": 1}
+{"prob_id": 3535, "image_path": "images/3535.png", "question": "如图,四边形ABCD是⊙O的内接四边形,若∠C=140°,则∠BOD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是⊙O的内接四边形,∴∠A+∠C=180°,∴∠A=40°,\n由圆周角定理得,∠BOD=2∠A=80°,\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["70°", "80°", "90°", "100°"], "choices": [70.0, 80.0, 90.0, 100.0], "label": 1}
+{"prob_id": 3536, "image_path": "images/3536.png", "question": "如图,在⊙O中,AB∥CD,∠BCD=100°,E为⁀{DC}上的任意一点,A、B、C、D是⊙O上的四个点,则∠AEC的角度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB∥CD,∠BCD=100°,∴∠ABC=180°-∠BCD=80°,∵四边形AECB是圆内接四边形,∴∠AEC+∠ABC=180°,∴∠AEC=100°,\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["110°", "70°", "80°", "100°"], "choices": [110.0, 70.0, 80.0, 100.0], "label": 3}
+{"prob_id": 3539, "image_path": "images/3539.png", "question": "如图．已知A、B、C三点在⊙O上,点C在劣弧AB上,且∠AOB=130°,则∠ACB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在优弧⁀{AB}上取一点D,连接AD、BD,∠D=\\frac{1}{2}∠AOB=65°,∵四边形ADBC是⊙O的内接四边形,∴∠D+∠ACB=180°,∴∠ACB=115°,\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "115.0", "org_choices": ["130°", "125°", "120°", "115°"], "choices": [130.0, 125.0, 120.0, 115.0], "label": 3}
+{"prob_id": 3545, "image_path": "images/3545.png", "question": "如图,四边形ABCD内接于⊙O,若∠ABC=40°,则∠ADC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD内接于⊙O,∴∠ABC+∠ADC=180°,\n又∵∠ABC=40°,∴∠ADC=140°．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["90°", "100°", "120°", "140°"], "choices": [90.0, 100.0, 120.0, 140.0], "label": 3}
+{"prob_id": 3558, "image_path": "images/3558.png", "question": "如图,四边形ABCD的一个外角∠DCE=70°,则∠BAD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD内接于⊙O,∴∠BAD=∠DCE=70°,\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["70°", "110°", "140°", "120°"], "choices": [70.0, 110.0, 140.0, 120.0], "label": 0}
+{"prob_id": 3569, "image_path": "images/3569.png", "question": "如图,四边形ABCD内接于⊙O,∠BOD=70°,则∠BCD的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠A与∠BOD是同弧所对的圆周角与圆心角,∠BOD=70°,∴∠A=\\frac{1}{2}∠BOD=35°．∵四边形ABCD是圆内接四边形,∴∠BCD=180°-∠A=180°-35°=145°．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "145.0", "org_choices": ["70°", "100°", "145°", "150°"], "choices": [70.0, 100.0, 145.0, 150.0], "label": 2}
+{"prob_id": 3573, "image_path": "images/3573.png", "question": "如图,四边形ABCD内接于⊙O,如果它的一个外角∠DCE=64°,那么∠BOD=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": ":∵四边形ABCD内接于⊙O,∴∠BAD+∠BCD=180°,∵∠BCD+∠DCE=180°,∴∠BAD=∠DCE=64°,∴∠BOD=2∠BAD=128°．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "128.0", "org_choices": ["128°", "100°", "64°", "32°"], "choices": [128.0, 100.0, 64.0, 32.0], "label": 0}
+{"prob_id": 3575, "image_path": "images/3575.png", "question": "如图,四边形ABCD是圆内接四边形,E是AD延长线上一点,若∠CBA=120°,则∠EDC的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是圆内接四边形,∠CBA=120°,∴∠ADC=180°-120°=60°．∵∠ADC+∠EDC=180°,∴∠EDC=180°-60°=120°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["60°", "120°", "150°", "130°"], "choices": [60.0, 120.0, 150.0, 130.0], "label": 1}
+{"prob_id": 3586, "image_path": "images/3586.png", "question": "如图,圆内接四边形ABCD中,圆心角∠1=100°,则圆周角∠ABC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵圆心角∠1=100°,∴∠ADC=\\frac{1}{2}∠1=50°,∵四边形ABCD是圆内接四边形,∴∠ABC=180°-∠ADC=180°-50°=130°．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["100°", "120°", "130°", "150°"], "choices": [100.0, 120.0, 130.0, 150.0], "label": 2}
+{"prob_id": 3593, "image_path": "images/3593.png", "question": "如图,在圆的内接四边形ABCD中,∠ABC=120°,则四边形ABCD的外角∠ADE的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是圆内接四边形,∴∠ADC+∠B=180°,∵∠ADC+∠ADE=180°,∴∠ADE=∠B．∵∠B=120°,∴∠ADE=120°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["130°", "120°", "110°", "100°"], "choices": [130.0, 120.0, 110.0, 100.0], "label": 1}
+{"prob_id": 3622, "image_path": "images/3622.png", "question": "如图,ABCD是⊙O的内接四边形,且∠ABC=115°,那么∠AOC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵ABCD是⊙O的内接四边形,且∠ABC=115°,∴∠ADC=180°-∠ABC=180°-115°=65°,∴∠AOC=2∠ADC=2×65°=130°．\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["115°", "120°", "130°", "135°"], "choices": [115.0, 120.0, 130.0, 135.0], "label": 2}
+{"prob_id": 3624, "image_path": "images/3624.png", "question": "如图,已知圆周角∠BAD=50°,那么圆周角∠BCD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD内接⊙O,∴∠BAD+∠BCD=180°,∴∠BCD=180°-∠A=180°-50°=130°．\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["130°", "100°", "50°", "40°"], "choices": [130.0, 100.0, 50.0, 40.0], "label": 0}
+{"prob_id": 3626, "image_path": "images/3626.png", "question": "如图,⊙O是四边形ABCD的外接圆,若∠O=110°,则∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由圆周角定理得,∠A=\\frac{1}{2}∠O=55°,∵⊙O是四边形ABCD的外接圆,∴∠A+∠C=180°,∴∠C=125°,\n故选:A．", "dataset_name": "Geoqa", "ground_truth": "125.0", "org_choices": ["125°", "120°", "105°", "90°"], "choices": [125.0, 120.0, 105.0, 90.0], "label": 0}
+{"prob_id": 3633, "image_path": "images/3633.png", "question": "如图,四边形ABCD内接于⊙O,若∠C=36°,则∠A的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD内接于⊙O,∴∠A+∠C=180°,\n而∠C=36°,∴∠A=180°-36°=144°．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "144.0", "org_choices": ["36°", "56°", "72°", "144°"], "choices": [36.0, 56.0, 72.0, 144.0], "label": 3}
+{"prob_id": 3635, "image_path": "images/3635.png", "question": "如图,⊙O上有A,B,C,D四点,其中∠A=80°,那么∠C的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是圆内接四边形,∠A=80°,∴∠C=180°-80°=100°．\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["40°", "60°", "80°", "100°"], "choices": [40.0, 60.0, 80.0, 100.0], "label": 3}
+{"prob_id": 3661, "image_path": "images/3661.png", "question": "如图,△ABC是⊙O的内接三角形,若∠ACB=30°,AB=6,则⊙O的半径是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接OA,OB,∵∠ACB=30°,∴∠AOB=2∠ACB=60°,∵OA=OB,∴△AOB是等边三角形,∴OA=AB=6,\n即⊙O的半径是6,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["3", "2√{3}", "6", "4√{3}"], "choices": [3.0, 3.464, 6.0, 6.928], "label": 2}
+{"prob_id": 3665, "image_path": "images/3665.png", "question": "如图,线段AB是⊙O的直径,弦CD丄AB,∠CAB=20°,则∠BOD等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵线段AB是⊙O的直径,弦CD丄AB,∴⁀{BC}=⁀{BD},∴∠BOD=2∠CAB=2×20°=40°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["20°", "40°", "80°", "70°"], "choices": [20.0, 40.0, 80.0, 70.0], "label": 1}
+{"prob_id": 3671, "image_path": "images/3671.png", "question": "如图,△ABC是⊙O的内接三角形,AB为⊙O的直径,点D为⊙O上一点,若∠ACD=40°,则∠BAD的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BD,∵AB为圆O的直径,∴∠ADB=90°,∵∠ACD=∠ABD=40°,∴∠BAD=90°-40°=50°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["35°", "50°", "40°", "60°"], "choices": [35.0, 50.0, 40.0, 60.0], "label": 1}
+{"prob_id": 3685, "image_path": "images/3685.png", "question": "如图,△ABC内接于⊙O,∠C=20°,则∠OAB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由圆周角定理得,∠AOB=2∠C=40°,∵OA=OB,∴∠OAB=∠OBA=\\frac{1}{2}×(180°-40°)=70°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["50°", "60°", "70°", "72°"], "choices": [50.0, 60.0, 70.0, 72.0], "label": 2}
+{"prob_id": 3699, "image_path": "images/3699.png", "question": "如图,△ABC内接于⊙O,连接OA,OB,若∠C=35°,则∠OBA的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠C=35°,∴∠AOB=70°,∵OA=OB,∴∠OAB=∠OBA=55°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["60°", "55°", "50°", "45°"], "choices": [60.0, 55.0, 50.0, 45.0], "label": 1}
+{"prob_id": 3700, "image_path": "images/3700.png", "question": "如图,已知△ABC内接于⊙O,∠BAC=50°,则∠BOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由圆周角定理得,∠BOC=2∠BAC=100°,\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["90°", "100°", "110°", "120°"], "choices": [90.0, 100.0, 110.0, 120.0], "label": 1}
+{"prob_id": 3705, "image_path": "images/3705.png", "question": "如图,△ABC中,AB=AC,∠BAC=70°,⊙O是△ABC的外接圆,点D在劣弧⁀{AC}上,则∠D的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB=AC,∠BAC=70°,∴∠B=∠ACB=55°,∵四边形ABCD是⊙O的内接四边形,∴∠D=180°-∠A=125°,\n故选:C．", "dataset_name": "Geoqa", "ground_truth": "125.0", "org_choices": ["55°", "110°", "125°", "140°"], "choices": [55.0, 110.0, 125.0, 140.0], "label": 2}
+{"prob_id": 3708, "image_path": "images/3708.png", "question": "如图,△ABC内接于⊙O,∠AOB=80°,则∠ACB的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵△ABC内接于⊙O,∠AOB=80°,∴∠ACB=\\frac{1}{2}∠AOB=40°．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["20°", "40°", "80°", "90°"], "choices": [20.0, 40.0, 80.0, 90.0], "label": 1}
+{"prob_id": 3746, "image_path": "images/3746.png", "question": "如图,△ABC是⊙O的内接三角形,∠C=30°,⊙O的半径为5,若点P是⊙O上的一点,在△ABP中,PB=AB,则PA的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OA、OB、OP,∵∠C=30°,∴∠APB=∠C=30°,∵PB=AB,∴∠PAB=∠APB=30°∴∠ABP=120°,∵PB=AB,∴OB⊥AP,AD=PD,∴∠OBP=∠OBA=60°,∵OB=OA,∴△AOB是等边三角形,∴AB=OA=5,\n则Rt△PBD中,PD=\\cos30°•PB=\\frac{√{3}}{2}×5=\\frac{5√{3}}{2},∴AP=2PD=5√{3},\n故选:D．", "dataset_name": "Geoqa", "ground_truth": "8.660254037844387", "org_choices": ["5", "\\frac{5√{3}}{2}", "5√{2}", "5√{3}"], "choices": [5.0, 4.33, 7.071, 8.66], "label": 3}
+{"prob_id": 3749, "image_path": "images/3749.png", "question": "如图,△ABC内接于⊙O,OC⊥OB,OD⊥AB于D交AC于E点,已知⊙O的半径为1,则AE²+CE²的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BE,∵OD⊥AB,∴AD=DB,∴EA=EB,∠EAO=∠EBO=∠ACO,∵∠ECB+∠EBC=∠ECO+45°+∠EBC=∠OBE+45°+∠EBC=90°,∴∠BEC=90°,\n在直角△BEC中,BE²+CE²=BC²,∵BC²=2OA²=2,∴BE²+CE²=2,即AE²+CE²=2．\n故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["1", "2", "3", "4"], "choices": [1.0, 2.0, 3.0, 4.0], "label": 1}
+{"prob_id": 3771, "image_path": "images/3771.png", "question": "如图,已知⊙O为△ABC的外接圆,且AB为⊙O的直径,若OC=5,AC=6,则BC长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB为⊙O的直径,∴∠ACB=90°．∵OC=5,AC=6,∴AB=2OC=10,∴BC=√{AB^{2}-AC^{2}}=√{10^{2}-6^{2}}=8．故选:C．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["10", "9", "8", "无法确定"], "choices": [10.0, 9.0, 8.0], "label": 3}
+{"prob_id": 3777, "image_path": "images/3777.png", "question": "如图,∠XOY=45°,一把直角三角尺ABC的两个顶点A、B分别在OX,OY上移动,其中AB=10,那么点O到顶点A的距离的最大值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵\\frac{AB}{sin45^{°}}=\\frac{AO}{sin∠ABO},∴当∠ABO=90°时,点O到顶点A的距离的最大．则OA=√{2}AB=10√{2}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "14.142135623730951", "org_choices": ["8", "10", "8√{2}", "10√{2}"], "choices": [8.0, 10.0, 11.314, 14.142], "label": 3}
+{"prob_id": 3789, "image_path": "images/3789.png", "question": "如图,△ABC中,∠BAC=70°,∠ABC=45°,点O是△ABC的外接圆的圆心,则∠AOB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BAC=70°,∠ABC=45°,∴∠C=180°-70°-45°=65°,∴∠AOB=2∠C=130°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["65°", "90°", "130°", "140°"], "choices": [65.0, 90.0, 130.0, 140.0], "label": 2}
+{"prob_id": 3796, "image_path": "images/3796.png", "question": "如图,⊙O是△ABD的外接圆,若∠A=135°,则∠BDO的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在优弧BD上任意找一点E,连接BE、DE,根据圆内接四边形的性质,得∠E=45°,根据圆周角定理,得∠BOD=2∠E=90°,∴∠BDO=45°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "45.0", "org_choices": ["30°", "67.5°", "45°", "135°"], "choices": [30.0, 67.5, 45.0, 135.0], "label": 2}
+{"prob_id": 3805, "image_path": "images/3805.png", "question": "如图,△ABC内接于⊙O,若∠AOB=110°,则∠ACB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ACB与∠AOB是同弧所对的圆周角与圆心角,∠AOB=110°,∴∠ACB=\\frac{1}{2}∠AOB=55°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["70°", "60°", "55°", "50°"], "choices": [70.0, 60.0, 55.0, 50.0], "label": 2}
+{"prob_id": 3837, "image_path": "images/3837.png", "question": "如图,已知⊙O的直径AB与弦AC的夹角为30°,过C点的切线PC与AB延长线交于点P,⊙O的半径为2,则PC为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PC为切线,∴OC⊥PC,∵OA=OC,∴∠OCA=∠A=30°,∴∠POC=∠A+∠OCA=60°,∴∠P=30°,在Rt△OCP中,PC=√{3}OC=2√{3}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "3.4641016151377544", "org_choices": ["4", "4√{3}", "6", "2√{3}"], "choices": [4.0, 6.928, 6.0, 3.464], "label": 3}
+{"prob_id": 3839, "image_path": "images/3839.png", "question": "如图,AB切⊙O于点B,AO交⊙O于点C,点D在⊙O上,若∠A=40°,则∠BDC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB,∵AB切⊙O于点B,∴OB⊥AB,∴∠OBA=90°,∵∠A=40°,∴∠BOA=90°-40°=50°,由圆周角定理得,∠BDC=\\frac{1}{2}∠BOA=25°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["50°", "30°", "25°", "20°"], "choices": [50.0, 30.0, 25.0, 20.0], "label": 2}
+{"prob_id": 3877, "image_path": "images/3877.png", "question": "如图,AB是⊙O的直径,点D在AB的延长线上,过点D作⊙O的切线,切点为C,若∠A=25°,则∠D=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC．∵OC=OA,∴∠OCA=∠A=25°,∴∠DOC=∠A+∠OCA=50°,∵CD是⊙O的切线,∴OC⊥CD,∴∠OCD=90°,∴∠D=90°-∠DOC=40°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["25°", "40°", "50°", "65°"], "choices": [25.0, 40.0, 50.0, 65.0], "label": 1}
+{"prob_id": 3883, "image_path": "images/3883.png", "question": "如图,在半径为2的⊙O中,C为直径AB延长线上一点,CD与圆相切于点D,连接AD,已知∠DAC=30°,则线段CD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵CD与圆相切于点D,∴OD⊥CD,∵∠DOC=2∠DAC=2×30°=60°,∴∠C=30°,∴CD=√{3}OD=2√{3}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "3.4641016151377544", "org_choices": ["1", "√{3}", "2", "2√{3}"], "choices": [1.0, 1.732, 2.0, 3.464], "label": 3}
+{"prob_id": 3896, "image_path": "images/3896.png", "question": "⊙O是半径为1的圆,点O到直线L的距离为3,过直线L上的任一点P作⊙O的切线,切点为Q；若以PQ为边作正方形PQRS,则正方形PQRS的面积最小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连结OQ、OP,作OH⊥l于H,如图,则OH=3,∵PQ为⊙O的切线,∴OQ⊥PQ,在Rt△POQ中,PQ=√{0P^{2}-0Q^{2}}=√{0P^{2}-1},当OP最小时,PQ最小,正方形PQRS的面积最小,而当OP=OH=3时,OP最小,所以PQ的最小值为√{3^{2}-1}=2√{2},所以正方形PQRS的面积最小值为8．故选:B．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["7", "8", "9", "10"], "choices": [7.0, 8.0, 9.0, 10.0], "label": 1}
+{"prob_id": 3916, "image_path": "images/3916.png", "question": "如图,AB是⊙O的直径,C是⊙O上的点,过点C作⊙O的切线交AB的延长线于点E,OD⊥AC于点D,若∠E=30°,CE=6,则OD的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC,∵CE为⊙O的切线,∴OC⊥EC,∴∠ECO=90°,∵∠E=30°,CE=6,∴OC=\\frac{6}{√{3}}=2√{3},∠EOC=60°,∵OA=OC,∴OA=2√{3},由圆周角定理得,∠EOC=2∠A,∴∠A=30°,∵OD⊥AC,∴∠ADO=90°,∴OD=\\frac{1}{2}OA=√{3},故选:B．", "dataset_name": "Geoqa", "ground_truth": "1.7320508075688772", "org_choices": ["1", "√{3}", "2", "2√{3}"], "choices": [1.0, 1.732, 2.0, 3.464], "label": 1}
+{"prob_id": 3920, "image_path": "images/3920.png", "question": "如图,直线AB与⊙O相切于点A,⊙O的半径为1,若∠OBA=30°,则OB长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵直线AB与⊙O相切于点A,连接OA则∠OAB=90°．∵OA=1,∴OB=\\frac{0A}{sinB}=\\frac{1}{\\frac{1}{2}}=2．故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["1", "2", "√{3}", "2√{3}"], "choices": [1.0, 2.0, 1.732, 3.464], "label": 1}
+{"prob_id": 3921, "image_path": "images/3921.png", "question": "如图,已知BA是⊙O的切线,切点为A,连接OB交⊙O于点C,若∠B=45°,AB长为2,则BC的长度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": ":连接OA,∵BA是⊙O的切线,切点为A,∴∠OAB=90°,∵∠B=45°,∴△OAB是等腰直角三角形,∵AB长为2,∴AO=2,则BO=2√{2},故BC=2√{2}-2,故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.8284271247461901", "org_choices": ["2√{2}-1", "√{2}", "2√{2}-2", "2-√{2}"], "choices": [1.828, 1.414, 0.828, 0.586], "label": 2}
+{"prob_id": 3941, "image_path": "images/3941.png", "question": "如图,AB是⊙O的直径,点P是⊙O外一点,PO交⊙O于点C,连接BC、PA．若∠P=36°,PA与⊙O相切,则∠B等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA是⊙O的切线,∴∠PAO=90°,∴∠AOP=90°-∠P=54°,∵OB=OC,∴∠AOP=2∠B,∴∠B=\\frac{1}{2}∠AOP=27°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "27.0", "org_choices": ["20°", "27°", "36°", "42°"], "choices": [20.0, 27.0, 36.0, 42.0], "label": 1}
+{"prob_id": 3949, "image_path": "images/3949.png", "question": "如图,AB、AC、BD是⊙O的切线,切点分别为P、C、D,若AB=5,AC=3,则BD的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AC、AP为⊙O的切线,∴AC=AP,∵BP、BD为⊙O的切线,∴BP=BD,∴BD=PB=AB-AP=5-3=2．故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["1.5", "2", "2.5", "3"], "choices": [1.5, 2.0, 2.5, 3.0], "label": 1}
+{"prob_id": 3967, "image_path": "images/3967.png", "question": "如图所示,AB是⊙O的直径,PA切⊙O于点A,线段PO交⊙O于点C,连结BC,若∠P=36°,则∠B等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA切⊙O于点A,∴∠OAP=90°,∵∠P=36°,∴∠AOP=54°,∴∠B=27°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "27.0", "org_choices": ["27°", "32°", "36°", "54°"], "choices": [27.0, 32.0, 36.0, 54.0], "label": 0}
+{"prob_id": 3981, "image_path": "images/3981.png", "question": "如图,PA和PB是⊙O的切线,点A和B的切点,AC是⊙O的直径,已知∠P=50°,则∠ACB的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB,如图,∵PA、PB是⊙O的切线,∴OA⊥PA,OB⊥PB,∴∠OAP=∠OBP=90°,∴∠AOB=360°-90°-90°-50°=130°,∵OB=OC,∴∠OCB=∠OBC,而∠AOB=∠OCB+∠OBC,∴∠OCB=\\frac{1}{2}×130°=65°,即∠ACB=65°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["65°", "60°", "55°", "50°"], "choices": [65.0, 60.0, 55.0, 50.0], "label": 0}
+{"prob_id": 4005, "image_path": "images/4005.png", "question": "如图,点A、B、C在⊙O上,过点A作⊙O的切线交OC的延长线于点P,∠B=30°,OP=3,则AP的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OA,∵∠B=30°,∴∠AOC=2∠B=60°,∵过点A作⊙O的切线交OC的延长线于点P,∴∠OAP=90°,∵OP=3,∴AP=OPsin60°=3×\\frac{√{3}}{2}=\\frac{3√{3}}{2},故选:D．", "dataset_name": "Geoqa", "ground_truth": "2.598076211353316", "org_choices": ["3", "\\frac{3}{2}", "\\frac{2}{3}√{3}", "\\frac{3}{2}√{3}"], "choices": [3.0, 1.5, 1.155, 2.598], "label": 3}
+{"prob_id": 4009, "image_path": "images/4009.png", "question": "如图,在⊙O中,AD,CD是弦,连接OC并延长,交过点A的切线于点B,若∠ADC=25°,则∠ABO的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接OA,∵∠ADC=25°,∴∠AOC=2∠ADC=50°,∵AB切⊙O于A,∴∠OAB=90°,∴∠ABO=90°-∠AOC=40°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["50°", "40°", "30°", "20°"], "choices": [50.0, 40.0, 30.0, 20.0], "label": 1}
+{"prob_id": 4026, "image_path": "images/4026.png", "question": "如图,直线PA、PB是⊙O的两条切线,A、B分别为切点,若∠APB=120°,⊙O的半径为10,则弦AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连OA,OB,∵直线PA,PB是⊙O的两条切线,∴OA⊥PA,OB⊥PB,∴∠OAP=∠OBP=90°∵∠APB=120°,∠OAP+∠OBP+∠APB+∠AOB=360°,∴∠AOB=60°,∵OA=OB,∴△AOB为等边三角形,∴AB=OA=10,故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["5", "10", "10√{3}", "5√{3}"], "choices": [5.0, 10.0, 17.321, 8.66], "label": 1}
+{"prob_id": 4027, "image_path": "images/4027.png", "question": "如图,AC是⊙O的切线,切点为C,BC是⊙O的直径,AB交⊙O于点D,连接OD,若∠BAC=50°,则∠COD的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AC是⊙O的切线,∴BC⊥AC,∴∠C=90°,∵∠BAC=50°,∴∠B=90°-∠BAC=40°,∴∠COD=2∠B=80°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["100°", "80°", "50°", "40°"], "choices": [100.0, 80.0, 50.0, 40.0], "label": 1}
+{"prob_id": 4039, "image_path": "images/4039.png", "question": "如图,AB是⊙O的直径,BP是⊙O的切线,AP与⊙O交于点G,点D为⁀{BC}上一点,若∠P=40°,则∠ADC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BC．∵PB是切线,∴AB⊥PB,∴∠ABP=90°,∵AB是直径,∴∠ACB=90°,∴∠ABC+∠BAC=90°,∠P+∠BAC=90°,∴∠ABC=∠P=40°,∴∠ADC=∠ABC=40°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["20°", "25°", "40°", "50°"], "choices": [20.0, 25.0, 40.0, 50.0], "label": 2}
+{"prob_id": 4053, "image_path": "images/4053.png", "question": "如图,AB是⊙O的直径,PA切⊙O于点A,OP交⊙O于点C,连接BC．若∠P=20°,则∠B的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接AC,根据切线的性质定理得AB⊥AP,∴∠AOP=70°,∵OA=OC,∴∠OAC=∠OCA=55°；∵AB是直径,∴∠ACB=90°,∴∠B=35°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["20°", "25°", "30°", "35°"], "choices": [20.0, 25.0, 30.0, 35.0], "label": 3}
+{"prob_id": 4074, "image_path": "images/4074.png", "question": "如图,PA、PB分别与⊙O相切于点A、B,⊙O的切线EF分别交PA、PB于点E、F,切点C在弧AB上,若PA长为2,则△PEF的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA、PB分别与⊙O相切于点A、B,⊙O的切线EF分别交PA、PB于点E、F,切点C在弧AB上,∴AE=CE,FB=CF,PA=PB=2,∴△PEF的周长=PE+EF+PF=PA+PB=4．故选:C．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["8", "6", "4", "2"], "choices": [8.0, 6.0, 4.0, 2.0], "label": 2}
+{"prob_id": 4079, "image_path": "images/4079.png", "question": "把直尺、三角尺和圆形螺母按如图所示放置于桌面上,∠CAB=60°,若量出AD=6cm,则圆形螺母的外直径是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设圆形螺母的圆心为O,与AB切于E,连接OD,OE,OA,如图所示:∵AD,AB分别为圆O的切线,∴AO为∠DAB的平分线,OD⊥AC,OD⊥AC,又∠CAB=60°,∴∠OAE=∠OAD=\\frac{1}{2}∠DAB=60°,在Rt△AOD中,∠OAD=60°,AD=6cm,∴tan∠OAD=tan60°=\\frac{OD}{AD},即\\frac{OD}{6}=√{3},∴OD=6√{3}cm,则圆形螺母的直径为12√{3}cm．故选:D．", "dataset_name": "Geoqa", "ground_truth": "20.784609690826528", "org_choices": ["12cm", "24cm", "6√{3}cm", "12√{3}cm"], "choices": [12.0, 24.0, 10.392, 20.785], "label": 3}
+{"prob_id": 4090, "image_path": "images/4090.png", "question": "AB是⊙O的直径,PA切⊙O于点A,PO交⊙O于点C；连接BC,若∠P=40°,则∠B等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA切⊙O于点A,∴∠PAB=90°,∵∠P=40°,∴∠POA=90°-40°=50°,∵OC=OB,∴∠B=∠BCO=25°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["20°", "25°", "30°", "40°"], "choices": [20.0, 25.0, 30.0, 40.0], "label": 1}
+{"prob_id": 4107, "image_path": "images/4107.png", "question": "如图,AB是圆O的直径,DB,DC分别切圆O于点B,C,若∠ACE=25°,则∠D的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BC,∵DB、DE分别切⊙O于点B、C,∴∠ACE=∠ABC,BD=DC,∵∠ACE=25°,∴∠ABC=25°,∵AB是⊙O的直径,∴∠ACB=90°,∴∠DBC=∠DCB=90°-25°=65°,∴∠D=50°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["50°", "55°", "60°", "65°"], "choices": [50.0, 55.0, 60.0, 65.0], "label": 0}
+{"prob_id": 4111, "image_path": "images/4111.png", "question": "如图,AB为⊙O的切线,A为切点,BO的延长线交⊙O于点C,∠OAC=35°,则∠B的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB为⊙O的切线,∴OA⊥AB,∴∠BAO=90°,∵OA=OC,∴∠C=∠OAC=35°,∴∠B=180°-∠C-∠BAC=180°-35°-35°-90°=20°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["15°", "20°", "25°", "35°"], "choices": [15.0, 20.0, 25.0, 35.0], "label": 1}
+{"prob_id": 4115, "image_path": "images/4115.png", "question": "如图,在△ABC中,∠B=20°,点O是BC边上一点,以O为圆心,OB为半径作圆,交AB边于点D,连结CD,若CD恰好与⊙O相切,则∠DCB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OD,∵DC为⊙O的切线,∴∠ODC=90°,∵OB=OD,∴∠B=∠ODB=20°,∴∠DCB=180°-90°-20°-20°=50°,故选:D．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["30°", "40°", "45°", "50°"], "choices": [30.0, 40.0, 45.0, 50.0], "label": 3}
+{"prob_id": 4128, "image_path": "images/4128.png", "question": "如图,PA、PB是⊙O的切线,点A和B是切点,AC是⊙O的直径,已知∠P=50°,则∠ACB的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB,如图,∵PA、PB是⊙O的切线,∴OA⊥PA,OB⊥PB,∴∠OAP=∠OBP=90°,∴∠AOB=360°-90°-90°-50°=130°,∵OB=OC,∴∠OCB=∠OBC,而∠AOB=∠OCB+∠OBC,∴∠OCB=\\frac{1}{2}×130°=65°,即∠ACB=65°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["60°", "65°", "70°", "75°"], "choices": [60.0, 65.0, 70.0, 75.0], "label": 1}
+{"prob_id": 4137, "image_path": "images/4137.png", "question": "如图,PA、PB分别切⊙O于A、B两点,点C在优弧⁀{ACB}上,∠P=80°,则∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA是圆的切线．∴∠OAP=90°,同理∠OBP=90°,根据四边形内角和定理可得:∠AOB=360°-∠OAP-∠OBP-∠P=360°-90°-90°-80°=100°,∴∠C=\\frac{1}{2}∠AOB=50°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["50°", "60°", "70°", "80°"], "choices": [50.0, 60.0, 70.0, 80.0], "label": 0}
+{"prob_id": 4141, "image_path": "images/4141.png", "question": "如图,⊙O是Rt△ABC的外接圆,∠ACB=90°,∠A=25°,过点C作⊙O的切线,交AB的延长线于点D,则∠D的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC,则∠COD=2∠A=50°,∵CD为⊙O的切线,∴OC⊥CD,∴∠OCD=90°,∴∠D=90°∠COD=40°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["25°", "30°", "40°", "55°"], "choices": [25.0, 30.0, 40.0, 55.0], "label": 2}
+{"prob_id": 4145, "image_path": "images/4145.png", "question": "如图,AB是⊙O的直径,点C在AB的延长线上,CD与⊙O相切,切点为D,如果∠A=35°,那么∠C=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接OD,∵CD是⊙O的切线,∴OD⊥CD,即∠ODC=90°,∵AB为直径,∴∠COD=2∠A=70°,∴∠C=90°-70°=20°,故选:D．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["55°", "35°", "30°", "20°"], "choices": [55.0, 35.0, 30.0, 20.0], "label": 3}
+{"prob_id": 4149, "image_path": "images/4149.png", "question": "如图,点P是⊙O的直径AB延长线上的一点,过点P作⊙O的切线PC,切点为C,若AO=OB=PB=1,则PC的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC．∵PC是切线,∴OC⊥PC．在直角△OPC中,OC=OB=1,OP=OB+PB=2．∴PC=√{0P^{2}-0C^{2}}=√{3}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "1.7320508075688772", "org_choices": ["1", "√{3}", "2", "√{5}"], "choices": [1.0, 1.732, 2.0, 2.236], "label": 1}
+{"prob_id": 4165, "image_path": "images/4165.png", "question": "如图,△ABC中,AB=5,BC=3,AC=4,以点C为圆心的圆与AB相切,则⊙C的半径为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在△ABC中,∵AB=5,BC=3,AC=4,∴AC²+BC²=3²+4²=5²=AB²,∴∠C=90°,如图:设切点为D,连接CD,∵AB是⊙C的切线,∴CD⊥AB,∵S_{△ABC}=\\frac{1}{2}AC•BC=\\frac{1}{2}AB•CD,∴AC•BC=AB•CD,即CD=\\frac{AC\\cdotBC}{AB}=\\frac{3×4}{5}=2.4,∴⊙C的半径为2.4,故选:C．", "dataset_name": "Geoqa", "ground_truth": "2.4", "org_choices": ["2.6", "2.5", "2.4", "2.3"], "choices": [2.6, 2.5, 2.4, 2.3], "label": 2}
+{"prob_id": 4170, "image_path": "images/4170.png", "question": "如图,点A,B,C是⊙O上的三点,直线CD与⊙O相切于点C,若∠DCB=40°,则∠CAB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵直线CD与⊙O相切于点C,∴∠OCD=90°,∵∠DCB=40°,∴∠OCB=50°,∵CO=BO,∴∠OBC=50°,∴∠COB=80°,∴∠CAB=\\frac{1}{2}×80°=40°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "50°", "80°", "100°"], "choices": [40.0, 50.0, 80.0, 100.0], "label": 0}
+{"prob_id": 4184, "image_path": "images/4184.png", "question": "如图,直线AB与⊙O相切于点A,⊙O的半径为2,若∠OBA=30°,则AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB为切线,∴∠OAB=90°,∵∠OBA=30°,OA=2,∴AB=\\frac{0A}{tan30^{°}}=\\frac{2}{\\frac{√{3}}{3}}=2√{3},故选:C．", "dataset_name": "Geoqa", "ground_truth": "3.4641016151377544", "org_choices": ["4√{3}", "4", "2√{3}", "2"], "choices": [6.928, 4.0, 3.464, 2.0], "label": 2}
+{"prob_id": 4188, "image_path": "images/4188.png", "question": "如图,AB是⊙O的直径,AC切⊙O于A,BC交⊙O于点D,若∠C=70°,则∠AOD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AC是圆O的切线,AB是圆O的直径,∴AB⊥AC．∴∠CAB=90°．又∵∠C=70°,∴∠CBA=20°．∴∠DOA=40°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["70°", "35°", "20°", "40°"], "choices": [70.0, 35.0, 20.0, 40.0], "label": 3}
+{"prob_id": 4193, "image_path": "images/4193.png", "question": "如图,PA、PB分别切⊙O于点A、B,点E是⊙O上一点,且∠AEB=60°,则∠P=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OA,BO；∵∠AOB=2∠E=120°,∴∠OAP=∠OBP=90°,∴∠P=180°-∠AOB=60°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["90°", "60°", "45°", "30°"], "choices": [90.0, 60.0, 45.0, 30.0], "label": 1}
+{"prob_id": 4201, "image_path": "images/4201.png", "question": "如图,PA、PB是⊙O的切线,AC是⊙O直径,∠c=55°,则∠APB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB,∵PA、PB是⊙O的切线,AC是⊙O直径,∴∠OAP=∠OBP=∠ABC=90°,∵∠C=55°,OC=OB,∴∠OBC=55°,∴∠AOB=110°,则在四边形AOBP中,∠APB=70°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["55°", "60°", "65°", "70°"], "choices": [55.0, 60.0, 65.0, 70.0], "label": 3}
+{"prob_id": 4224, "image_path": "images/4224.png", "question": "如图,PA,PB分别与⊙O相切于A,B两点,∠P=70°,则∠C为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OA、OB,∵直线PA、PB分别与⊙O相切于点A、B,∴OA⊥PA,OB⊥PB,∵∠P=70°,∴∠AOB=110°,∵C是⊙O上一点,∴∠ACB=55°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["55°", "70°", "110°", "140°"], "choices": [55.0, 70.0, 110.0, 140.0], "label": 0}
+{"prob_id": 4234, "image_path": "images/4234.png", "question": "如图,线段AB是⊙O的直径,点C、D为⊙O上的点,过点C作⊙O的切线交AB的延长线于点E,若∠E=50°,则∠CDB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC,∵CE是⊙O的切线,∴∠OCE=90°,∵∠E=50°,∴∠COE=90°-50°=40°,∴∠CDB=\\frac{1}{2}∠COE=20°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["20°", "25°", "30°", "40°"], "choices": [20.0, 25.0, 30.0, 40.0], "label": 0}
+{"prob_id": 4239, "image_path": "images/4239.png", "question": "直线AB与⊙O相切于点A,如图,若∠OBA=60°,AB=1,则⊙O的半径为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵直线AB与⊙O相切于点A,∴OA⊥AB,∵∠OBA=60°,∴∠BOA=30°,∵AB=1,∴OB=2,∴OA=√{0B^{2}-AB^{2}}=√{2^{2}-1^{2}}=√{3},∴⊙O的半径为√{3}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "1.7320508075688772", "org_choices": ["√{5}", "√{3}", "1", "2"], "choices": [2.236, 1.732, 1.0, 2.0], "label": 1}
+{"prob_id": 4248, "image_path": "images/4248.png", "question": "如图,Rt△ABC中,AC=4,AB=5,∠C=90°,经过点C且与边AB相切的圆与△ABC的边CB,CA分别相交于点E、F,线段EF长度的最小值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:取EF的中点O,作OG⊥AB于G,CH⊥AB于H,连结OC,如图,在Rt△ABC中,∵AC=4,AB=5,∠C=90°,∴BC=√{5^{2}-4^{2}}=3,∵\\frac{1}{2}CH•AB=\\frac{1}{2}BC•AC,∴CH=\\frac{3×4}{5}=2.4,∵∠ECF=90°,∴EF为经过点C且与边AB相切的圆的直径,点O为圆心,∵AB为⊙O的切线,∴OG为⊙O的半径,∴EF=OC+OG,当OC、OG共线时,OC+OG的值最小,最小值为CH的长,∴EF的最小值为2.4．故选:A．", "dataset_name": "Geoqa", "ground_truth": "2.4", "org_choices": ["2.4", "2", "2.5", "2√{2}"], "choices": [2.4, 2.0, 2.5, 2.828], "label": 0}
+{"prob_id": 4255, "image_path": "images/4255.png", "question": "如图,两个同心圆的半径分别为3cm和5cm,大圆的一条弦AB与小圆相切,则弦AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC和OB,∵弦AB与小圆相切,∴OC⊥AB,在Rt△OBC中,BC=√{OB^{2}-OC^{2}}=√{5^{2}-3^{2}}=4cm,∴AB=2BC=8cm．故选:D．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["3cm", "4cm", "6cm", "8cm"], "choices": [3.0, 4.0, 6.0, 8.0], "label": 3}
+{"prob_id": 4261, "image_path": "images/4261.png", "question": "如图,⊙O是△ABC的外接圆,AD是⊙O的直径,EA是⊙O的切线．若∠EAC=120°,则∠ABC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵EA是⊙O的切线,AD是⊙O的直径,∴∠EAD=90°,∵∠EAC=120°,∴∠DAC=∠EAC-∠EAD=30°,∵AD是⊙O的直径,∴∠ACD=90°,∴∠ADC=180°-∠ACD-∠DAC=60°,∴∠ABC=∠ADC=60°(圆周角定理),故选:C．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["80°", "70°", "60°", "50°"], "choices": [80.0, 70.0, 60.0, 50.0], "label": 2}
+{"prob_id": 4264, "image_path": "images/4264.png", "question": "如图,⊙O的半径为2,点O到直线l的距离为3,点P是直线l上的一个动点．若PB切⊙O于点B,则PB的最小值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连结OB,作OP′⊥l于P′如图,OP′=3,∵PB切⊙O于点B,∴OB⊥PB,∴∠PBO=90°,∴PB=√{OP^{2}-OB^{2}}=√{OP^{2}-2^{2}},当点P运动到点P′的位置时,OP最小时,则PB最小,此时OP=3,∴PB的最小值为√{3^{2}-2^{2}}=√{5}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.23606797749979", "org_choices": ["√{13}", "√{5}", "3", "2"], "choices": [3.606, 2.236, 3.0, 2.0], "label": 1}
+{"prob_id": 4268, "image_path": "images/4268.png", "question": "如图,PA、PB、CD是⊙O的切线,A、B、E是切点,CD分别交线段PA、PB于C、D两点,若∠APB=40°,则∠COD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意得,连接OA、OC、OE、OD、OB,所得图形如下:由切线性质得,OA⊥PA,OB⊥PB,OE⊥CD,DB=DE,AC=CE,∵AO=OE=OB,∴△AOC≌△EOC(SAS),△EOD≌△BOD(SAS),∴∠AOC=∠EOC,∠EOD=∠BOD,∴∠COD=\\frac{1}{2}∠AOB,∵∠APB=40°,∴∠AOB=140°,∴∠COD=70°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["50°", "60°", "70°", "75°"], "choices": [50.0, 60.0, 70.0, 75.0], "label": 2}
+{"prob_id": 4282, "image_path": "images/4282.png", "question": "如图,AB是⊙O直径,点C在⊙O上,AE是⊙O的切线,A为切点,连接BC并延长交AE于点D．若∠AOC=80°,则∠ADB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB是⊙O直径,AE是⊙O的切线,∴∠BAD=90°,∵∠B=\\frac{1}{2}∠AOC=40°,∴∠ADB=90°-∠B=50°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["40°", "50°", "60°", "20°"], "choices": [40.0, 50.0, 60.0, 20.0], "label": 1}
+{"prob_id": 4283, "image_path": "images/4283.png", "question": "如图,AC是⊙O的切线,切点为C,BC是⊙O的直径,AB交⊙O于点D,连接OD．若∠BAC=55°,则∠COD的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AC是⊙O的切线,∴BC⊥AC,∴∠C=90°,∵∠BAC=55°,∴∠B=90°-∠BAC=35°,∴∠COD=2∠B=70°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["70°", "60°", "55°", "35°"], "choices": [70.0, 60.0, 55.0, 35.0], "label": 0}
+{"prob_id": 4284, "image_path": "images/4284.png", "question": "如图,在△ABC中,AB=3,AC=2．当∠B最大时,BC的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:以A为圆心,AC为半径作⊙O,当BC为⊙O的切线时,即BC⊥AC时,∠B最大,此时BC=√{AB^{2}-AC^{2}}=√{3^{2}-2^{2}}=√{5}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.23606797749979", "org_choices": ["1", "√{5}", "√{13}", "5"], "choices": [1.0, 2.236, 3.606, 5.0], "label": 1}
+{"prob_id": 4295, "image_path": "images/4295.png", "question": "如图,AB是半圆的直径,点O是圆心,点C是AB延长线的一点,CD与半圆相切于点D．若AB=6,CD=4,则sin∠C的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OD,∵AB是半圆的直径,AB=6,∴OD=3,∵CD与半圆相切于点D,∴∠CDO=90°,∵CD=4,∴OC=√{CD^{2}+OD^{2}}=5,∴sin∠C=\\frac{OD}{OC}=\\frac{3}{5},故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.6", "org_choices": ["\\frac{3}{4}", "\\frac{3}{5}", "\\frac{4}{5}", "\\frac{2}{3}"], "choices": [0.75, 0.6, 0.8, 0.667], "label": 1}
+{"prob_id": 4305, "image_path": "images/4305.png", "question": "如图,在Rt△ABC中,∠C=90°,∠A=30°,BC=2,⊙C的半径为1,点P是斜边AB上的点,过点P作⊙C的一条切线PQ(点Q是切点),则线段PQ的最小值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接CP、CQ；如图所示:∵PQ是⊙C的切线,∴CQ⊥PQ,∠CQP=90°,根据勾股定理得:PQ²=CP²-CQ²,∴当PC⊥AB时,线段PQ最短,∵在Rt△ACB中,∠A=30°,BC=2,∴AB=2BC=4,AC=2√{3},∴CP\\frac{AC\\cdotBC}{AB}=\\frac{2√{3}}{2}=√{3},∴PQ√{CP^{2}-CQ^{2}}=√{3-1}=√{2},∴PQ的最小值是√{2},故选:C．", "dataset_name": "Geoqa", "ground_truth": "1.4142135623730951", "org_choices": ["2", "√{3}", "√{2}", "2-\\frac{√{3}}{3}"], "choices": [2.0, 1.732, 1.414, 1.423], "label": 2}
+{"prob_id": 4317, "image_path": "images/4317.png", "question": "如图,AB、AC是⊙O的两条弦,过点B的切线与OC的延长线交于点D,若∠D=36°,则∠CAB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB,∵BD是⊙O的切线,∴OB⊥BD,∴∠OBD=90°,∵∠D=36°,∴∠DOB=∠OBD-∠D=90°-36°=54°,∵∠DOB与∠CAB对着同一条弧,∴∠CAB=\\frac{1}{2}∠DOB=\\frac{1}{2}×54^{°}=27^{°}．故选:C．", "dataset_name": "Geoqa", "ground_truth": "27.0", "org_choices": ["54°", "44°", "27°", "22°"], "choices": [54.0, 44.0, 27.0, 22.0], "label": 2}
+{"prob_id": 4334, "image_path": "images/4334.png", "question": "如图,两个同心圆的直径分别为6cm和10cm,大圆的一条弦AB与小圆相切,则弦AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作OC⊥AB于C,连结OA,如图,∵弦AB与小圆相切,∴OC=3cm,在Rt△OAC中,∵OA=5,OC=3,∴AC=√{OA^{2}-OC^{2}}=4,∵OC⊥AB,∴AC=BC,∴AB=2AC=8cm．故选:C．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["4cm", "6cm", "8cm", "10cm"], "choices": [4.0, 6.0, 8.0, 10.0], "label": 2}
+{"prob_id": 4364, "image_path": "images/4364.png", "question": "如图,AP、BP分别切⊙O于点A、B,∠P=60°,点C在优弧AB上,则∠C度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AP、BP分别切⊙O于点A、B,∴∠OAP=∠OBP=90°,∴∠AOB=360°-60°-90°-90°=120°,∴∠C=\\frac{1}{2}∠AOB=60°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["30°", "60°", "40°", "72°"], "choices": [30.0, 60.0, 40.0, 72.0], "label": 1}
+{"prob_id": 4369, "image_path": "images/4369.png", "question": "如图,P是⊙O的直径AB延长线上一点,PC切⊙O于C,∠P=50°,∠A为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OP,∵CP为圆O的切线,∴OC⊥CP,在Rt△OPC中,∠P=50°,∴∠POC=40°,∵OA=OC,∴∠A=∠OCA,∵∠POC为△AOC的外角,∴∠A=\\frac{1}{2}∠POC=20°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["40°", "35°", "25°", "20°"], "choices": [40.0, 35.0, 25.0, 20.0], "label": 3}
+{"prob_id": 4390, "image_path": "images/4390.png", "question": "如图,PA、PB是⊙O的切线,切点为A、B,若∠OAB=30°,则∠P的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠OAB=30°,∴∠AOB=180°-2×30°=120°,又∵PA、PB是⊙O的切线,∴∠OAP=∠OBP=90°,∴∠P=360°-90°-90°-120°=60°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["60°", "90°", "120°", "无法确定"], "choices": [60.0, 90.0, 120.0], "label": 0}
+{"prob_id": 4400, "image_path": "images/4400.png", "question": "如图,PA,PB是⊙O是切线,A,B为切点,AC是O的直径,若∠BAC=25°,则∠P为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA,PB是⊙O是切线,∴∠OAP=∠OBP=90°,∵OA=OB,∠BAC=25°,∴∠AOB=180°-2∠BAC=130°,又∵∠OAP+∠OBP+∠AOB+∠P=360°,∴∠P=360°-∠OAP-∠OBP-∠AOB=360°-90°-90°-130°=50°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["25°", "50°", "30°", "65°"], "choices": [25.0, 50.0, 30.0, 65.0], "label": 1}
+{"prob_id": 4403, "image_path": "images/4403.png", "question": "如图,直线BC与⊙O相切于点A,AD是⊙O的弦,连接OD,若∠DAC=50°,则∠ODA的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵直线BC与⊙O相切于点A,∴OA⊥BC,∴∠OAC=90°,∵∠DAC=50°,∴∠OAD=40°,∵OD=OA,∴∠ODA=∠OAD=40°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["30°", "40°", "50°", "60°"], "choices": [30.0, 40.0, 50.0, 60.0], "label": 1}
+{"prob_id": 4404, "image_path": "images/4404.png", "question": "如图所示,某宾馆大厅要铺圆环形的地毯,工人师傅只测量了与小圆相切的大圆的弦AB的长,就计算出了圆环的面积．若测量得AB的长为8米,则圆环的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过O作OC⊥AB于C,连OA,如图,∴AC=BC,而AB=8米,∴AC=4米,∵AB与小圆相切,∴OC为小圆的半径,∴圆环的面积=π•OA²-π•OC²=π(OA²-OC²)=π•AC²=16π(平方米)．故选:D．", "dataset_name": "Geoqa", "ground_truth": "50.26548245743669", "org_choices": ["16平方米", "8π平方米", "64平方米", "16π平方米"], "choices": [16.0, 25.133, 64.0, 50.265], "label": 3}
+{"prob_id": 4406, "image_path": "images/4406.png", "question": "如图,AB是⊙O的直径,CD切于点D,AB的延长线交CD于点C,若∠ACD=40°,则∠A=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接OD．∵AB是⊙O的直径,CD切于点D,∴∠CDO=90°．又∵∠ACD=40°,∴∠COD=50°．∴∠A=\\frac{1}{2}∠COD=25°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["45°", "40°", "30°", "25°"], "choices": [45.0, 40.0, 30.0, 25.0], "label": 3}
+{"prob_id": 4414, "image_path": "images/4414.png", "question": "如图,AB是⊙O的直径,点D在AB的延长线上,DC切⊙O于点C,若∠A=26°,则∠D等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如右图所示,连接BC,∵AB是直径,∴∠BCA=90°,又∵∠A=26°,∴∠CBA=90°-26°=64°,∵DC是切线,∴∠BCD=∠A=26°,∴∠D=∠CBA-∠BCD=64°-26°=38°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "38.0", "org_choices": ["38°", "50°", "60°", "570°"], "choices": [38.0, 50.0, 60.0, 570.0], "label": 0}
+{"prob_id": 4424, "image_path": "images/4424.png", "question": "如图,△ABC中,AB=AC,∠BA0=45°,△ABC内接于⊙O,D为⊙O上一点,过点D作⊙O的切线交BC的延长线于E,若DE⊥BC,AD=2√{2},则DE的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过点A作AH⊥BC于点H,连接OC,OD,∵AB=AC,∴AH=CH,∴AH过点O,∵DE是⊙O的切线,∴OD⊥DE,∵DE⊥BC,∴∠OHE=∠E=∠EDO=90°,∴四边形ODEH是矩形,∴∠AOD=90°,∵AD=2√{2},∴OA=OD=2,∵∠BAC=45°,∴∠COH=45°,∵OC=2,∴OH=CH=√{2},∴DE=OH=√{2}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "1.4142135623730951", "org_choices": ["2", "1", "\\frac{3}{2}", "√{2}"], "choices": [2.0, 1.0, 1.5, 1.414], "label": 3}
+{"prob_id": 4426, "image_path": "images/4426.png", "question": "如图,AB是⊙O的切线,B为切点,AO与⊙O交于点C,若∠BAO=40°,则∠OCB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB是⊙O的切线,B为切点,∴OB⊥AB,即∠OBA=90°,∵∠BAO=40°,∴∠O=50°,∵OB=OC(都是半径),∴∠OCB=\\frac{1}{2}(180°-∠O)=65°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["40°", "50°", "65°", "75°"], "choices": [40.0, 50.0, 65.0, 75.0], "label": 2}
+{"prob_id": 4436, "image_path": "images/4436.png", "question": "如图,⊙O与AB切于点C,∠BCE=60°,DC=6,DE=4,则S_{△CDE}为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过C作CF⊥DE,交DE于点F,∵AB与圆O相切,CE为圆O的弦,∴∠CDE=∠BCE=60°,在Rt△CDF中,DC=6,∠CDE=60°,∴CF=DCsin60°=3√{3},又DE=4,则S_{△CDE}=\\frac{1}{2}DE•CF=6√{3}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.392304845413264", "org_choices": ["6√{5}", "6√{3}", "6√{2}", "6"], "choices": [13.416, 10.392, 8.485, 6.0], "label": 1}
+{"prob_id": 4440, "image_path": "images/4440.png", "question": "如图,AB切⊙O于B,割线ACD经过圆心O,若∠BCD=70°,则∠A的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OB=OC,∠BCD=70°,∴∠OBC=∠BCD=70°,∴∠BOC=180°-∠BCD-∠OBC=40°,∵AB切⊙O于B,∴OB⊥AB,∴∠ABO=90°,∴∠A=90°-∠BOC=50°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["20°", "50°", "40°", "80°"], "choices": [20.0, 50.0, 40.0, 80.0], "label": 1}
+{"prob_id": 4445, "image_path": "images/4445.png", "question": "如图,在△ABC中,AB=15,AC=12,BC=9,经过点C且与边AB相切的动圆与CB、CA分别相交于点E、F,则线段EF长度的最小值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:结合题意,易知△ABC为RT△,∠C=90°,即知EF为圆的直径,设圆与AB的切点为D,连接CD,当CD垂直于AB时,即CD是圆的直径的时候,EF长度最小,最小值是\\frac{9×12}{15}=\\frac{36}{5}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "7.2", "org_choices": ["\\frac{12}{5}", "\\frac{36}{5}", "\\frac{15}{2}", "8"], "choices": [2.4, 7.2, 7.5, 8.0], "label": 1}
+{"prob_id": 4458, "image_path": "images/4458.png", "question": "如图,BC与⊙O相切于点C,BO的延长线交⊙O于点A,连结AC,若∠ACB=120°,则∠A的度数等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接OC．∵BC与⊙O相切于点C,∴OC⊥BC,即∠OCB=90°．∵A=OC,∴∠A=∠ACO=∠ACB-∠OCB=120°-90°=30°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["30°", "40°", "50°", "60°"], "choices": [30.0, 40.0, 50.0, 60.0], "label": 0}
+{"prob_id": 4473, "image_path": "images/4473.png", "question": "如图,一块四边形绿化园地,四角都做有半径为2的圆形喷水池,则这四个喷水池占去的绿化园地的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:圆形喷水池形成四边形,四边形的内角和为360°,阴影部分的面积和为一个圆面积,故圆形喷水池的面积为π•2²=4π．故选:A．", "dataset_name": "Geoqa", "ground_truth": "12.566370614359172", "org_choices": ["4π", "8π", "16π", "不能确定"], "choices": [12.566, 25.133, 50.265], "label": 0}
+{"prob_id": 4475, "image_path": "images/4475.png", "question": "如图,在边长为4的正方形ABCD中,先以点A为圆心,AD的长为半径画弧,再以AB边的中点为圆心,AB长的一半为半径画弧,则两弧之间的阴影部分面积是()(结果保留π)．. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:根据题意得,S_{阴影部分}=S_{扇形BAD}-S_{半圆BA},∵S_{扇形BAD}=\\frac{90π\\cdot4^{2}}{360}=4πS_{半圆BA}=\\frac{1}{2}•π•2²=2π,∴S_{阴影部分}=4π-2π=2π．故选:B．", "dataset_name": "Geoqa", "ground_truth": "6.283185307179586", "org_choices": ["π", "2π", "3π", "4π"], "choices": [3.142, 6.283, 9.425, 12.566], "label": 1}
+{"prob_id": 4508, "image_path": "images/4508.png", "question": "如图,在△ABC中,DE∥BC,AE=3,AC=9,AD=4,则AB的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴\\frac{AD}{AB}=\\frac{AE}{AC},即\\frac{4}{AB}=\\frac{3}{9},∴AB=12．故选:D．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["6", "8", "9", "12"], "choices": [6.0, 8.0, 9.0, 12.0], "label": 3}
+{"prob_id": 4513, "image_path": "images/4513.png", "question": "如图,AB∥CD,AD与BC相交于点O,若AO=2,DO=4,BO=3,则BC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB∥CD,∴\\frac{BO}{CO}=\\frac{AO}{DO}；∵AO=2,DO=4,BO=3,∴\\frac{3}{CO}=\\frac{2}{4},解得:CO=6,∴BC=BO+CO=3+6=9．故选:B．", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["6", "9", "12", "15"], "choices": [6.0, 9.0, 12.0, 15.0], "label": 1}
+{"prob_id": 4528, "image_path": "images/4528.png", "question": "如图,已知a∥b∥c,AB=1,BC=2,EF=4,则DE=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵a∥b∥c,AB=1,BC=2,EF=4,∴\\frac{AB}{BC}=\\frac{DE}{EF},即\\frac{1}{2}=\\frac{DE}{4},DE=2,故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["1", "2", "3", "4"], "choices": [1.0, 2.0, 3.0, 4.0], "label": 1}
+{"prob_id": 4534, "image_path": "images/4534.png", "question": "如图,直线a、b、c分别与直线m、n交于点A、B、C、D、E、F．已知直线a∥b∥c,若AB=2,BC=3,则\\frac{DE}{EF}的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵直线a∥b∥c,∴\\frac{DE}{EF}=\\frac{AB}{BC}=\\frac{2}{3},故选:A．", "dataset_name": "Geoqa", "ground_truth": "0.6666666666666666", "org_choices": ["\\frac{2}{3}", "\\frac{3}{2}", "\\frac{2}{5}", "\\frac{3}{5}"], "choices": [0.667, 1.5, 0.4, 0.6], "label": 0}
+{"prob_id": 4535, "image_path": "images/4535.png", "question": "如图所示,在△ABC中,DE∥BC,若AD=1,DB=2,则\\frac{AE}{AC}的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AD=1,DB=2,∴AB=3,∴\\frac{AD}{AB}=\\frac{1}{3}∵\\frac{AD}{DB}=\\frac{AE}{AC},∴\\frac{AE}{AC}=\\frac{1}{3}；故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.3333333333333333", "org_choices": ["\\frac{2}{3}", "\\frac{1}{3}", "\\frac{1}{4}", "\\frac{1}{2}"], "choices": [0.667, 0.333, 0.25, 0.5], "label": 1}
+{"prob_id": 4539, "image_path": "images/4539.png", "question": "如图,在△ABC中,M是AC的中点,E是AB上一点,AE=\\frac{1}{4}AB,连接EM并延长,交BC的延长线于D,则\\frac{BC}{CD}=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,过C点作CP∥AB,交DE于P,∵PC∥AE,∴△AEM∽△CPM,∴\\frac{PC}{AE}=\\frac{CM}{AM},∵M是AC的中点,∴AM=CM,∴PC=AE,∵AE=\\frac{1}{4}AB,∴CP=\\frac{1}{4}AB,∴CP=\\frac{1}{3}BE,∵CP∥BE,∴△DCP∽△DBE,∴\\frac{CP}{BE}=\\frac{CD}{BD}=\\frac{1}{3},∴BD=3CD,∴BC=2CD,即\\frac{BC}{CD}=2．故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["\\frac{1}{2}", "2", "\\frac{2}{3}", "\\frac{3}{2}"], "choices": [0.5, 2.0, 0.667, 1.5], "label": 1}
+{"prob_id": 4542, "image_path": "images/4542.png", "question": "如图,在矩形ABCD中,AB=3,BC=4,点M在BC边上,且满足BM=1,过D作DN⊥AM交AM于点N,则DN的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接DM,如图所示:∵四边形ABCD是矩形,∴∠B=90°,AD=BC=4,△AMD底边AD上的高为AB,AM=√{AB^{2}+BM^{2}}=√{3^{2}+1^{2}}=√{10},∵△ADM的面积=\\frac{1}{2}AM×DN=\\frac{1}{2}AD×AB,∴DN=\\frac{AD×AB}{AM}=\\frac{4×3}{√{10}}=\\frac{6√{10}}{5}；故选:D．", "dataset_name": "Geoqa", "ground_truth": "3.794733192202055", "org_choices": ["\\frac{7}{2}√{5}", "\\frac{3}{5}√{5}", "\\frac{3}{2}√{10}", "\\frac{6}{5}√{10}"], "choices": [7.826, 1.342, 4.743, 3.795], "label": 3}
+{"prob_id": 4546, "image_path": "images/4546.png", "question": "已知如图,在△ABC中,点D、点E分别在AB、BC边上,且DE∥AC,BE=2,CE=1,△BDE的面积为4,则△ABC的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BE=2,CE=1,∴BC=BE+CE=2+1=3,∵DE∥AC,∴△BDE∽△BAC,∴\\frac{BE}{BC}=\\frac{BD}{AB}=\\frac{2}{3},∴\\frac{S△BDE}{S△ABC}=(\\frac{2}{3})^{2}=\\frac{4}{9},∵△BDE的面积为4,∴S△ABC=\\frac{9}{4}×4=9,故选:D．", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["5", "6", "8", "9"], "choices": [5.0, 6.0, 8.0, 9.0], "label": 3}
+{"prob_id": 4553, "image_path": "images/4553.png", "question": "如图,在△ABC中,DE∥BC,若AB=7cm,AC=5cm,AD=3cm,则DE=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB=7,AD=3,∴BD=BA-AD=4,∵DE∥BC,∴△BDE∽△BAC,∴\\frac{BD}{BA}=\\frac{DE}{AC},即\\frac{4}{7}=\\frac{DE}{5},解得,DE=\\frac{20}{7}(cm),故选:D．", "dataset_name": "Geoqa", "ground_truth": "2.857142857142857", "org_choices": ["\\frac{15}{4}cm", "\\frac{20}{3}cm", "\\frac{15}{7}cm", "\\frac{20}{7}cm"], "choices": [3.75, 6.667, 2.143, 2.857], "label": 3}
+{"prob_id": 4558, "image_path": "images/4558.png", "question": "如图,在▱ABCD中,点E在边AD上,CE交BD于点F,若EF=\\frac{1}{3}FC,则\\frac{AE}{ED}=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在▱ABCD中,∵AD∥BC,AD=BC,∴△DEF∽△BCF,∴\\frac{DE}{BC}=\\frac{EF}{FC}=\\frac{1}{3},∴\\frac{DE}{AD}=\\frac{1}{3},∴\\frac{AE}{ED}=2,故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["\\frac{3}{2}", "2", "\\frac{5}{3}", "3"], "choices": [1.5, 2.0, 1.667, 3.0], "label": 1}
+{"prob_id": 4590, "image_path": "images/4590.png", "question": "如图,已知点M为平行四边形ABCD边AB的中点,线段CM交BD于点E,S△BEM=2,则图中阴影部分的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AB=CD,AB∥CD,∴S△DMB=S△CBM,∴S△DEM=S△CEB,∵AM=BM=\\frac{1}{2}AB=\\frac{1}{2}CD,∴\\frac{CE}{EM}=\\frac{CD}{BM}=2,∴S△CEB=2S△BME=4,∴S阴=4+4=8,故选:C．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["5", "4", "8", "6"], "choices": [5.0, 4.0, 8.0, 6.0], "label": 2}
+{"prob_id": 4591, "image_path": "images/4591.png", "question": "如图,四边形ABCD中,AD∥BC,对角线AC、BD相交于O,若\\frac{S_{\riangleADO}}{S_{\riangleDOC}}=\\frac{1}{3},则的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵\\frac{S_{\riangleADO}}{S_{\riangleDOC}}=\\frac{1}{3},∴\\frac{OA}{OC}=\\frac{1}{3},∵AD∥BC,∴△ADO∽△CBO,∴\\frac{AD}{BC}=\\frac{OA}{OC}=\\frac{1}{3},故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.3333333333333333", "org_choices": ["\\frac{1}{2}", "\\frac{1}{3}", "\\frac{1}{9}", "\\frac{√{3}}{3}"], "choices": [0.5, 0.333, 0.111, 0.577], "label": 1}
+{"prob_id": 4598, "image_path": "images/4598.png", "question": "如图,▱ABCD中,∠C=120°,AB=AE=5,AE与BD交于点F,AF=2EF．则BC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AD=BC,AD∥BC,∴△AFD∽△EFB,∴\\frac{BE}{AD}=\\frac{EF}{AF},∵AF=2EF,∴AD=BC=2BE,∵BE=5,∴BC=10,故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["12", "10", "8", "6"], "choices": [12.0, 10.0, 8.0, 6.0], "label": 1}
+{"prob_id": 4614, "image_path": "images/4614.png", "question": "如图,D,E为△ABC的边AB,AC上的点,DE∥BC,若AD:DB=1:3,AE=2,则AC的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴\\frac{AE}{AC}=\\frac{AD}{AB}=\\frac{1}{3+1}=\\frac{1}{4}．∵AE=2,∴AC=8故选:B．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["10", "8", "6", "4"], "choices": [10.0, 8.0, 6.0, 4.0], "label": 1}
+{"prob_id": 4619, "image_path": "images/4619.png", "question": "如图,已知AB∥CD∥EF,AD:AF=3:5,BE=15,那么CE的长等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB∥CD∥EF,∴\\frac{BC}{BE}=\\frac{AD}{AF},即\\frac{BC}{15}=\\frac{3}{5},∴BC=9,∴CE=BE-BC=15-9=6．故选:B．", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["9", "6", "\\frac{15}{2}", "\\frac{9}{2}"], "choices": [9.0, 6.0, 7.5, 4.5], "label": 0}
+{"prob_id": 4620, "image_path": "images/4620.png", "question": "如图,AD∥BE∥CF,直线l1,l2与这三条平行线分别交于点A,B,C,D,E,F,\\frac{AB}{BC}=\\frac{2}{3},DE=6,则EF的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AD∥BE∥CF,∴\\frac{AB}{BC}=\\frac{DE}{EF},即\\frac{6}{EF}=\\frac{2}{3},∴EF=9．故选:C．", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["4", "6", "9", "12"], "choices": [4.0, 6.0, 9.0, 12.0], "label": 2}
+{"prob_id": 4621, "image_path": "images/4621.png", "question": "如图,已知直线a∥b∥c,直线m,n与a,b,c分别交于点A,C,E,B,D,F,若AC=4,AE=10,BD=3,则DF的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵a∥b∥c,∴image_023087.png\\frac{AC}{AE}=\\frac{BD}{BF},即\\frac{4}{10}=\\frac{3}{BF},解得,BF=\\frac{15}{2},则DF=BF-BD=4.5,故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.5", "org_choices": ["4", "4.5", "5", "5.5"], "choices": [4.0, 4.5, 5.0, 5.5], "label": 1}
+{"prob_id": 4642, "image_path": "images/4642.png", "question": "如图所示,在△ABC中,DE∥BC,若AD=1,DB=2,则\\frac{AD}{AB}的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AD=1,DB=2,∴AB=3,∴\\frac{AD}{AB}=\\frac{1}{3}；故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.3333333333333333", "org_choices": ["\\frac{2}{3}", "\\frac{1}{4}", "\\frac{1}{3}", "\\frac{1}{2}"], "choices": [0.667, 0.25, 0.333, 0.5], "label": 2}
+{"prob_id": 4652, "image_path": "images/4652.png", "question": "如图,直线a∥b∥c,直线m、n与a、b、c分别交于点A、C、E和B、D、F,若AC=4,AE=10,BF=\\frac{15}{2},则DF的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AC=4,AE=10,∴CE=6,∵直线a∥b∥c,∴\\frac{AE}{CE}=\\frac{BF}{DF},即\\frac{10}{6}=\\frac{\\frac{15}{2}}{DF},∴DF=\\frac{9}{2},故选:A．", "dataset_name": "Geoqa", "ground_truth": "4.5", "org_choices": ["\\frac{9}{2}", "10", "3", "\\frac{7}{2}"], "choices": [4.5, 10.0, 3.0, 3.5], "label": 0}
+{"prob_id": 4653, "image_path": "images/4653.png", "question": "如图,已知a∥b∥c,AC=6,AB=2,EF=5,则DF的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵直线a∥b∥c,AC=6,AB=2,EF=5,∴\\frac{AB}{AC}=\\frac{DE}{DF},即\\frac{2}{6}=\\frac{DF-5}{DF},解得DF=\\frac{15}{2}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "7.5", "org_choices": ["\\frac{5}{3}", "\\frac{5}{2}", "\\frac{10}{3}", "\\frac{15}{2}"], "choices": [1.667, 2.5, 3.333, 7.5], "label": 3}
+{"prob_id": 4665, "image_path": "images/4665.png", "question": "如图,在△ABC中,DE∥BC,\\frac{AD}{DB}=\\frac{1}{2},DE=4,则BC的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵\\frac{AD}{DB}=\\frac{1}{2},∴\\frac{AD}{AB}=\\frac{1}{3},∵在△ABC中,DE∥BC,∴\\frac{DE}{BC}=\\frac{AD}{AB}=\\frac{1}{3},∵DE=4,∴BC=3DE=12．故选:D．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["8", "10", "11", "12"], "choices": [8.0, 10.0, 11.0, 12.0], "label": 3}
+{"prob_id": 4676, "image_path": "images/4676.png", "question": "如图,在△ABC中,点D,E分别在边AB,AC上,DE∥BC,已知EC=6,\\frac{AD}{DB}=\\frac{2}{3},则AE的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴\\frac{AD}{DB}=\\frac{AE}{EC},∵EC=6,\\frac{AD}{DB}=\\frac{2}{3},∴\\frac{AE}{6}=\\frac{2}{3},解得:AE=4．故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["1", "4", "5", "9"], "choices": [1.0, 4.0, 5.0, 9.0], "label": 1}
+{"prob_id": 4687, "image_path": "images/4687.png", "question": "如图,在△ABC中,D,E分别是AB和AC上的点,满足AD=3,AE=2,EC=1,DE∥BC,则AB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴\\frac{AD}{DB}=\\frac{AE}{EC},∵AD=3,AE=2,EC=1,∴\\frac{3}{DB}=\\frac{2}{1},∴DB=\\frac{3}{2}=1.5,∴AB=AD+DB=3+1.5=4.5,故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.5", "org_choices": ["6", "4.5", "2", "1.5"], "choices": [6.0, 4.5, 2.0, 1.5], "label": 1}
+{"prob_id": 4700, "image_path": "images/4700.png", "question": "如图,AB∥CD∥EF,AC与BD相交于点E,若CE=5,CF=4,AE=BC,则\\frac{CD}{AB}的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设AE=x,则BC=x,∵EF∥AB,∴\\frac{CE}{CA}=\\frac{CF}{CB},即\\frac{5}{5+x}=\\frac{4}{x},解得x=20,即AE=20,∵CD∥AB,∴△ECD∽△EAB,∴\\frac{CD}{AB}=\\frac{CE}{AE}=\\frac{5}{20}=\\frac{1}{4}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "0.25", "org_choices": ["\\frac{2}{3}", "\\frac{1}{2}", "\\frac{1}{3}", "\\frac{1}{4}"], "choices": [0.667, 0.5, 0.333, 0.25], "label": 3}
+{"prob_id": 4701, "image_path": "images/4701.png", "question": "如图,在△ABC中,点D、E分别在AB、AC边上,DE∥BC．若\\frac{AE}{AC}=\\frac{3}{4},AD=9,则AB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴\\frac{AD}{AB}=\\frac{AE}{AC}=\\frac{3}{4},又AD=9,∴AB=12,故选:C．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["10", "11", "12", "16"], "choices": [10.0, 11.0, 12.0, 16.0], "label": 2}
+{"prob_id": 4711, "image_path": "images/4711.png", "question": "如图,直线l_{1}∥l_{2}∥l_{3},已知:AB=4,BC=6,DE=3,则EF=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵l_{1}∥l_{2}∥l_{3},∴\\frac{AB}{BC}=\\frac{DE}{EF},即\\frac{4}{6}=\\frac{3}{EF},∴EF=\\frac{9}{2}．故选:C．", "dataset_name": "Geoqa", "ground_truth": "4.5", "org_choices": ["8", "6", "4.5", "2"], "choices": [8.0, 6.0, 4.5, 2.0], "label": 2}
+{"prob_id": 4739, "image_path": "images/4739.png", "question": "如图,平行四边形ABCD中,F是边AB上的点,DF交AC于点E,如果CD=10,\\frac{AE}{EC}=\\frac{2}{5},那么BF的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如右图所示,∵四边形ABCD是▱,∴AB∥CD,∴△AEF∽△CED,∴AE:CE=AF:CD,又∵\\frac{AE}{EC}=\\frac{2}{5},∴AF=4,∴BF=AB-AF=10-4=6．故选:C．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["4", "5", "6", "8"], "choices": [4.0, 5.0, 6.0, 8.0], "label": 2}
+{"prob_id": 4747, "image_path": "images/4747.png", "question": "如图,E是平行四边形ABCD的AD边上一点,过点E作EF∥AB交BD于F,若DE:EA=2:3,EF=4,则CD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE:EA=2:3,∴DE:DA=2:5,∵EF∥AB,∴\\frac{DE}{DA}=\\frac{EF}{AB},∵EF=4,∴\\frac{2}{5}=\\frac{4}{AB},解得:AB=10,∵四边形ABCD是平行四边形,∴CD=AB=10．故选:C．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["\\frac{16}{3}", "8", "10", "16"], "choices": [5.333, 8.0, 10.0, 16.0], "label": 2}
+{"prob_id": 4749, "image_path": "images/4749.png", "question": "如图,已知l_{1}∥l_{2}∥l_{3},如果AB:BC=2:3,DE=4,则EF的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵l_{1}∥l_{2}∥l_{3},∴\\frac{AB}{BC}=\\frac{DE}{EF},又AB:BC=2:3,DE=4,∴EF=6．故选:B．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["\\frac{10}{3}", "6", "4", "25"], "choices": [3.333, 6.0, 4.0, 25.0], "label": 1}
+{"prob_id": 4758, "image_path": "images/4758.png", "question": "如图DE∥BC,AD=3,DB=4,AE=1.5,则EC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵△ABC中,DE∥BC,∴\\frac{AD}{BD}=\\frac{AE}{EC},∵AD=3,DB=6,AE=2,∴\\frac{3}{4}=\\frac{1.5}{EC},∴EC=2．故选:C．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["1", "1.5", "2", "2.5"], "choices": [1.0, 1.5, 2.0, 2.5], "label": 2}
+{"prob_id": 4770, "image_path": "images/4770.png", "question": "如图,在△ABC中,点D、E分别在边AB、AC上,DE∥BC,且AE=1,AC=5,AB=6,则AD的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴\\frac{AE}{AC}=\\frac{AD}{AB},∵AE=1,AC=5,AB=6,∴\\frac{1}{5}=\\frac{AD}{6},解得:AD=\\frac{6}{5}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "1.2", "org_choices": ["1", "1.2", "2", "2.5"], "choices": [1.0, 1.2, 2.0, 2.5], "label": 1}
+{"prob_id": 4781, "image_path": "images/4781.png", "question": "如图,D、E是△ABC边AB、AC上的点,且DE∥BC,若DE:BC=3:5,AD=6,则AB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴\\frac{DE}{BC}=\\frac{AD}{AB}=\\frac{3}{5},∴\\frac{6}{AB}=\\frac{3}{5},∴AB=10．故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["9", "10", "6", "15"], "choices": [9.0, 10.0, 6.0, 15.0], "label": 1}
+{"prob_id": 4799, "image_path": "images/4799.png", "question": "如图,△ABC∽△AED,∠ADE=80°,∠A=60°,则∠B等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ADE+∠A+∠AED=180°,∴∠AED=180°-∠ADE-∠A=180°-80°-60°=40°,又∵△ABC∽△AED,∴∠B=∠AED=40°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "60°", "80°", "100°"], "choices": [40.0, 60.0, 80.0, 100.0], "label": 0}
+{"prob_id": 4817, "image_path": "images/4817.png", "question": "如图,Rt△ABC中,∠C=90°,BC=3,AC=4,若△ABC∽△BDC,则CD=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵△ABC∽△BDC,∴\\frac{BC}{CD}=\\frac{AC}{BC},即\\frac{3}{CD}=\\frac{4}{3},解得CD=\\frac{9}{4}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "2.25", "org_choices": ["2", "\\frac{3}{2}", "\\frac{4}{3}", "\\frac{9}{4}"], "choices": [2.0, 1.5, 1.333, 2.25], "label": 3}
+{"prob_id": 4828, "image_path": "images/4828.png", "question": "如图,△ABC∽△DEF,相似比为1:2,若EF=2,则BC的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵△ABC∽△DEF,相似比为1:2,∴\\frac{BC}{EF}=\\frac{1}{2},∴BC=\\frac{1}{2}EF=1,故选:A．", "dataset_name": "Geoqa", "ground_truth": "1.0", "org_choices": ["1", "2", "3", "4"], "choices": [1.0, 2.0, 3.0, 4.0], "label": 0}
+{"prob_id": 4846, "image_path": "images/4846.png", "question": "如图,DE是△ABC的中位线,已知△ABC的面积为8cm^{2},则△ADE的面积为()cm^{2}．. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE为中位线,∴DE∥BC,DE=\\frac{1}{2}BC,∴△ADE∽△ABC,∴S△ADE:S△ABC=1:4,∵S△ABC=8cm^{2},∴S△ADE=2cm^{2}．故选:A．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["2", "4", "6", "8"], "choices": [2.0, 4.0, 6.0, 8.0], "label": 0}
+{"prob_id": 4859, "image_path": "images/4859.png", "question": "如图,D是△ABC的边BC上一点,已知AB=6,AD=3,AC=4,∠DAC=∠B,则BD长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠DAC=∠B,∠C=∠C,∴△ACD∽△BCA,∵AB=6,AD=3,AC=4,∴\\frac{AC}{BC}=\\frac{AD}{AB},即\\frac{4}{BC}=\\frac{3}{6},可得:BC=8,∵△ACD∽△BCA,∴\\frac{CD}{AC}=\\frac{AC}{BC},即\\frac{CD}{4}=\\frac{4}{8},可得；CD=2,∴BD=BC-CD=8-2=6,故选:B．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["4", "6", "8", "9"], "choices": [4.0, 6.0, 8.0, 9.0], "label": 1}
+{"prob_id": 4865, "image_path": "images/4865.png", "question": "如图,若△ABC∽△ACD,∠A=60°,∠ACD=40°,则∠BCD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵△ABC∽△ACD,∠A=60°,∠ACD=40°,∴∠B=∠ACD=40°,∴∠ACB=180°-∠A-∠B=80°,∴∠BCD=∠ACB-∠ACD=80°-40°=40°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["30°", "40°", "50°", "30°或50°"], "choices": [30.0, 40.0, 50.0], "label": 1}
+{"prob_id": 4873, "image_path": "images/4873.png", "question": "如图,两条直线被三条平行线所截,AB=2,BC=3,则\\frac{EF}{EG}等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AE∥BF∥CG,∴\\frac{EF}{EG}=\\frac{AB}{AC},∵AB=2,BC=3,∴AC=AB+BC=5,∴\\frac{EF}{EG}=\\frac{2}{5},故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.4", "org_choices": ["\\frac{2}{3}", "\\frac{2}{5}", "\\frac{3}{2}", "\\frac{5}{6}"], "choices": [0.667, 0.4, 1.5, 0.833], "label": 1}
+{"prob_id": 4875, "image_path": "images/4875.png", "question": "如图所示,在△ABC中,DE∥BC,若\\frac{AD}{AB}=\\frac{1}{3},则\\frac{AE}{AC}=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在△ABC中,∵DE∥BC,\\frac{AD}{AB}=\\frac{1}{3},∴\\frac{AD}{AB}=\\frac{AE}{AC}=\\frac{1}{3},故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.3333333333333333", "org_choices": ["\\frac{1}{2}", "\\frac{1}{3}", "\\frac{2}{3}", "\\frac{1}{4}"], "choices": [0.5, 0.333, 0.667, 0.25], "label": 1}
+{"prob_id": 4906, "image_path": "images/4906.png", "question": "如图,C、M是线段AB上的两点,且点M是线段AC的中点,若AB=8cm,BC=2cm,则AM的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】:由图形可知AC=AB-BC=8-2=6cm,∵M是线段AC的中点,∴AM=AC=3cm．故AM的长为3cm．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["2cm", "3cm", "4cm", "6cm"], "choices": [2.0, 3.0, 4.0, 6.0], "label": 1}
+{"prob_id": 4918, "image_path": "images/4918.png", "question": "如图,C,D是线段AB上两点,若CB=4cm,DB=7cm,且D是AC的中点,则AC的长等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:由线段的和差,得DC=DB-CB=7-4=3cm,由D是AC中点,得AC=2DC=6cm．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["14cm", "11cm", "6cm", "3cm"], "choices": [14.0, 11.0, 6.0, 3.0], "label": 2}
+{"prob_id": 4920, "image_path": "images/4920.png", "question": "如图,BC=\\frac{1}{2}AB,D为AC的中点,若DC=3,则AB的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵D为AC的中点,DC=3,∴AC=2DC=2×3=6,∵BC=\\frac{1}{2}AB,∴AB=\\frac{2}{3}AC=\\frac{2}{3}×6=4,", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["3", "4", "5", "6"], "choices": [3.0, 4.0, 5.0, 6.0], "label": 1}
+{"prob_id": 4927, "image_path": "images/4927.png", "question": "如图,小林从P点向西直走12米后,向左转,转动的角度为α,再走12米,如此重复,小林共走了108米回到点P,则α-5的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:设边数为n,根据题意,n=108÷12=9,∴α=360°÷9=40°．所以α-5=35°,", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["35°", "40°", "50°", "不存在"], "choices": [35.0, 40.0, 50.0], "label": 0}
+{"prob_id": 4929, "image_path": "images/4929.png", "question": "如图,已知AD是△ABC的中线,且△ABD的周长比△ACD的周长大3cm,则AB与AC的差为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵AD是△ABC的中线,∴BD=DC,∴△ABD与△ACD的周长之差=(AB+AD+BD)-(AC+AD+CD)=AB-AC,∵△ABD比△ACD的周长大3cm,∴AB与AC的差为3cm．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["2cm", "3cm", "4cm", "6cm"], "choices": [2.0, 3.0, 4.0, 6.0], "label": 1}
+{"prob_id": 4962, "image_path": "images/4962.png", "question": "如图,在△ABC中,AB=AC,M,N分别是AB,AC的中点,D,E为BC上的点,连结DN,EM．若AB=13cm,BC=10cm,DE=5cm,则图中阴影部分面积为cm2．(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:连接MN,过点A作AF⊥BC于F,则MN是△ABC的中位线,因此MN=\\frac{1}{2}BC=5cm；则AF=√{AB²-BF²}=12cm．∵图中阴影部分的三个三角形的底长都是5cm,且高的和为12cm；因此S阴影=\\frac{1}{2}×5×12=30cm2．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["25", "35", "30", "42"], "choices": [25.0, 35.0, 30.0, 42.0], "label": 2}
+{"prob_id": 4968, "image_path": "images/4968.png", "question": "如图,C是以AB为直径的半圆O上一点,连结AC,BC,分别以AC,BC为边向外作正方形ACDE,BCFG．DE,FG,⁀{\\mathrm{AC}},⁀{\\mathrm{BC}}的中点分别是M,N,P,Q．若MP+NQ=14,AC+BC=18,则AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:连接OP,OQ,∵DE,FG,⁀{\\mathrm{AC}},⁀{\\mathrm{BC}}的中点分别是M,N,P,Q,∴OP⊥AC,OQ⊥BC,∴H、I是AC、BD的中点,∴OH+OI=\\frac{1}{2}(AC+BC)=9,∵MH+NI=AC+BC=18,MP+NQ=14,∴PH+QI=18-14=4,∴AB=OP+OQ=OH+OI+PH+QI=9+4=13,", "dataset_name": "Geoqa", "ground_truth": "13.0", "org_choices": ["9√{2}", "\\frac{90}{7}", "13", "16"], "choices": [12.728, 12.857, 13.0, 16.0], "label": 2}
+{"prob_id": 4985, "image_path": "images/4985.png", "question": "如图,在四边形ABCD中,点P是对角线BD的中点,点E、F分别是AB、CD的中点,AD=BC,∠FPE=136°,则∠PFE的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵P是对角线BD的中点,E是AB的中点,∴EP=\\frac{1}{2}AD,同理,FP=\\frac{1}{2}BC,∵AD=BC,∴PE=PF,∵∠FPE=136°,∴∠PFE=∠PEF=22°,", "dataset_name": "Geoqa", "ground_truth": "22.0", "org_choices": ["15°", "20°", "22°", "44°"], "choices": [15.0, 20.0, 22.0, 44.0], "label": 2}
+{"prob_id": 4990, "image_path": "images/4990.png", "question": "如图,已知直线a∥b∥c,直线d与它们分别垂直且相交于A,B,C三点,若AB=3,AC=8,则平行线b,c之间的距离是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵直线a∥b∥c,直线d与它们分别垂直且相交于A,B,C三点,∴AB长为直线a和b之间的距离,BC长为直线b和c之间的距离,AC长为直线a和c之间的距离,又∵AB=3,AC=8,∴BC=8-3=5,即直线b与直线c之间的距离为5．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["3", "5", "8", "11"], "choices": [3.0, 5.0, 8.0, 11.0], "label": 1}
+{"prob_id": 500, "image_path": "images/500.png", "question": "如图,已知∠1＋∠2=100°,则∠3=()．. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠1+∠2=100^{°},∠1=∠2,∴∠1=50^{°},∴∠3=180°-∠1=130°,故选C.", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["50°", "80°", "130°", "120°"], "choices": [50.0, 80.0, 130.0, 120.0], "label": 2}
+{"prob_id": 501, "image_path": "images/501.png", "question": "如图,有一池塘,要测池塘两端A,B间的距离,可先在平地上取一个不经过池塘可以直接到达点A和B的点C,连接AC并延长至D,使CD=CA,连接BC并延长至E,使CE=CB,连接ED．若量出DE=58米,则A,B间的距离为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:在△ABC和△DEC中,AC=CD⊥∠ACD=∠DCEBC=CE△ABC\\omega△DEC(SAS),∴AB=DE=58{米},故选B.", "dataset_name": "Geoqa", "ground_truth": "58.0", "org_choices": ["29米", "58米", "60米", ".116米A120°"], "choices": [29.0, 58.0, 60.0, 120.0], "label": 1}
+{"prob_id": 520, "image_path": "images/520.png", "question": "如图,平行线a、b被直线c所截,若∠1=50°,则∠2的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵直线a//b,∠1=50°,∴∠3=∠1=50°,∴∠2=180^{°}-∠3=180^{°}-50^{°}=130°故选B.", "dataset_name": "Geoqa", "ground_truth": "130.0", "org_choices": ["150°", "130°", "110°", "100°"], "choices": [150.0, 130.0, 110.0, 100.0], "label": 1}
+{"prob_id": 521, "image_path": "images/521.png", "question": "如图,已知∠1=60°,∠A+∠B+∠C+∠D+∠E+∠F=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠1+∠B+∠C+∠D+∠E=180°,∠1+∠A+∠F=180°,∠1=60°,∴∠B+∠C+∠D+∠E=120°,∠A+∠F=120°,∴∠A+∠B+∠C+∠D+∠E+∠F=240°.故选:C", "dataset_name": "Geoqa", "ground_truth": "240.0", "org_choices": ["360°", "540°", "240°", "280°"], "choices": [360.0, 540.0, 240.0, 280.0], "label": 2}
+{"prob_id": 540, "image_path": "images/540.png", "question": "如图,等腰三角形ABC中,AB=AC,BD是AC边上的高,若∠A=36°,则∠DBC的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB=AC,∠A=36^{°},∴∠ABC=∠ACB=72^{°}.∵BD是AC边上的高,∴BD⊥AC,∴∠DBC=90^{°}-72^{°}=18^{°}故选A.", "dataset_name": "Geoqa", "ground_truth": "18.0", "org_choices": ["18°", "36°", "54°", "72°"], "choices": [18.0, 36.0, 54.0, 72.0], "label": 0}
+{"prob_id": 550, "image_path": "images/550.png", "question": "如图,若a∥b,∠1=115°,则∠2=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵a//b,∴∠1+∠2=180°,∵∠1=115°,∴∠2=65°故选C.", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["55°", "60°", "65°", "75°"], "choices": [55.0, 60.0, 65.0, 75.0], "label": 2}
+{"prob_id": 551, "image_path": "images/551.png", "question": "如图,在△ABC中∠A=80°．点D是BC延长线上一点,∠ACD=150°,则∠B=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠ACD=∠A+∠B,∠A=80°,∠ACD=150°,∴∠B=70°.故选C.", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["60°", "50°", "70°", "165°"], "choices": [60.0, 50.0, 70.0, 165.0], "label": 2}
+{"prob_id": 569, "image_path": "images/569.png", "question": "如图,a∥b,点B在直线a上,且AB⊥BC,∠1=35°,那么∠2=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:如图∵AB⊥BC,∠1=35°,∴∠3=90^{°}-35^{°}=55^{°}.∵a//b,∴∠2=∠3=55^{°}.故选C.", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["45°", "50°", "55°", "60°"], "choices": [45.0, 50.0, 55.0, 60.0], "label": 2}
+{"prob_id": 576, "image_path": "images/576.png", "question": "如图,直线AB与CD相交于E,在∠CEB的平分线上有一点F,FM∥AB．当∠3=10°时,∠F的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠1+∠2+∠3=180°,∠3=10°,∴∠1+∠2=170°,即∠CEB=170,∵EF平分∠CEB,∴∠1=∠2=85°,∴FM//AB,∴∠F=∠2=85°.故选D.", "dataset_name": "Geoqa", "ground_truth": "85.0", "org_choices": ["80°", ".82°", "83°", "85°"], "choices": [80.0, 0.82, 83.0, 85.0], "label": 3}
+{"prob_id": 580, "image_path": "images/580.png", "question": "如图,已知直线a、b被直线c所截．若a∥b,∠1=120°,则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:如图,∠3=180°-∠1=180°-120°=60°,∵a//b,∴∠2=∠3=60°.故选B.", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["50°", "60°", "120°", "130°"], "choices": [50.0, 60.0, 120.0, 130.0], "label": 1}
+{"prob_id": 587, "image_path": "images/587.png", "question": "如图,C、D是以线段AB为直径的⊙O上两点,若CA=CD,且∠CAB=25°,则∠ACD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵CD是直径,∴∠ACB=90°,∵∠CAB=25°,∴∠ABC=65°,∴∠ADC=65°,∵CA=CD,∴∠CAD=∠ADC=65°,∴∠ACD=180°-2×65°=50°故选D.", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["25°", "30°", "40°", "50°"], "choices": [25.0, 30.0, 40.0, 50.0], "label": 3}
+{"prob_id": 593, "image_path": "images/593.png", "question": "如图,AB∥EF,CD⊥EF于点D,若∠BCD=140°,则∠ABC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "过点C作CG//AB,由题意可得:AB//EF//CG,故∠B=∠BCG,∵CD⊥EF于点D,∴∠GCD=90°∵∠BCD=140°.∴∠BCG=50^{°},∴∠ABC=50^{°},故选:B.", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["60°", "50°", "40°", "30°"], "choices": [60.0, 50.0, 40.0, 30.0], "label": 1}
+{"prob_id": 596, "image_path": "images/596.png", "question": "如图,在△ABC中,∠B=40°,过点C作CD∥AB,∠ACD=65°,则∠ACB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵CD//AB,∴∠A=∠ACD=65°,∴∠ACB=180°-∠A-∠B=180°-65°-40°=75°,即∠ACB的度数为75°.故选D.", "dataset_name": "Geoqa", "ground_truth": "75.0", "org_choices": ["60°", "65°", "70°", "75°"], "choices": [60.0, 65.0, 70.0, 75.0], "label": 3}
+{"prob_id": 598, "image_path": "images/598.png", "question": "将一副直角三角板如图放置,使含30°角的三角板的直角边和含45°角的三角板的一条直角边在同一条直线上,则∠1的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "方法一:∠1的对顶角所在的三角形中另两个角的度数分别为60°,45°,∴∠1=180°-(60°+45°)=75°.方法二:∠1可看作是某个三角形的外角,根据三角形的外角等于与它不相邻的两个内角的和计算.故选A.", "dataset_name": "Geoqa", "ground_truth": "75.0", "org_choices": ["75°", "65°", "45°", "30°"], "choices": [75.0, 65.0, 45.0, 30.0], "label": 0}
+{"prob_id": 603, "image_path": "images/603.png", "question": "已知直线a∥b,一块直角三角板如图所示放置,若∠1=37°,则∠2的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "作直线AB//a,∵a//b∴AB//a//b,∵AB//a,∴∠1=∠3,∵AB//b,∴∠2=∠4,∵∠3+∠4=90°,∴∠1+∠2=90°,∵∠1=37°,∴∠2=90^{°}-37^{°}=53^{°}故选B", "dataset_name": "Geoqa", "ground_truth": "53.0", "org_choices": ["37°", "53°", "63°", "27°"], "choices": [37.0, 53.0, 63.0, 27.0], "label": 1}
+{"prob_id": 620, "image_path": "images/620.png", "question": "如图所示,矩形ABCD的对角线AC、BD相交于点O,CE∥BD,DE∥AC,若AB=4,BC=3,则四边形CODE的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "首先由CE||BD,DE||AC,可证得四边形CODE是平行四边形,又由四边形ABCD是矩形,根据矩形的性质,易得OC=OD=2,即可判定四边形CODE是菱形,继而求得答案.解:∵CE||BD1DE||AC,∴四边形CODE是平行四边形,.四边形ABCD是矩形,∴AC=BD=4,OA=OC,OB=OD,∴OD=OC,AC=√{AB²+BC²}=√{4²+3²}=5.∴四边形CODE是菱形,且OC=\\frac{1}{2}AC=2.5∴四边形CODE的周长为:2.5×4=10.故选A", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["10", "12", "18", "24"], "choices": [10.0, 12.0, 18.0, 24.0], "label": 0}
+{"prob_id": 631, "image_path": "images/631.png", "question": "如图,将含30°角的三角板的直角顶点放在直尺的一边上,若∠1=35°,则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图,∵∠1=35°,∠3=30°,∴∠4=115°,∵∠2+∠4=180°,∴∠2=65°.故选B.", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["80°", "65°", "60°", "55°"], "choices": [80.0, 65.0, 60.0, 55.0], "label": 1}
+{"prob_id": 654, "image_path": "images/654.png", "question": "如图,在▱ABCD中,F是AD上的一点,CF=CD.若∠B=72°,则∠AFC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "已知四边形ABCD是平行四边形,根据平行四边形的性质可得∠D=∠B=72°,再因CF=CD,根据等腰三角形的性质可得∠DFC=∠D=72°,所以∠AFC=180°∠DFC=108°1故选B", "dataset_name": "Geoqa", "ground_truth": "108.0", "org_choices": ["144°", "108°", "102°", ".78°A菱形的对角线互相垂直"], "choices": [144.0, 108.0, 102.0], "label": 1}
+{"prob_id": 691, "image_path": "images/691.png", "question": "从棱长为4的正方体毛坯的一角,挖去一个棱长为2的小正方体,得到一个如图所示的零件,则这个零件的表面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:棱长为4的正方体毛坯的一角挖去一个棱长为2的小正方体,得到的图形与原图形表面积相等,则表面积是4×4×6=96,故答案为:96", "dataset_name": "Geoqa", "ground_truth": "96.0", "org_choices": ["90", "92", "94", "96"], "choices": [90.0, 92.0, 94.0, 96.0], "label": 3}
+{"prob_id": 703, "image_path": "images/703.png", "question": "如图,点B,O,D在同一直线上,若∠1=15°,∠2=105°,则∠AOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠2=105°,∴∠BOC=180^{°}-∠2=75^{°}∴∠AOC=∠1+∠BOC=15^{°}+75^{°}=90^{°}故选C.", "dataset_name": "Geoqa", "ground_truth": "90.0", "org_choices": ["70", "80", "90", "100"], "choices": [70.0, 80.0, 90.0, 100.0], "label": 2}
+{"prob_id": 717, "image_path": "images/717.png", "question": "如图,将两块三角板的直角顶点重合后叠放在一起,若∠1=40°,则∠2的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图:∵∠1+∠BOC=90^{°},∠2+∠BOC=90^{°},∴∠2=∠1=40^{°},故选:C.", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["60°", "50°", "40°", "30°"], "choices": [60.0, 50.0, 40.0, 30.0], "label": 2}
+{"prob_id": 722, "image_path": "images/722.png", "question": "如图所示,一辆汽车经过一段公路两次拐弯后,和原来的行驶方向相同,也就是拐弯前后的两条路互相平行.第一次拐的角∠B等于142°,第二次拐的角∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题分析:∵拐弯前后的两条路互相平行,∴∠C=∠B=142°(两直线平行,内错角相等).故选B", "dataset_name": "Geoqa", "ground_truth": "142.0", "org_choices": ["38°", "142°", "130°", "140°"], "choices": [38.0, 142.0, 130.0, 140.0], "label": 1}
+{"prob_id": 728, "image_path": "images/728.png", "question": "如图△ABC中,∠ACB=90°,AD平分∠BAC交BC于D,DE垂直AB于E,若DE=1.5cm,BD=3cm,则BC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∠ACB=90^{°},DE垂直AB于E,AD平分∠BAC交BC于D,所以DC=DE=1.5.BD=3cm∴BC=4.5cm所以选D.", "dataset_name": "Geoqa", "ground_truth": "4.5", "org_choices": ["3cm", "7.5cm", "6cm", "4.5cm"], "choices": [3.0, 7.5, 6.0, 4.5], "label": 3}
+{"prob_id": 731, "image_path": "images/731.png", "question": "如图所示,AB=AC,AD=AE,∠BAC=∠DAE,∠1=25°,∠2=30°,则∠3=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:∵∠BAC=∠DAE,∴∠BAC-∠DAC=∠DAE-∠DAC∴∠1=∠EAC,在△BAD和△EAC中,AB=AC∠BAD=∠EACAD=AE∴△BAD≌△EAC(SAS),∠2=∠ABD=30^{°},∵∠1=25°∴∠3=∠1+∠AB∠ABD=25^{°}+30^{°}=55^{°}故选B.", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["60°", "55°", "50°", "无法计算"], "choices": [60.0, 55.0, 50.0], "label": 1}
+{"prob_id": 734, "image_path": "images/734.png", "question": "如图,在△ABC中,∠B=46°,∠C=54°,AD平分∠BAC,交BC于D,则∠BAD的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠B=46°∠C=54°.∠BAC=180°-∠B-∠C=180^{°}-46^{°}-54^{°}=80^{°},AD平分∠BAC,∠BAD=40°所以选C.", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["45°", "54°", "40°", "50°"], "choices": [45.0, 54.0, 40.0, 50.0], "label": 2}
+{"prob_id": 735, "image_path": "images/735.png", "question": "如图,已知D为BC上一点,∠B=∠1,∠BAC=78°,则∠2=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠2=∠B+∠BAD,∠BAC=∠1+∠BAD,又∵∠B=∠1,∴∠2=∠BAC,∵∠BAC=78°,∴∠2=78°.故选A.", "dataset_name": "Geoqa", "ground_truth": "78.0", "org_choices": ["78°", "80°", "50°", "60°"], "choices": [78.0, 80.0, 50.0, 60.0], "label": 0}
+{"prob_id": 758, "image_path": "images/758.png", "question": "如图,在△ABC中,∠ACB=90°,沿CD折叠△CBD,使点B恰好落在AC边上的点E处．若∠A=24°,则∠BDC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "在△ABC中,∠ACB=90°,∠A=24°,∠B=90^{°}-∠A=66^{°}.由折叠的性质可得:∠BCD=\\frac{1}{2}∠ACB=45^{°}∴∠BDC=180°-∠BCD-∠B=69°故选C.", "dataset_name": "Geoqa", "ground_truth": "69.0", "org_choices": ["42°", "66°", "69°", "77°"], "choices": [42.0, 66.0, 69.0, 77.0], "label": 2}
+{"prob_id": 777, "image_path": "images/777.png", "question": "如图,DE为△ABC的边BC的垂直平分线,交BC于E,交AB于D,且∠B=40°,∠A=60°,则∠ACD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "试题解析:∵∠B=40°,∠A=60°,∴∠ACB=180^{°}-60^{°}-40^{°}=80^{°},∵DE为△ABC边BC的垂直平分线,∴∠BCD=∠B=40°,∴∠ACD=∠ACB-angleBCD=80^{°}-40^{°}=40^{°}.故选A.", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "50°", "30°", "45°"], "choices": [40.0, 50.0, 30.0, 45.0], "label": 0}
+{"prob_id": 829, "image_path": "images/829.png", "question": "如图,在半径为5cm的⊙O中,AB为一条弦,OC⊥AB于点C,且OC=3cm,则AB的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "连接OA,OC⊥AB,点O是圆心,∴AB=2AC,∠ACO=90°,∴AC=√{OA²-OC²}=√{5²-3²}=4cm,∴AB=8cm,故选D", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["3cm", "4cm", "6cm", "8cm"], "choices": [3.0, 4.0, 6.0, 8.0], "label": 3}
+{"prob_id": 869, "image_path": "images/869.png", "question": "已知如图,在⊙O中,OA⊥OB,∠A=35°,则弧CD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC,∵OA⊥OB,∴∠AOB=90°,∵∠A=35°,∴∠OBC=∠OCB=55°,∴OB=OC,∴∠OBC=∠OCB=55°,∴∠COB=70°,∴弧CD的度数为20°,故选:A.", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["20°", "25°", "30°", "35°"], "choices": [20.0, 25.0, 30.0, 35.0], "label": 0}
+{"prob_id": 884, "image_path": "images/884.png", "question": "如图,在△ABC中,DE是AC的垂直平分线,AE=3cm,△ABD的周长为13cm,则△ABC的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵DE是AC的垂直平分线,AE=3cm,∴AE=CE=3cm,AD=DC,又△ABD的周长为13cm,即AB+BD+AD=13cm,△ABC的周长=AB+BC+AC=AB+BD+DC+2AE=AB+BD+AD+2AE=13+6=19cm故选C.", "dataset_name": "Geoqa", "ground_truth": "19.0", "org_choices": ["16cm", "13cm", "19cm", "10cm"], "choices": [16.0, 13.0, 19.0, 10.0], "label": 2}
+{"prob_id": 887, "image_path": "images/887.png", "question": "如图,⊿ABC内接于⊙O,若∠OAB=28°则∠C的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "连接OB,∵OA=OB,∠OAB=28°∠OBA=∠OAB=28°,∴∠AOB=180°-28°-28°=124°,∵∠ACB、∠AOB是\\hat{AB}所对的圆周角和圆心角,∴∠ACB=\\frac{1}{2}∠AOB=62^{°},故选C", "dataset_name": "Geoqa", "ground_truth": "62.0", "org_choices": ["56°", "60°", "62°", "28°"], "choices": [56.0, 60.0, 62.0, 28.0], "label": 2}
+{"prob_id": 907, "image_path": "images/907.png", "question": "如图,已知PA、PB是⊙O的切线,A、B为切点,AC是⊙O的直径,∠P=40°,则∠BAC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BC,OB,AC是直径,则∠ABC=90°PA、PB是⊙O的切线,A、B为切点,则∠OAP=∠OBP=90°,∴∠AOB=180°-∠P=140°由圆周角定理知,∠C=\\frac{1}{2}∠AOB=70^{°},∴∠BAC=90°-∠C=20°.故选B.", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["10°", "20°", "30°", "40°"], "choices": [10.0, 20.0, 30.0, 40.0], "label": 1}
+{"prob_id": 936, "image_path": "images/936.png", "question": "如图,在Rt△ABC中,∠B=90°,AB=6,AC=10将△ABC沿ED折叠,使点C与点A重合,则△ABE的周长等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "在直角△ABC中,BC=√{AC²-AB²}=√{10²-6²}=8cm∵AE=EC,∴△ABE的周长=AB+BE+AE=AB+BE+EC=AB+BC=6+8=14(cm).故选A.", "dataset_name": "Geoqa", "ground_truth": "14.0", "org_choices": ["14", "12", "10", "15"], "choices": [14.0, 12.0, 10.0, 15.0], "label": 0}
+{"prob_id": 942, "image_path": "images/942.png", "question": "如图,一把矩形直尺沿直线断开并错位,点E、D、B、F在同一条直线上,若∠ADE=125°,则∠DBC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "延长CB,延长CB,∵AD//CB,∴∠1=∠ADE=145°,∴∠DBC=180^{°}-∠1=180^{°}-125^{°}=55^{°}.故答案选:D.", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["125°", "75°", "65°", "55°"], "choices": [125.0, 75.0, 65.0, 55.0], "label": 3}
+{"prob_id": 948, "image_path": "images/948.png", "question": "如图,圆心角∠AOB=60∘,则圆周角∠ACB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠AOB=60°∴∠ACB=\\frac{1}{2}∠AOB=30^{°}故选A.", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["30°", "60°", "90°", "120°"], "choices": [30.0, 60.0, 90.0, 120.0], "label": 0}
+{"prob_id": 964, "image_path": "images/964.png", "question": "如图,△ABC中,∠A=90°,AB=AC,BD平分∠ABE,DE⊥BC,如果BC=10cm,则△DEC的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BD平分∠ABE,DE⊥BC,DA⊥ABAD=DE又∵BD=BD,∴△BAD≌△BED(HL)AB=BE又∵AB=ACBE=ACBC=BE+EC=AC+EC=AD+DC+EC=DE+DC+EC=10cm∴△DEC的周长是10cm,故选B.", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["8cm", "10cm", "11cm", "12cm"], "choices": [8.0, 10.0, 11.0, 12.0], "label": 1}
+{"prob_id": 968, "image_path": "images/968.png", "question": "如图,圆外切等腰梯形ABCD的中位线EF=15cm,那么等腰梯形ABCD的周长等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "根据梯形的中位线等于两底和的一,得梯形的两底和等于梯形的中位线的2倍,即30cm;根据圆外切四边形的两组对边和相等,得梯形的两腰的和等于两底和,即30cm.则梯形的周长等于30+30=60(cm).故选:D.", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["15cm", "20cm", "30cm", "60cm"], "choices": [15.0, 20.0, 30.0, 60.0], "label": 3}
+{"prob_id": 970, "image_path": "images/970.png", "question": "如图,若CB=4cm,DB=7cm,且D是AC的中点,则AC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵CB=4cm,DB=7cm∴CD=7-4=3(cm);∵D是AC的中点,∴AD=CD=3cm,∴AC=AD+DC=3+3=6(cm).故选:A.", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["6cm", "7cm", "4cm", "5cm"], "choices": [6.0, 7.0, 4.0, 5.0], "label": 0}
+{"prob_id": 979, "image_path": "images/979.png", "question": "如图,在△ABC中,∠ABC=120°,若DE、FG分别垂直平分AB、BC,那么∠EBF的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE、FG分别垂直平分AB、BC,∴AE=BE,BF=CF,∴∠A=∠ABE,∠C=∠CBF,∵∠A+∠C+∠ABC=180°,∠ABC=120°,∴∠A+∠C=60°∴∠ABE+∠CBF=60°∴∠EBF=120°60°=60°,故选C.", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["30°", "45°", "60°", "75°"], "choices": [30.0, 45.0, 60.0, 75.0], "label": 2}
+{"prob_id": 996, "image_path": "images/996.png", "question": "如图,在Rt△ABC中,∠BAC=90°,将△ABC绕点A顺时针旋转90°后得到△AB′C′(点B的对应点是点B′,点C的对应点是点C′),连接CC′,若∠CC′B′=33°,则∠B的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵将△ABC绕点A顺时针旋转90°后得到△AB'C'∴AC=AC',∠CAC'=90°,∠AB'C'=∠B∴∠ACC'=45°∵∠AB'C'=∠ACC'+∠CC'B'∴∠AB'C=45°+33°=78°∴∠B=78°故选D.", "dataset_name": "Geoqa", "ground_truth": "78.0", "org_choices": ["33°", "45°", "57°", "78°"], "choices": [33.0, 45.0, 57.0, 78.0], "label": 3}
+{"prob_id": 5012, "image_path": "images/5012.png", "question": "如图,点C在线段AB上,点D是AC的中点,如果CD=3cm,AB=10cm,那么BC的长度是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵点D是AC的中点,∴AC=2CD=2×3=6cm,∴BC=AB-AC=10-6=4cm．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["3cm", "4cm", "6cm", "7cm"], "choices": [3.0, 4.0, 6.0, 7.0], "label": 1}
+{"prob_id": 5049, "image_path": "images/5049.png", "question": "如图,AD是△ABC的中线,已知△ABD的周长为22cm,AB比AC长3cm,则△ACD的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:由题意得,AB=AC+3,∵AD是△ABC的中线,∴BD=DC,∵△ABD的周长为22,∴AB+BD+AD=AC+3+DC+AD=22,则AC+DC+AD=19,∴△ACD的周长=AC+DC+AD=19(cm),", "dataset_name": "Geoqa", "ground_truth": "19.0", "org_choices": ["19cm", "22cm", "25cm", "31cm"], "choices": [19.0, 22.0, 25.0, 31.0], "label": 0}
+{"prob_id": 5059, "image_path": "images/5059.png", "question": "如图,线段AB=20,C为AB的中点,D为CB上一点,E为DB的中点,且EB=3,则CD等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵E为DB的中点,且EB=3,∴BD=2BE=6,∵线段AB=20,C为AB的中点,∴CB=AC=10,∵CD=BC-BD∴CD=4", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["10", "6", "4", "2"], "choices": [10.0, 6.0, 4.0, 2.0], "label": 2}
+{"prob_id": 5073, "image_path": "images/5073.png", "question": "如图,C,D是线段AB上两点．若CB=4cm,DB=7cm,且D是AC的中点,则AB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵CB=4cm,DB=7cm,∴CD=7-4=3(cm)；∵D是AC的中点,∴AD=CD=3cm,∴AB=AD+DB=3+7=10(cm)．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["10cm", "11cm", "12cm", "14cm"], "choices": [10.0, 11.0, 12.0, 14.0], "label": 0}
+{"prob_id": 5075, "image_path": "images/5075.png", "question": "如图,一辆超市购物车放置在水平地面上,其侧面四边形ABCD与地面某条水平线在同一平面内,且AB∥l,若∠A=93°,∠D=111°,则直线CD与l所夹锐角的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:如图所示,根据题意可知直线CD与l所夹锐角即为∠AED,据题意可得∠ADE=180°-∠ADC=69°,∠DAE=180°-∠BAD=87°,∴∠AED=180°-∠ADE-∠DAE=24°．", "dataset_name": "Geoqa", "ground_truth": "24.0", "org_choices": ["15°", "18°", "21°", "24°"], "choices": [15.0, 18.0, 21.0, 24.0], "label": 3}
+{"prob_id": 5082, "image_path": "images/5082.png", "question": "如图,在△ABC中,∠B=∠C,D为BC边上一点,E点在AC边上,∠ADE=∠AED,若∠BAD=24°,则∠CDE=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵∠ADC是△ABD的外角,∴∠ADC=∠B+∠BAD=∠B+24°,∵∠AED是△CDE的外角,∴∠AED=∠C+∠EDC,∵∠B=∠C,∠ADE=∠AED,∴∠C+∠EDC=∠ADC-∠EDC=∠B+24°-∠EDC,解得∠EDC=12°．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["24°", "20°", "15°", "12°"], "choices": [24.0, 20.0, 15.0, 12.0], "label": 3}
+{"prob_id": 5096, "image_path": "images/5096.png", "question": "如图,AB是⊙O的弦,OC⊥AB于点D,交⊙O于点C,若半径为5,OD=3,则弦AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:连接AO,∵OC⊥AB,∴D为AB的中点,即AD=BD=\\frac{1}{2}AB,在Rt△AOD中,OA=5,OD=3,根据勾股定理得:AD=√{AO²-DO²}=4,则AB=2AD=8．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["5", "6", "7", "8"], "choices": [5.0, 6.0, 7.0, 8.0], "label": 3}
+{"prob_id": 5112, "image_path": "images/5112.png", "question": "如图,AB是⊙O的直径,O是圆心,弦CD⊥AB于E,AB=10,CD=8,则OE的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:连接OC,∵直径AB=10,∴OC=5,∵CD⊥AB,AB为直径,∴CD=2CE=8,∠OEC=90°,∴CE=4,由勾股定理得:OE=√{5²-4²}=3．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["2", "3", "4", "5"], "choices": [2.0, 3.0, 4.0, 5.0], "label": 1}
+{"prob_id": 5118, "image_path": "images/5118.png", "question": "如图,⊙O的半径为OA=5,以A为圆心,OA为半径的弧交⊙O于B,C两点,则弦BC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:连接AB,OB,∵⊙O的半径为OA=5,以A为圆心,OA为半径的弧交⊙O于B,C两点,∴OA=AB=OB,BC⊥OA,∴∠BOA=60°,∵BC⊥OA,∴BC=5√{3}．", "dataset_name": "Geoqa", "ground_truth": "8.660254037844387", "org_choices": ["5√{3}", "\\frac{5}{2}√{3}", "8", "5√{2}"], "choices": [8.66, 4.33, 8.0, 7.071], "label": 0}
+{"prob_id": 5159, "image_path": "images/5159.png", "question": "如图,C、D是线段AB上两点,若BC=3cm,BD=5cm,且D是AC的中点,则AC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵BC=3cm,BD=5cm,∴CD=BD-BC=2cm,∵D是AC的中点,∴AC=2CD=4cm,", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["2cm", "4cm", "8cm", "13cm"], "choices": [2.0, 4.0, 8.0, 13.0], "label": 1}
+{"prob_id": 5181, "image_path": "images/5181.png", "question": "如图,在⊙O中,AB是弦,OC⊥AB,垂足为C,若AB=16,OC=6,则⊙O的直径等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵在⊙O中,AB是弦,OC⊥AB,垂足为C,AB=16,∴AC=\\frac{1}{2}AB=\\frac{1}{2}×16=8,在Rt△AOC中,∵OC=6,AC=8,∴OA=√{OC²+AC²}=√{6²+8²}=10,∴⊙O的直径=2OA=2×10=20．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["16", "20", "10", "8"], "choices": [16.0, 20.0, 10.0, 8.0], "label": 1}
+{"prob_id": 5184, "image_path": "images/5184.png", "question": "如图,在半径为10的⊙O中,半径OC垂直于弦AB于点D,AB=16,则CD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:连接OA,∵半径OC垂直于弦AB,AB=16,∴AD=8,∠ADO=90°,∵OA=10,∴在Rt△ADO中,由勾股定理得:OD=6,∴CD=10-6=4,", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["2", "4", "6", "8"], "choices": [2.0, 4.0, 6.0, 8.0], "label": 1}
+{"prob_id": 5192, "image_path": "images/5192.png", "question": "如图所示,P是⊙O的弦AB上的一点,AB=10cm,AP=4cm,OP=5cm,则⊙O的半径为cm．(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:过O作OD⊥AB,D为垂足,连接OB,∵AB=10cm,AP=4cm,∴BD=5cm,DP=1cm,在Rt△ODP中,OD=√{OP²-DP²}=√{5²-1²}=2√{6}；在Rt△ODB中,OB=√{OD²+BD²}=√{(2√{6})²+5²}=7cm．", "dataset_name": "Geoqa", "ground_truth": "7.0", "org_choices": ["5", "7", "6", "6.5"], "choices": [5.0, 7.0, 6.0, 6.5], "label": 1}
+{"prob_id": 5193, "image_path": "images/5193.png", "question": "如图,矩形与⊙O相交,若AB=4,BC=5,DE=3,则EF的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:作OM⊥BC于M,交EF于N点,则OM⊥EF．∵OM⊥BC,∴BM=CM=\\frac{1}{2}BC=2.5,∴AM=AB+BM=6.5,由题意得:四边形ADNM是矩形,∴DN=AM=6.5,∴EN=3.5,∵ON⊥EF,∴EF=2EN=7,", "dataset_name": "Geoqa", "ground_truth": "7.0", "org_choices": ["3.5", "6.5", "7", "8"], "choices": [3.5, 6.5, 7.0, 8.0], "label": 2}
+{"prob_id": 5195, "image_path": "images/5195.png", "question": "如图,AB是⊙O的直径,CD是弦,AB⊥CD,垂足为点E,连接OD、CB、AC,∠DOB=60°,EB=2,那么CD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵∠DOB=60°,∴∠BCE=30°．在Rt△BCE中,∵BE=2,∠BCE=30°,∴BC=4,CE=√{BC²-BE²}=√{4²-3²}=2√{3},∵AB是⊙O的直径,AB⊥CD,∴CD=2CE=4√{3},", "dataset_name": "Geoqa", "ground_truth": "6.928203230275509", "org_choices": ["√{3}", "2√{3}", "3√{3}", "4√{3}"], "choices": [1.732, 3.464, 5.196, 6.928], "label": 3}
+{"prob_id": 5198, "image_path": "images/5198.png", "question": "如图,AB是⊙O的直径,CD是弦,AB⊥CD于点E,若半径为5,OE=3,则CD的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵AB是⊙O的直径,CD是弦,AB⊥CD于点E,∴CE=\\frac{1}{2}CD．在Rt△OCE中,∵OC=5,OE=3,∴CE=√{OC²-OE²}=√{5²-3²}=4,∴CD=2CE=8．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["4", "6", "8", "7"], "choices": [4.0, 6.0, 8.0, 7.0], "label": 2}
+{"prob_id": 5215, "image_path": "images/5215.png", "question": "如图,半径为5的圆O中,弦AB的长为8,则圆心O到弦AB的距离为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:连接AO,∵OC⊥AB,OC过O,∴AC=BC=\\frac{1}{2}AB=4,在Rt△OAC中,由勾股定理得:OC=√{5²-4²}=3,", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["3", "4", "5", "6"], "choices": [3.0, 4.0, 5.0, 6.0], "label": 0}
+{"prob_id": 5225, "image_path": "images/5225.png", "question": "如图,AB=8cm,AD=BC=5cm,则CD等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵AB=8cm,AD=5cm,∴BD=AB-AD=3cm,∵BC=5cm,∴CD=CB-BD=2cm,", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["1cm", "2cm", "3cm", "4cm"], "choices": [1.0, 2.0, 3.0, 4.0], "label": 1}
+{"prob_id": 5251, "image_path": "images/5251.png", "question": "如图,C,D是线段AB上两点,若CB=4cm,DB=7cm,且D是AC的中点,则AB的长等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵CB=4cm,DB=7cm,∴CD=7-4=3(cm)；∵D是AC的中点,∴AD=CD=3cm,∴AB=AD+DB=3+7=10(cm)．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["6cm", "7cm", "10cm", "11cm"], "choices": [6.0, 7.0, 10.0, 11.0], "label": 2}
+{"prob_id": 5301, "image_path": "images/5301.png", "question": "如图,点C在线段AB上,点E是AC中点,点D是BC中点．若ED=6,则线段AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵点E是AC中点,点D是BC中点,∴AE=CE=\\frac{1}{2}AC,CD=BD=\\frac{1}{2}BC,∴CE+CD=\\frac{1}{2}AC+\\frac{1}{2}BC,即ED=\\frac{1}{2}(AC+BC)=\\frac{1}{2}AB,∴AB=2ED=12；", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["6", "9", "12", "18"], "choices": [6.0, 9.0, 12.0, 18.0], "label": 2}
+{"prob_id": 5319, "image_path": "images/5319.png", "question": "如图,已知∠1=40°,∠A+∠B=140°,则∠C+∠D的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:连接CD,如图:∵∠1=40°,∠1+∠2+∠3=180°,∴∠2+∠3=180°-40°=140°,∵∠A+∠B+∠ADC+∠BCD=360°,∠A+∠B=140°,∴∠ADC+∠BCD=360°-140°=220°,∴∠BCE+∠ADE=(∠ADC+∠BCD)-(∠2+∠3)=220°-140°=80°,", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["40°", "60°", "80°", "100°"], "choices": [40.0, 60.0, 80.0, 100.0], "label": 2}
+{"prob_id": 5350, "image_path": "images/5350.png", "question": "如图,四边形ABCD的对角线AC⊥BD,垂足为O,且AC=12,BD=9,则四边形ABCD的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵AC⊥BD,AC=12,BD=9,∴S四边形ABCD=S_{△AOD}+S_{△COD}+S_{△BOC}+S_{△AOB}=\\frac{1}{2}OA\\cdotOD+\\frac{1}{2}OC\\cdotOD+\\frac{1}{2}OC\\cdotOB+\\frac{1}{2}OB\\cdotOA=\\frac{1}{2}OD(OA+OC)+\\frac{1}{2}OB(OA+OC)=\\frac{1}{2}OD\\cdotAC+\\frac{1}{2}OB\\cdotAC=\\frac{1}{2}AC\\cdot(OD+OC)=\\frac{1}{2}AC\\cdotBD=\\frac{1}{2}×12×9=54．", "dataset_name": "Geoqa", "ground_truth": "54.0", "org_choices": ["60", "54", "30", "27"], "choices": [60.0, 54.0, 30.0, 27.0], "label": 1}
+{"prob_id": 5357, "image_path": "images/5357.png", "question": "如图,已知△ABC,点D在BC的延长线上,∠ACD=140°,∠ABC=50°,则∠A的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵∠ACD=∠A+∠ABC,∴∠A=∠ACD-∠ABC,∵∠ACD=140°,∠ABC=50°,∴∠A=140°-50°=90°", "dataset_name": "Geoqa", "ground_truth": "90.0", "org_choices": ["50°", "140°", "120°", "90°"], "choices": [50.0, 140.0, 120.0, 90.0], "label": 3}
+{"prob_id": 5360, "image_path": "images/5360.png", "question": "如图,点O在直线AB上,若∠2=140°,则∠1的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵∠1+∠2=180°且∠2=140°,∴∠1=40°,", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "60°", "140°", "150°"], "choices": [40.0, 60.0, 140.0, 150.0], "label": 0}
+{"prob_id": 5366, "image_path": "images/5366.png", "question": "如图所示,线段AB=10,M为线段AB的中点,C为线段MB的中点,N为线段AM的一点,且MN=1,线段NC的长(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵线段AB=10,M为线段AB的中点,∴MB=\\frac{1}{2}AB=5,∵C为线段MB的中点,∴MC=\\frac{1}{2}BM=2.5,∴NC=NM+MC=3.5．", "dataset_name": "Geoqa", "ground_truth": "3.5", "org_choices": ["2", "2.5", "3", "3.5"], "choices": [2.0, 2.5, 3.0, 3.5], "label": 3}
+{"prob_id": 5369, "image_path": "images/5369.png", "question": "设BF交AC于点P,AE交DF于点Q．若∠APB=126°,∠AQF=100°,则∠A-∠F=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:如图:∵∠1=∠APB-∠A=126°-∠A,∠2=180°-∠AQF-∠F=180°-100°-∠F=80°-∠F；∵∠1=∠2,∴126°-∠A=80°-∠F；∴∠A-∠F=46°．", "dataset_name": "Geoqa", "ground_truth": "46.0", "org_choices": ["60°", "46°", "26°", "45°"], "choices": [60.0, 46.0, 26.0, 45.0], "label": 1}
+{"prob_id": 5376, "image_path": "images/5376.png", "question": "如图,BD,CE分别是△ABC的高线和角平分线,且相交与点O,若∠BCA=70°,则∠BOE的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵B⊥AC,∴∠BDC=90°,∵CE平分∠ACB,∠ACB=70°,∴∠DCO=35°,∴∠BOE=∠COD=90°-35°=55°,", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["60°", "55°", "50°", "40°"], "choices": [60.0, 55.0, 50.0, 40.0], "label": 1}
+{"prob_id": 5380, "image_path": "images/5380.png", "question": "如图,已知点A、B、C在同一直线上,AB=7,BC=3,点D为线段AC的中点,线段DB的长度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵AB=7,BC=3,∴AC=AB+BC=10．∵点D为线段AC的中点,∴CD=\\frac{1}{2}AC=5,∴DB=CD-BC=2．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["2", "4", "6", "8"], "choices": [2.0, 4.0, 6.0, 8.0], "label": 0}
+{"prob_id": 5389, "image_path": "images/5389.png", "question": "如图,在四边形ABCD中,∠DAB的角平分线与∠ABC的外角平分线相交于点P,且∠∠D+∠C=200°,则∠P=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:如图,∵∠D+∠C=200°,∠DAB+∠ABC+∠C+∠D=360°,∴∠DAB+∠ABC=160°．又∵∠DAB的角平分线与∠ABC的外角平分线相交于点P,∴∠PAB+∠ABP=\\frac{1}{2}∠DAB+∠ABC+\\frac{1}{2}(180°-∠ABC)=90°+\\frac{1}{2}(∠DAB+∠ABC)=170°,∴∠P=180°-(∠PAB+∠ABP)=10°．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["10°", "20°", "30°", "40°"], "choices": [10.0, 20.0, 30.0, 40.0], "label": 0}
+{"prob_id": 5458, "image_path": "images/5458.png", "question": "如图,BP平分∠ABC交CD于点F,DP平分∠ADC交AB于点E,若∠A=40°,∠P=38°,则∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵BP平分∠ABC,DP平分∠ADC,∴∠ADP=∠PDF,∠CBP=∠PBA,∵∠A+∠ADP=∠P+∠ABP,∠C+∠CBP=∠P+∠PDF,∴∠A+∠C=2∠P,∵∠A=40°,∠P=38°,∴∠C=2×38°-40°=36°,", "dataset_name": "Geoqa", "ground_truth": "36.0", "org_choices": ["36°", "39°", "38°", "40°"], "choices": [36.0, 39.0, 38.0, 40.0], "label": 0}
+{"prob_id": 5465, "image_path": "images/5465.png", "question": "如图,延长长度为8的线段AB到C,使BC=4,M、N分别是AB、BC的中点,则MN的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "【解答】解:∵M、N分别是AB、BC的中点,∴MB=\\frac{1}{2}AB=4,BN=\\frac{1}{2}BC=2,∴MN=MB+BN=4+2=6．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["2", "4", "6", "4或6"], "choices": [2.0, 4.0, 6.0], "label": 2}
+{"prob_id": 5470, "image_path": "images/5470.png", "question": "如图,A,B,C,D四点都在⊙O上,∠BOD=110°,则∠BCD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由圆周角定理得,∠A=\\frac{1}{2}∠BOD=55°,∵四边形ABCD是圆内接四边形,∴∠BCD=180°-∠A=125°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "125.0", "org_choices": ["70°", "110°", "125°", "130°"], "choices": [70.0, 110.0, 125.0, 130.0], "label": 2}
+{"prob_id": 5474, "image_path": "images/5474.png", "question": "如图,四边形ABCD为⊙O的内接四边形,∠BCD=110°,则∠BOD的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD为⊙O的内接四边形,∠BCD=110°,∴∠A=180°-∠BCD=70°,由圆周角定理得,∠BOD=2∠A=140°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["70°", "120", "140°", "160°"], "choices": [70.0, 120.0, 140.0, 160.0], "label": 2}
+{"prob_id": 5487, "image_path": "images/5487.png", "question": "如图,某货船以24海里/时的速度从A处向正东方向的D处航行,在点A处测得某岛C在北偏东60°的方向．该货船航行30分钟后到达B处,此时测得该岛在北偏东30°的方向上．则货船在航行中离小岛C的最短距离是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作CE⊥AB交AB的延长线于E,由题意得,AB=24×\\frac{1}{2}=12,∠CBE=60°,∠CAE=30°,∴∠ACB=30°,∴∠CAE=∠ACB,∴BC=AB=12,在Rt△CBE中,sin∠CBE=\\frac{CE}{BC},∴CE=BC×sin∠CBE=12×\\frac{√{3}}{2}=6√{3}(海里),故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.392304845413264", "org_choices": ["12海里", "6√{3}海里", "12√{3}海里", "24√{3}海里"], "choices": [12.0, 10.392, 20.785, 41.569], "label": 1}
+{"prob_id": 5501, "image_path": "images/5501.png", "question": "如图,PA,PB切⊙O于点A,B,点C是⊙O上一点,且∠P=36°,则∠ACB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图所示,连接OA、OB．p<(\\phi,7)∵PA、PB都为圆O的切线,∴∠PAO=∠PBO=90°．∵∠P=36°,∴∠AOB=144°．∴∠C=\\frac{1}{2}∠AOB=\\frac{1}{2}=72°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "72.0", "org_choices": ["54°", "72°", "108°", "144°"], "choices": [54.0, 72.0, 108.0, 144.0], "label": 1}
+{"prob_id": 5508, "image_path": "images/5508.png", "question": "如图,PA,PB分别与⊙O相切于A,B两点,∠C=55°,则∠P等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB、OA,如图,∵PA、PB分别与圆O相切于A、B两点,∴OA⊥PA,OB⊥PB,∴∠OAP=∠OBP=90°,∴∠AOB=180°-∠P,∵∠C=55°,∴∠AOB=2∠C=110°,∴∠P=180°-110°=70°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["110°", "70°", "140°", "55°"], "choices": [110.0, 70.0, 140.0, 55.0], "label": 1}
+{"prob_id": 5544, "image_path": "images/5544.png", "question": "如图,在边长为1的正方形网格中,连接格点D、N和E、C,DN和EC相交于点P,tan∠CPN为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接格点MN、DM,如图所示:则四边形MNCE是平行四边形,△DAM和△MBN都是等腰直角三角形,∴EC∥MN,∠DMA=∠NMB=45°,DM=√{2}AD=2√{2},MN=√{2}BM=√{2},∴∠CPN=∠DNM,∴tan∠CPN=tan∠DNM,∵∠DMN=180°-∠DMA-∠NMB=180°-45°-45°=90°,∴tan∠CPN=tan∠DNM=\\frac{DM}{MN}=\\frac{2√{2}}{√{2}}=2,故选:B．\\lbrack\\frac{D}{M}\\rbrack:\\frac{c}{\\omega}≥q\\rbrace", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["1", "2", "√{3}", "√{5}"], "choices": [1.0, 2.0, 1.732, 2.236], "label": 1}
+{"prob_id": 5576, "image_path": "images/5576.png", "question": "如图,在Rt△ABC中,∠C=90°,AB=10,AC=8,则sinB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,在Rt△ABC中,∠C=90°,AB=10,AC=8．所以sinB=\\frac{AC}{AB}=\\frac{8}{10}=\\frac{4}{5}．故选:A．", "dataset_name": "Geoqa", "ground_truth": "0.8", "org_choices": ["\\frac{4}{5}", "\\frac{3}{5}", "\\frac{3}{4}", "\\frac{4}{3}"], "choices": [0.8, 0.6, 0.75, 1.333], "label": 0}
+{"prob_id": 5596, "image_path": "images/5596.png", "question": "如图,四边形ABCD是⊙O的外切四边形,且AB=10,CD=12,则四边形ABCD的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是⊙O的外切四边形,∴AD+BC=AB+CD=22,∴四边形ABCD的周长=AD+BC+AB+CD=44,故选:A．", "dataset_name": "Geoqa", "ground_truth": "44.0", "org_choices": ["44", "42", "46", "47"], "choices": [44.0, 42.0, 46.0, 47.0], "label": 0}
+{"prob_id": 5609, "image_path": "images/5609.png", "question": "已知水平放置的圆柱形排水管道,管道截面半径是1m,若水面高0.2m．则排水管道截面的水面宽度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作OC⊥AB于C,交⊙O于D,连接OB,如图所示:则AB=2BC,∠OCB=90°,OB=OD=1m,CD=0.2m,∴OC=OD-CD=0.8m,∴BC=√{0B^{2}-0c^{2}}=√{1^{2}-0.8^{2}}=0.6(m),∴AB=2AC=1.2m,∴排水管道截面的水面宽度为1.2m,故选:C．", "dataset_name": "Geoqa", "ground_truth": "1.2", "org_choices": ["0.6m", "0.8m", "1.2m", "1.6m"], "choices": [0.6, 0.8, 1.2, 1.6], "label": 2}
+{"prob_id": 5621, "image_path": "images/5621.png", "question": "如图,A,B,C是⊙O上的三点,AB,AC的圆心O的两侧,若∠ABO=20°,∠ACO=30°,则∠BOC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过A作⊙O的直径,交⊙O于D．在△OAB中,OA=OB,则∠BOD=∠ABO+∠OAB=2×20°=40°,同理可得:∠COD=∠ACO+∠OAC=2×30°=60°,故∠BOC=∠BOD+∠COD=100°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["100°", "110°", "125°", "130°"], "choices": [100.0, 110.0, 125.0, 130.0], "label": 0}
+{"prob_id": 5668, "image_path": "images/5668.png", "question": "如图,在直角坐标系xOy中,点A在y轴正半轴上,点B、C在x正半轴上,且∠BAC=∠ACB=30°,AC=4,点D是x轴上的一个动点,点D关于直线AB、AC的对称点为E、F,则线段EF的最小值等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接AD,AE．AF．由题意,AD=AE=AF,∠DAB=∠BAE,∠DAC=∠CAF,∵∠BAC=∠ACB=30°,AC=4,∠AOC=90°,∴OA=≥ft.\\begin{array}{l}{x_{1}^{′}\\cdots\\cdots\\cdotsf^{r}}\\\\{\\frac{i}{o}:;}{√[3]{f}AC=2,∠OAC=60°,∠CAE+∠EAB=30°,∴∠EAF=∠CAE+∠CAF=∠CAE+∠CAE+∠DAE=2(∠CAE+∠BAE)=60°,∵AE=AF,∴△AEF是等边三角形,轨迹垂线段最短可知,当点D与O重合时,AD的值最小,∴AE的最小值=OA=2,∴EF的最小值为2,故选:A．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["2", "3", "4", "5"], "choices": [2.0, 3.0, 4.0, 5.0], "label": 0}
+{"prob_id": 5675, "image_path": "images/5675.png", "question": "如图,∠BAC=110°,若A,B关于直线MP对称,A,C关于直线NQ对称,则∠PAQ的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BAC=110°,∴∠B+∠C=70°,∵A,B关于直线MP对称,A,C关于直线NQ对称,又∵MP,NQ为AB,AC的垂直平分线,∴∠BAP=∠B,∠QAC=∠C,∴∠BAP+∠CAQ=70°,∴∠PAQ=∠BAC-∠BAP-∠CAQ=110°-70°=40°故选:C．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["70°", "55°", "40°", "30°"], "choices": [70.0, 55.0, 40.0, 30.0], "label": 2}
+{"prob_id": 5677, "image_path": "images/5677.png", "question": "如图,AB∥CD,BE垂直平分AD,DC=BC,若∠A=70°,则∠C=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BE垂直平分AD,∴AB=DB,∴∠ABE=∠DBE,又∵∠A=70°,∴∠ABE=20°,∴∠ABD=40°,又∵AB∥CD,∴∠CDB=∠ABD=40°,又∵DC=BC,∴∠C=180°-2×40°=100°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["100°", "110°", "115°", "120°"], "choices": [100.0, 110.0, 115.0, 120.0], "label": 0}
+{"prob_id": 5682, "image_path": "images/5682.png", "question": "如图,在△ABC中,AB=10cm,AC=18cm,点M从点A出发以每秒2cm的速度向点B运动,点N从点C出发以每秒3cm的速度向点A运动,其中一个动点到达端点,另一个动点也随之停止,当△AMN是以MN为底边的等腰三角形时,运动的时间是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设运动的时间为x,在△ABC中,AB=10cm,AC=18cm,点M从点A出发以每秒2cm的速度向点B运动,点N从点C出发以每秒3cm的速度向点A运动,当△AMN是等腰三角形时,AM=AN,AN=18-3x,AM=2x即18-3x=2x,解得x=3.6．故选:D．", "dataset_name": "Geoqa", "ground_truth": "3.6", "org_choices": ["1.6秒", "2秒", "2.4秒", "3.6秒"], "choices": [1.6, 2.0, 2.4, 3.6], "label": 3}
+{"prob_id": 5704, "image_path": "images/5704.png", "question": "如图,在△ABC中,∠ABC=110°,AM=AN,CN=CP,则∠MNP=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ABC=110°,∴∠A+∠C=180°-110°=70°．∵AM=AN,CN=CP,∴∠ANM=\\frac{180^{°}-∠A}{2},∠CNP=\\frac{180^{°}-∠C}{2},∴∠MNP=180°-\\frac{180^{°}-∠A}{2}-\\frac{180^{°}-∠C}{2}=180°-90°+\\frac{1}{2}∠A-90°+\\frac{1}{2}∠C=\\frac{1}{2}(∠A+∠C)=\\frac{1}{2}×70°=35°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["25°", "30^°^", "35°", "45°"], "choices": [25.0, 30.0, 35.0, 45.0], "label": 2}
+{"prob_id": 5713, "image_path": "images/5713.png", "question": "如图,已知▱ABCD的四个内角的平分线分别相交于点E、F、G、H,连接AC．若EF=2,FG=GC=5,则AC的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,作AP⊥CH交CH的延长线与P．∵四边形ABCD是平行四边形,▱ABCD的四个内角的平分线分别相交于点E、F、G、H,∴易证四边形EFGH是矩形,四边形AEHP是矩形,△ABE≌△CDG,可得PA=FG=5,AE=PH=CG=5,CP=CG+PH+GH=2+10=12,在Rt△APC中,AC=∠\\beta=∠ZZN=√{PA^{2}+PC^{2}}=13．故选:B．", "dataset_name": "Geoqa", "ground_truth": "13.0", "org_choices": ["12", "13", "6√{5}", "8√{3}"], "choices": [12.0, 13.0, 13.416, 13.856], "label": 1}
+{"prob_id": 5719, "image_path": "images/5719.png", "question": "如图,▱ABCD中,点E、F分别在AD、AB上,依次连接EB、EC、FC、FD,图中阴影部分的面积分别为S~1~、S~2~、S~3~、S~4~,已知S~1~=2、S~2~=12、S~3~=3,则S~4~的值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设平行四边形的面积为S,则S~△CBE~=S~△CDF~=\\frac{1}{2}S,由图形可知,△CDF面积+△CBE面积+(S~1~+S~4~+S~3~)-S~2~=平行四边形ABCD的面积∴S=S~△CBE~+S~△CDF~+2+S~4~+3-12,即S=\\frac{1}{2}S+\\frac{1}{2}S+2+S~4~+3-12,解得S~4~=7,故选:D．", "dataset_name": "Geoqa", "ground_truth": "7.0", "org_choices": ["4", "5", "6", "7"], "choices": [4.0, 5.0, 6.0, 7.0], "label": 3}
+{"prob_id": 5725, "image_path": "images/5725.png", "question": "如图,在▱ABCD中,对角线AC,BD相交于点O,点E,F分别是AB,AO的中点,连接EF,若EF=3,则BD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵点E,F分别是AB,AO的中点,连接EF,EF=3,∴EF是△OAB的中位线,则OB=2EF=6,∵在▱ABCD中,∴BD=2OB=12,故选:C．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["6", "9", "12", "15"], "choices": [6.0, 9.0, 12.0, 15.0], "label": 2}
+{"prob_id": 5728, "image_path": "images/5728.png", "question": "如图,▱ABCD的对角线AC,BD相交于O,EF经过点O,分别交AD,BC于E,F,已知▱ABCD的面积是20cm^2^,则图中阴影部分的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AD∥BC,OA=OC,∴∠OAE=∠OCF,∵∠AOE=∠COF,∴△AOE≌△COF,∴S~阴~=S~△BOC~=\\frac{1}{4}S~平行四边形ABCD~=5(cm^2^),故选:D．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["12cm^2^", "10cm^2^", "8cm^2^", "5cm^2^"], "choices": [12.0, 10.0, 8.0, 5.0], "label": 3}
+{"prob_id": 5729, "image_path": "images/5729.png", "question": "如图,在▱ABCD中,∠BCD的平分线交AD于点E,交BA的延长线于点F,BF=4AF,BC=12,则AF的长度是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD为平行四边形,∴AD∥BC,AB∥DC,AB=CD,AD=BC=12,∴∠DEC=∠ECB,∵CF平分∠BCD,∴∠ECD=∠ECB,∴∠DEC=∠ECD,∴DE=DC,∴AE=AD-DE=12-DE,∵BF∥CD,∴△AEF∽△DEC,∵BF=4AF,∴\\frac{AF}{CD}=\\frac{AE}{DE},即\\frac{1}{3}=\\frac{12-DE}{DE},则DE=9．∴DE=DC=AB=9,∴AF=3,故选:D．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["6", "5", "4", "3"], "choices": [6.0, 5.0, 4.0, 3.0], "label": 3}
+{"prob_id": 5739, "image_path": "images/5739.png", "question": "如图,在▱ABCD中,AB=10cm,AD=15cm,AC、BD相交于点O．OE⊥BD交AD于E,则△ABE的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在▱ABCD中,点O是BD中点,EO⊥BD,∴EO是线段BD的中垂线,∴BE=ED,∴△ABE的周长=AB+AE+BE=AB+AD=10+15=25(cm)．故选:C．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["20cm", "22cm", "25cm", "30cm"], "choices": [20.0, 22.0, 25.0, 30.0], "label": 2}
+{"prob_id": 5740, "image_path": "images/5740.png", "question": "如图,平行四边形ABCD中,E,F分别是AD,BC的中点,P是边DC上的动点,G,H分别是PE,PF的中点,已知DC=10cm,则GH的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接EF,∵四边形ABCD是平行四边形,∴AB=CD,AD=BD,AD∥BC,∵E,F分别是AD,BC的中点,∴AE=BF,∴四边形ABFE是平行四边形,∴AB=EF=10cm,∵G,H分别是PE,PF的中点,∴GH是△PEF的中位线,∴GH=\\frac{1}{2}EF=\\frac{1}{2}×10=5cm,故选:C．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["7cm", "6cm", "5cm", "4cm"], "choices": [7.0, 6.0, 5.0, 4.0], "label": 2}
+{"prob_id": 5761, "image_path": "images/5761.png", "question": "如图,在平行四边形ABCD中,对角线AC、BD相交于点O,点E是边CD的中点,连接OE．若平行四边形ABCD的周长为24,BD=8,则△DOE的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵平行四边形ABCD的周长为24,∴BC+CD=12．∵O是BD中点,E是CD中点,∴OE=\\frac{1}{2}BC,DE=\\frac{1}{2}CD,OD=\\frac{1}{2}BD=4∴△DOE周长=OE+DE+OD=6+4=10．故选:A．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["10", "12", "14", "16"], "choices": [10.0, 12.0, 14.0, 16.0], "label": 0}
+{"prob_id": 5763, "image_path": "images/5763.png", "question": "如图,在平行四边形ABCD中,点E是AB边上一点,连接DE、CE．若DE、CE分别是∠ADC、∠BCD的角平分线,且AB=4,则平行四边形ABCD的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE、CE分别是∠ADC、∠BCD的平分线,∴∠ADE=∠CDE,∠DCE=∠BCE,∵四边形ABCD是平行四边形,∴AB∥DC,AD=BC,CD=AB=4,∴∠CDE=∠DEA,∠DCE=∠CEB,∴∠ADE=∠AED,∠BCE=∠CEB,∴AD=AE,BE=BC,∴AD+BC=AE+BE=AB=4,∴平行四边形ABCD的周长=2(AB+AD)=3AB=12；故选:D．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["10", "8√{2}", "5√{5}", "12"], "choices": [10.0, 11.314, 11.18, 12.0], "label": 3}
+{"prob_id": 5768, "image_path": "images/5768.png", "question": "如图,过三角形内一点分别作三边的平行线,如果三角形的周长为6cm,则图中三个阴影三角形的周长和为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵EN∥BC,PM∥AB,DQ∥AC,∴四边形EFBP,FQCN,ADFM是平行四边形,∴DF=AM,FM=AD,EF=BP,PF=BE,FQ=NC,FN=CQ,∴三个阴影三角形的周长和为:DE+EF+FD+FM+FN+MN+FP+PQ+FQ=DE+BP+AM+AD+QC+MN+BE+PQ+NC=(AD+DE+BE)+(BP+PQ+CQ)+(NC+MN+AM)=AB+BC+AC=6(cm)．故选:A．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["6cm", "8cm", "9cm", "10cm"], "choices": [6.0, 8.0, 9.0, 10.0], "label": 0}
+{"prob_id": 5781, "image_path": "images/5781.png", "question": "如图,在△ABC中,过顶点A的直线DE∥BC,∠ABC、∠ACB的平分线分别交DE于点E、D,若AC=3,AB=4,则DE的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由分析得:∠EBC=∠ABE,∠ACD=∠DCB；根据平行线的性质得:∠DCB=∠CDE,∠EBC=∠BED；所以∠ADC=∠ACD,∠ABE=∠AEB,则AD=AC,AB=AE；所以DE=AD+AE=AB+AC=3+4=7；故选:B．", "dataset_name": "Geoqa", "ground_truth": "7.0", "org_choices": ["6", "7", "8", "9"], "choices": [6.0, 7.0, 8.0, 9.0], "label": 1}
+{"prob_id": 5783, "image_path": "images/5783.png", "question": "如图所示．△ABC中,∠B=∠C,D在BC上,∠BAD=50°,AE=AD,则∠EDC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,∠AED=∠EDC+∠C,∠ADC=∠B+∠BAD,∵AD=AE,∴∠AED=∠ADE,∵∠B=∠C,∴∠B+∠BAD=∠EDC+∠C+∠EDC,即∠BAD=2∠EDC,∵∠BAD=50°,∴∠EDC=25°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["15°", "25°", "30°", "50°"], "choices": [15.0, 25.0, 30.0, 50.0], "label": 1}
+{"prob_id": 5791, "image_path": "images/5791.png", "question": "如图,在四边形ABCD中,AD∥BC,BF平分∠ABC,交AD于点F,CE平分∠BCD,交AD于点E,AB=8,CD=6,EF=2,则AD长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BF平分∠ABC、CE平分∠BCD,∴∠ABF=∠CBF、∠DCE=∠BCE,∵AD∥BC,∴∠CBF=∠AFB、∠DEC=∠BCE,∴∠ABF=∠AFB、∠DCE=∠DEC,∴AB=AF=8、CD=DE=6,∵EF=2,∴AD=AF+DE-EF=8+6-2=12,故选:C．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["8", "10", "12", "14"], "choices": [8.0, 10.0, 12.0, 14.0], "label": 2}
+{"prob_id": 5797, "image_path": "images/5797.png", "question": "如图,在△ABC中,AB=10,AC=6,过点A的直线DE∥CB,∠ABC与∠ACB的平分线分别交DE于E,D,则DE的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴∠E=∠EBC．∵BE平分∠ABC,∴∠ABE=∠EBC,∴∠E=∠ABE,∴AB=AE=10．同理可得:AD=AC=6,∴DE=AD+AE=AB+AC=16．故选:B．", "dataset_name": "Geoqa", "ground_truth": "16.0", "org_choices": ["14", "16", "10", "12"], "choices": [14.0, 16.0, 10.0, 12.0], "label": 1}
+{"prob_id": 5806, "image_path": "images/5806.png", "question": "如图,已知等腰△ABC的一腰AB长为4厘米,过底边BC上任意一点D作两腰的平行线,分别交两腰于E、F,则四边形AEDF的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥AC,DF∥AB,∴∠EDB=∠C,∠FDC=∠B,∵AB=AC,∴∠B=∠C,∴∠EDB=∠B,∠FDC=∠C,∴DE=BE,DF=FC,∴四边形AEDF的周长是AE+ED+DF+AF=AE+BE+CF+AF=AB+AC=2AB=2×4=8厘米．故选:B．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["4厘米", "8厘米", "12厘米", "16厘米"], "choices": [4.0, 8.0, 12.0, 16.0], "label": 1}
+{"prob_id": 5827, "image_path": "images/5827.png", "question": "如图,在等边△ABC中,BD平分∠ABC交AC于点D,过点D作DE⊥BC于点E,且CE=1.5,则AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵△ABC是等边三角形,∴∠ABC=∠C=60°,AB=BC=AC,∵DE⊥BC,∴∠CDE=30°,∵EC=1.5,∴CD=2EC=3,∵BD平分∠ABC交AC于点D,∴AD=CD=3,∴AB=AC=AD+CD=6．故选:C．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["3", "4.5", "6", "7.5"], "choices": [3.0, 4.5, 6.0, 7.5], "label": 2}
+{"prob_id": 5854, "image_path": "images/5854.png", "question": "一艘轮船由海平面上A地出发向南偏西40°的方向行驶40海里到达B地,再由B地向北偏西20°的方向行驶40海里到达C地,则A、C两地相距(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意得∠ABC=60°,AB=BC,∴△ABC是等边三角形,∴AC=AB=40海里．故选:B．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["30海里", "40海里", "50海里", "60海里"], "choices": [30.0, 40.0, 50.0, 60.0], "label": 1}
+{"prob_id": 5861, "image_path": "images/5861.png", "question": "如图是\"人字形\"钢架,其中斜梁AB=AC,顶角∠BAC=120°,跨度BC=10m,AD为支柱(即底边BC的中线),两根支撑架DE⊥AB,DF⊥AC,则DE+DF等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB=AC,∠BAC=120°,∴∠B=∠C=30°,∵DE⊥AB,DF⊥AC,垂足为E,F,∴DE=\\frac{1}{2}BD,DF=\\frac{1}{2}DC,∴DE+DF=\\frac{1}{2}BD+\\frac{1}{2}DC=\\frac{1}{2}(BD+DC)\\frac{1}{2}BC．∴DE+DF=\\frac{1}{2}BC=\\frac{1}{2}×10=5m．故选:B．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["10m", "5m", "2.5m", "9.5m"], "choices": [10.0, 5.0, 2.5, 9.5], "label": 1}
+{"prob_id": 5868, "image_path": "images/5868.png", "question": "将△ABC沿CB向右平移得到△DEF,若四边形ABED的面积等于32,则平移距离等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设平移的距离为x,即AD=BE=x,∵∠C=90°,∠ABC=30°,∴AC=\\frac{1}{2}AB=8,由平移的性质可知,四边形ABED的平行四边形,则8x=32,解答,x=4,故选:A．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["4", "6", "8", "16"], "choices": [4.0, 6.0, 8.0, 16.0], "label": 0}
+{"prob_id": 5879, "image_path": "images/5879.png", "question": "如图,在△ABC中,∠ACB=90°,∠ABC=60°,BD平分∠ABC,P点是BD的中点,若BD=6,则CP的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ACB=90°,∠ABC=60°,∴∠A=30°,∵BD平分∠ABC,∴∠CBD=∠DBA=30°,∴BD=AD=6,∵P点是BD的中点,∴CP=\\frac{1}{2}BD=3,故选:A．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["3", "3.5", "4", "4.5"], "choices": [3.0, 3.5, 4.0, 4.5], "label": 0}
+{"prob_id": 5889, "image_path": "images/5889.png", "question": "如图,一辆货车车厢底板离地面的高度为\\frac{3}{2}米,为了方便下货,常用一块木板搭成一个斜面,要使斜面与水平地面的夹角不大于30°,则这块木板的长度至少为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图:AC为车厢底板离地面的高度\\frac{3}{2}米,AB是要求木板的长度,因为在直角三角形ABC中,∠B=30°,所以AB=2AC=2×\\frac{3}{2}=3(米)．故选:A．z=\\lambda^{2}-|➝{ZI}|^{-2}", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["3米", "2.5米", "2.6米", "0.87米"], "choices": [3.0, 2.5, 2.6, 0.87], "label": 0}
+{"prob_id": 5905, "image_path": "images/5905.png", "question": "如图,在Rt△ABC中,∠ACB=90°,AC=6,BC=8,AD是∠BAC的平分线．若P,Q分别是AD和AC上的动点,则PC+PQ的最小值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,过点C作CM⊥AB交AB于点M,交AD于点P,过点P作PQ⊥AC于点Q,∵AD是∠BAC的平分线．∴PQ=PM,这时PC+PQ有最小值,即CM的长度,∵AC=6,BC=8,∠ACB=90°,∴AB=√{AC^{2}+BC^{2}}=√{6^{2}+8^{2}}=10．∵S~△ABC~=\\frac{1}{2}AB•CM=\\frac{1}{2}AC•BC,∴CM=\\frac{AC\\cdotBC}{AB}=\\frac{6×8}{10}=\\frac{24}{5},即PC+PQ的最小值为\\frac{24}{5}．故选:C．", "dataset_name": "Geoqa", "ground_truth": "4.8", "org_choices": ["\\frac{12}{5}", "4", "\\frac{24}{5}", "5"], "choices": [2.4, 4.0, 4.8, 5.0], "label": 2}
+{"prob_id": 5914, "image_path": "images/5914.png", "question": "如图,在四边形ABCD中,∠BAD=130°,∠B=∠D=90°,点E,F分别是线段BC,DC上的动点．当△AEF的周长最小时,则∠EAF的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作A关于BC和CD的对称点A′,A″,连接A′A″,交BC于E,交CD于F,则A′A″即为△AEF的周长最小值．作DA延长线AH,∵∠DAB=130°,∴∠HAA′=50°,∴∠AA′E+∠A″=∠HAA′=50°,∵∠EA′A=∠EAA′,∠FAD=∠A″,∴∠EAA′+∠A″AF=50°,∴∠EAF=130°-50°=80°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["90°", "80°", "70°", "60°"], "choices": [90.0, 80.0, 70.0, 60.0], "label": 1}
+{"prob_id": 5919, "image_path": "images/5919.png", "question": "如图,△ABC的周长为16．点D是AB边的中点,BD=2,过点D作AB的垂线l,E是l上任意一点,则△AEC的周长最小值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵点D是AB边的中点,BD=2,∴AB=2BD=4,∵△ABC的周长为16,∴AC+BC=12,如图,连接BE,∵点D是AB边的中点,l⊥AB,∴l是AB的垂直平分线,∴AE=BE,∴AE+CE=BE+CE,∵BE+CE≥BC,∴当B,E,C在同一直线上时,BE+CE的最小值等于BC的长,而AC长不变,∴△AEC的周长最小值等于AC+BC=12,故选:A．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["12", "14", "16", "18"], "choices": [12.0, 14.0, 16.0, 18.0], "label": 0}
+{"prob_id": 5927, "image_path": "images/5927.png", "question": "如图,OA、OB分别是线段MC、MD的垂直平分线,MD=5cm,MC=7cm,CD=10cm,一只小蚂蚁从点M出发爬到OA边上任意一点E,再爬到OB边上任意一点F,然后爬回M点处,则小蚂蚁爬行的路径最短可为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设CD与OA的交点为E,与OB的交点于F,∵OA、OB分别是线段MC、MD的垂直平分线,∴ME=CE,MF=DF,∴小蚂蚁爬行的路径最短=CD=10cm,故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["12cm", "10cm", "7cm", "5cm"], "choices": [12.0, 10.0, 7.0, 5.0], "label": 1}
+{"prob_id": 5942, "image_path": "images/5942.png", "question": "如图,在△ABC中,BF平分∠ABC,过A点作AF⊥BF,垂足为F并延长交BC于点G,D为AB中点,连接DF延长交AC于点E．若AB=12,BC=20,则线段EF的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在△BFA和△BFG中,≥ft\\lbrace\\begin{array}{l}{∠ABF=∠GBF}\\\\{BF=BF}\\\\{∠BFA=∠BFG}\\end{array}\\right.,∴△BFA≌△BFG(ASA)∴BG=AB=12,AF=FG,∴GC=BC-BG=8,∵AF=FG,AE=EC,∴EF=\\frac{1}{2}GC=4,故选:C．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["2", "3", "4", "5"], "choices": [2.0, 3.0, 4.0, 5.0], "label": 2}
+{"prob_id": 5946, "image_path": "images/5946.png", "question": "如图,在△ABC中,点D、E分别是AB、AC的中点,若DE=1.5,则BC的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵点D、E分别是AB、AC的中点,∴BC=2DE=3,故选:A．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["3", "4", "2", "1"], "choices": [3.0, 4.0, 2.0, 1.0], "label": 0}
+{"prob_id": 5958, "image_path": "images/5958.png", "question": "如图,在△ABC中,BD、CE是角平分线,AM⊥BD于点M,AN⊥CE于点N．△ABC的周长为30,BC=12．则MN的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "证明:∵△ABC的周长为30,BC=12．∴AB+AC=30-BC=18．延长AN、AM分别交BC于点F、G．如图所示:∵BN为∠ABC的角平分线,∴∠CBN=∠ABN,∵BN⊥AG,∴∠ABN+∠BAN=90°,∠G+∠CBN=90°,∴∠BAN=∠AGB,∴AB=BG,∴AN=GN,同理AC=CF,AM=MF,∴MN为△AFG的中位线,GF=BG+CF-BC,∴MN=\\frac{1}{2}(AB+AC-BC)=\\frac{1}{2}(18-12)=3．故选:D．z\\in\\hat{x}(\\lambda)", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["15", "9", "6", "3"], "choices": [15.0, 9.0, 6.0, 3.0], "label": 3}
+{"prob_id": 5965, "image_path": "images/5965.png", "question": "如图,△ABC中,D,E分别是BC,AC的中点,BF平分∠ABC,交DE于点F,若BC=6,则DF的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵D,E分别是BC,AC的中点,∴DE∥AB,∴∠BFD=∠ABF,∵BF平分∠ABC,∴∠DBF=∠ABF,∴∠BFD=∠DBF,∴DF=DB=\\frac{1}{2}BC=3,故选:A．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["3", "4", "5", "6"], "choices": [3.0, 4.0, 5.0, 6.0], "label": 0}
+{"prob_id": 5984, "image_path": "images/5984.png", "question": "同学们都玩过跷跷板的游戏,如图是一个跷跷板的示意图,立柱OC与地面垂直,OA=OB．当跷跷板的一头A着地时,∠AOA′=50°,则当跷跷板的另一头B着地时,∠COB′等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA=OB=\\frac{1}{2}AB,∴OA′=OB′=\\frac{1}{2}A′B′,∵AB=A′B′,∴OA=OB′,∵∠AOA′=50°,∴∠AOB′=180°-50°=130°,∵OC⊥AB′,∴∠COB′=\\frac{1}{2}∠AOB′=65°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["25°", "50°", "65°", "130°"], "choices": [25.0, 50.0, 65.0, 130.0], "label": 2}
+{"prob_id": 5985, "image_path": "images/5985.png", "question": "如图,在△ABC中,AB=AC,∠A=40°,DE垂直平分AC,则∠BCD的度数等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB=AC,∠A=40°,∴∠ABC=∠ACB=70°．∵DE垂直平分AC,∴AD=CD,∴∠A=∠ACD=40°∴∠BCD=∠ACB-∠ACD=30°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["20°", "30°", "40°", "50°"], "choices": [20.0, 30.0, 40.0, 50.0], "label": 1}
+{"prob_id": 6528, "image_path": "images/6528.png", "question": "如图,PA、PB是半径为1的⊙O的两条切线,点A、B分别为切点,∠APB=60°,OP与弦AB交于点C,与⊙O交于点D．则图中阴影部分的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA、PB是半径为1的⊙O的两条切线,∴OA⊥PA,OB⊥PB,OP平分∠APB,而∠APB=60°,∴∠APO=30°,∠POA=90°-30°=60°,又∵OP垂直平分AB,∴△AOC≌△BOC,∴S~△AOC~=S~△BOC~,∴S~阴影部分~=S~扇形OAD~=\\frac{60π×1^{2}}{360}=\\frac{π}{6}．故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.5235987755982989", "org_choices": ["\\frac{1}{3}π", "\\frac{1}{3}π-\\frac{√{3}}{4}", "\\frac{1}{6}π", "\\frac{1}{6}π-\\frac{√{3}}{4}"], "choices": [1.047, 0.614, 0.524, 0.091], "label": 2}
+{"prob_id": 6563, "image_path": "images/6563.png", "question": "如图,在△ABC中,∠A=90°,AB=AC=3,现将△ABC绕点B逆时针旋转一定角度,点C′恰落在边BC上的高所在的直线上,则边BC在旋转过程中所扫过的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作高AD,则C′点在AD的反向延长线上,如图,∵∠A=90°,AB=AC=3,∴△ABC为等腰直角三角形,∴BC=√{2}AB=3√{2},BD=CD,∵△ABC绕点B逆时针旋转一定角度,点C′恰落在边BC上的高所在的直线上,∴BC′=BC=3√{2},∴BD=\\frac{1}{2}BC′,∴∠BC′D=30°,∴∠DBC′=60°,∴边BC在旋转过程中所扫过的面积=\\frac{60\\cdotπ\\cdot(3√{2})^{2}}{360}=3π．故选:C．", "dataset_name": "Geoqa", "ground_truth": "9.42477796076938", "org_choices": ["π", "2π", "3π", "4π"], "choices": [3.142, 6.283, 9.425, 12.566], "label": 2}
+{"prob_id": 6711, "image_path": "images/6711.png", "question": "如图,圆心角都是90°的扇形OAB与扇形OCD叠放在一起,OA=3,OC=1,分别连接AC、BD,则图中阴影部分的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由图可知,将△OAC顺时针旋转90°后可与△ODB重合,∴S~△OAC~=S~△OBD~；因此S_{阴影}=S~扇形OAB~+S~△OBD~-S~△OAC~-S~扇形OCD~=S~扇形OAB~-S~扇形OCD~=\\frac{1}{4}π×(9-1)=2π．故选:C．", "dataset_name": "Geoqa", "ground_truth": "6.283185307179586", "org_choices": ["\\frac{1}{2}π", "π", "2π", "4π"], "choices": [1.571, 3.142, 6.283, 12.566], "label": 2}
+{"prob_id": 6717, "image_path": "images/6717.png", "question": "如图,为了绿化环境,在矩形空地的四个角划出四个半径为1的扇形空地进行绿化,则绿化的总面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:利用扇形面积可得,一个小扇形的面积=\\frac{90π×1}{360}=\\frac{π}{4},则四个图形的面积就是π,故选B．", "dataset_name": "Geoqa", "ground_truth": "3.141592653589793", "org_choices": ["\\frac{π}{2}", "π", "2π", "\\frac{π}{4}"], "choices": [1.571, 3.142, 6.283, 0.785], "label": 1}
+{"prob_id": 6770, "image_path": "images/6770.png", "question": "某楼梯的侧面如图所示,已测得AB的长为3米,楼梯斜坡BC的坡度比是1:2,则该楼梯的斜坡BC长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB的长为3米,楼梯斜坡BC的坡度比是1:2,∴$\\frac{AB}{AC}=\\frac{1}{2}$,∴AC=2AB=6米,∴BC$=√{AB^{2}+BC^{2}}=√{3^{2}+6^{2}}=$3$√{5}$(米)．故选:D．", "dataset_name": "Geoqa", "ground_truth": "6.708203932499369", "org_choices": ["3米", "6米", "3√{3}米", "3√{5}米"], "choices": [3.0, 6.0, 5.196, 6.708], "label": 3}
+{"prob_id": 6818, "image_path": "images/6818.png", "question": "某时刻海上点P处有一客轮,测得灯塔A位于P的北偏东30°方向,且相距50海里．客轮以60海里/小时的速度沿北偏西60°方向航行$\\frac{2}{3}$小时到达B处,那么tan∠BAP=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵灯塔A位于客轮P的北偏东30°方向,且相距50海里．∴AP=50,∵客轮以60海里/小时的速度沿北偏西60°方向航行$\\frac{2}{3}$小时到达B处,∴∠APB=90°,BP=60$×\\frac{2}{3}=$40,∴tan∠BAP$=\\frac{BP}{AP}=\\frac{40}{50}=\\frac{4}{5}$；故选:A．", "dataset_name": "Geoqa", "ground_truth": "0.8", "org_choices": ["\\frac{4}{5}", "\\frac{6}{5}", "\\frac{√{5}}{5}", "\\frac{2√{5}}{5}"], "choices": [0.8, 1.2, 0.447, 0.894], "label": 0}
+{"prob_id": 6833, "image_path": "images/6833.png", "question": "如图,已知灯塔M方圆一定范围内有镭射辅助信号,一艘轮船在海上从南向北方向以一定的速度匀速航行,轮船在A处测得灯塔M在北偏东30°方向,行驶1小时后到达B处,此时刚好进入灯塔M的镭射信号区,测得灯塔M在北偏东45°方向,则轮船通过灯塔M的镭射信号区的时间为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接MC,过M点作MD⊥AC于D．在Rt△ADM中,∵∠MAD=30°,∴AD$=√{3}$MD,在Rt△BDM中,∵∠MBD=45°,∴BD=MD,∴BC=2MD,∴BC:AB=2MD:($√{3}-$1)MD=2:$√{3}+$1．故轮船通过灯塔M的镭射信号区的时间为($√{3}+$1)小时．故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.732050807568877", "org_choices": ["(√{3}-1)小时", "(√{3}+1)小时", "2小时", "√{3}小时"], "choices": [0.732, 2.732, 2.0, 1.732], "label": 1}
+{"prob_id": 6834, "image_path": "images/6834.png", "question": "如图,上午8时,一艘船从A处出发,以15海里/时的速度向正北方向航行,9时40分到达B处,从A处测得灯塔C在北偏西26°方向,从B处测得灯塔C在北偏西52°方向,则B处到灯塔C的距离是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:据题意得,∠A=26°,∠DBC=52°,∵∠DBC=∠A+∠C,∴∠A=∠C=26°,∴AB=BC,∵AB=15×\\frac{5}{3}=25,∴BC=25(海里)．故选:B．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["36海里", "25海里", "20海里", "21海里"], "choices": [36.0, 25.0, 20.0, 21.0], "label": 1}
+{"prob_id": 6835, "image_path": "images/6835.png", "question": "上午9时,一船从A处出发,以每小时40海里的速度向正东方向航行,9时30分到达B处,如图所示,从A,B两处分别测得小岛M在北偏东45°和北偏东15°方向,那么B处与小岛M的距离为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由已知得,AB=40$×\\frac{1}{2}=$20海里,∠ABM=105°．过点B作BN⊥AM于点N．在直角△ABN中,BN=AB•sin45°=10$√{2}$；在直角△BNM中,∠MBN=60°,则∠M=30°,∴BM=2BN=20$√{2}$(海里)．故选:B．", "dataset_name": "Geoqa", "ground_truth": "28.284271247461902", "org_choices": ["20海里", "20√{2}海里", "15海里", "20海里"], "choices": [20.0, 28.284, 15.0, 20.0], "label": 1}
+{"prob_id": 6839, "image_path": "images/6839.png", "question": "为了测量两岸平行的河宽AB,测得∠ACB=30°,∠ADB=60°,CD=60m,则河宽AB为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ACB=30°,∠ADB=60°,∴∠CAD=30°,∴AD=CD=60m,在Rt△ABD中,AB=AD•sin∠ADB=60$×\\frac{√{3}}{2}=$30$√{3}$(m)．故选:B．", "dataset_name": "Geoqa", "ground_truth": "51.96152422706632", "org_choices": ["30m", "30√{3}m", "(30√{3}+30)m", "(30√{3}-30)m"], "choices": [30.0, 51.962, 81.962, 21.962], "label": 1}
+{"prob_id": 6852, "image_path": "images/6852.png", "question": "如图,已知一渔船上的渔民在A处看见灯塔M在北偏东60°方向,这艘渔船以28海里/时的速度向正东方向航行,半小时后到达B处,在B处看见灯塔M在北偏东15°方向,此时灯塔M与渔船的距离是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由已知得,AB=\\frac{1}{2}×28=14海里,∠A=30°,∠ABM=105°．过点B作BN⊥AM于点N．∵在直角△ABN中,∠BAN=30°∴BN=\\frac{1}{2}AB=7海里．在直角△BNM中,∠MBN=45°,则直角△BNM是等腰直角三角形．即BN=MN=7海里,∴BM=√{BN^{2}+MN^{2}}=√{7^{2}+7^{2}}=7√{2}海里．故选:A．", "dataset_name": "Geoqa", "ground_truth": "9.899494936611665", "org_choices": ["7√{2}海里", "14√{2}海里", "7海里", "14海里"], "choices": [9.899, 19.799, 7.0, 14.0], "label": 0}
+{"prob_id": 7508, "image_path": "images/7508.png", "question": "如图,已知\\frac{OA}{DO}=\\frac{BO}{CO}=\\frac{1}{2},△AOB的面积是100cm²,则△DOC的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵\\frac{OA}{DO}=\\frac{BO}{CO}=\\frac{1}{2},∠AOB=∠COD,∴△AOB∽△COD,∴\\frac{S_{\\bigtriangleupAOB}}{S_{\\bigtriangleupCOD}}=(\\frac{OA}{DO})²,∴S~△DOC~=400故选:C．", "dataset_name": "Geoqa", "ground_truth": "400.0", "org_choices": ["200cm²", "300cm²", "400cm²", "500cm²"], "choices": [200.0, 300.0, 400.0, 500.0], "label": 2}
+{"prob_id": 7522, "image_path": "images/7522.png", "question": "如图所示,△ABC中,∠BAC=90°,AD⊥BC于D,若AB=3,BC=5,则DC的长度(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠B=∠B,∠ADB=∠CAB=90°,∴△ABD∽△ABC,∴AB²=BD•BC,∴BD=\\frac{9}{5}∴DC=BC-BD=5-\\frac{9}{5}=\\frac{16}{5}故选:A．", "dataset_name": "Geoqa", "ground_truth": "3.2", "org_choices": ["\\frac{16}{5}", "\\frac{4}{5}", "\\frac{8}{5}", "\\frac{22}{5}"], "choices": [3.2, 0.8, 1.6, 4.4], "label": 0}
+{"prob_id": 7544, "image_path": "images/7544.png", "question": "如图,在平行四边形ABCD中,AE:EB=1:2,S~△AEF~=3,则S~△FCD~为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,AE:EB=1:2,∴AE:CD=1:3,∵AB∥CD,∴∠EAF=∠DCF,∵∠DFC=∠AFE,∴△AEF∽△CDF,∵S~△AEF~=3,∴\\frac{S_{\\bigtriangleupAEF}}{S_{\\bigtriangleupFCD}}=\\frac{3}{S_{\\bigtriangleupFCD}}=(\\frac{1}{3})²,解得S~△FCD~=27．故选:B．", "dataset_name": "Geoqa", "ground_truth": "27.0", "org_choices": ["3", "27", "6", "12"], "choices": [3.0, 27.0, 6.0, 12.0], "label": 1}
+{"prob_id": 7573, "image_path": "images/7573.png", "question": "如图,在平行四边形ABCD中,AE=EB,AF=2,则FC的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AB=CD,AB∥CD,∴∠CDE=∠AED,∠DCA=∠CAB,∴△AEF∽△CDF,∴AF:CF=AE:CD,∵AE=EB,∴AE=\\frac{1}{2}AB,∴AE=\\frac{1}{2}CD,即AE:CD=1:2,∵AF=2,∴CF=4,故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["5", "4", "3", "2"], "choices": [5.0, 4.0, 3.0, 2.0], "label": 1}
+{"prob_id": 7578, "image_path": "images/7578.png", "question": "如图,在Rt△ABC中,∠BAC=90°,AD⊥BC于D,DE⊥AB于E,AD=3,DE=2,则CD的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AD⊥BC,DE⊥AB,∴∠ADC=∠AED=90°,∵∠BAC=90°,∴∠DAE=∠C,∴Rt△ACD∽Rt△DAE,∴\\frac{AD}{AC}=\\frac{DE}{AD},∵AD=3,DE=2,∴\\frac{3}{AC}=\\frac{2}{3},∴AC=\\frac{9}{2},在Rt△ACD中,CD²+AD²=AC²,∴CD=√{(\\frac{9}{2})²-3²}=\\frac{3√{5}}{2},故选:D．", "dataset_name": "Geoqa", "ground_truth": "3.3541019662496847", "org_choices": ["\\frac{21}{2}", "\\frac{√{15}}{2}", "\\frac{9}{2}", "\\frac{3√{5}}{2}"], "choices": [10.5, 1.936, 4.5, 3.354], "label": 3}
+{"prob_id": 7600, "image_path": "images/7600.png", "question": "如图,已知点D是AB边的中点,AF∥BC,CG:GA=3:1,BC=8,则AF等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AF∥BC,∴△AFD∽△BED,∴AF:BE=AD:BD,∵D为AB中点,∴AF:BE=1,即AF=BE,∵AF∥BC,∴△AFG∽△CEG,∴CE:AF=CG:GA=3:1,∴CE=3AF,∴BC=2AF=8,∴AF=4,故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["2", "4", "16", "8"], "choices": [2.0, 4.0, 16.0, 8.0], "label": 1}
+{"prob_id": 7603, "image_path": "images/7603.png", "question": "如图,已知⊙O的半径为6,M是⊙O外一点,且OM=12,过M的直线与⊙O交于A、B,点A、B关于OM的对称点分别为C、D,AD与BC交于点P,则OP的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图所示,连接AC,与MO交于点N,连接OA,OC,根据对称性可知:MN⊥AC且AN=CN,∴点P在MN上；则AP=CP,∴∠APN=∠CPN,∴∠BPM=∠APO,根据垂径定理知:∠AON=∠CON=\\frac{1}{2}∠AOC,又∠ABC=\\frac{1}{2}∠AOC(同弧圆周角是圆心角的一半),∴∠AON=∠ABC,∵∠AON=180°-(∠OAM+∠AMO),∠ABC=180°-(∠BPM+∠AMO),∴∠OAM=∠BPM,∴∠OAM=∠APO．又∠AOP=∠MOA,∵△AOP∽△MOA,∴\\frac{OP}{OA}=\\frac{OA}{OM}；即\\frac{OP}{6}=\\frac{6}{12},解得:OP=3．故选:C．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["4", "3.5", "3", "2.5"], "choices": [4.0, 3.5, 3.0, 2.5], "label": 2}
+{"prob_id": 7612, "image_path": "images/7612.png", "question": "如图,在▱ABCD中,E为CD的中点,AE交BD于点O,S~△DCE~=12,则S~△AOD~等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在▱ABCD中,E为CD中点,∴DE∥AB,DE=\\frac{1}{2}AB,在△DOE与△BOA中,∠DOE=∠BOA,∠OBA=∠ODE,∴△DOE∽△BOA,∴\\frac{EO}{AO}=\\frac{DE}{BA}=\\frac{1}{2},∴S~△AOD~=2S~△DOE~=2×12=24．故选:A．", "dataset_name": "Geoqa", "ground_truth": "24.0", "org_choices": ["24", "36", "48", "60"], "choices": [24.0, 36.0, 48.0, 60.0], "label": 0}
+{"prob_id": 7618, "image_path": "images/7618.png", "question": "如图,在△ABC中,∠ACB=90°,D是AB上一点,连接CD,∠ACD=∠B,若BC=13cm,CD=5cm,则BD=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠A=∠A,∠ACD=∠B,∴△ADC∽△ACB；∴∠BDC=∠ACB=90°,∴BD=√{BC²-CD²}=√{13²-5²}=12,故选:D．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["8cm", "9cm", "10cm", "12cm"], "choices": [8.0, 9.0, 10.0, 12.0], "label": 3}
+{"prob_id": 7761, "image_path": "images/7761.png", "question": "如图,已知D、E分别是△ABC中AB、AC边上的点,DE∥BC且\\frac{AD}{AB}=\\frac{1}{3},△ADE的周长2,则△ABC的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴△ADE∽△ABC,∴\\frac{AD+DE+AE}{AB+BC+AC}=\\frac{AD}{AB}=\\frac{1}{3}∵AD+DE+AE=2,∴AB+BC+AC=6．故选:B．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["4", "6", "8", "18"], "choices": [4.0, 6.0, 8.0, 18.0], "label": 1}
+{"prob_id": 7770, "image_path": "images/7770.png", "question": "如图所示,在△ABC中D为AC边上一点,若∠DBC=∠A,BC=3,AC=6,则CD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠DBC=∠A,∠C=∠C,∴△BCD∽△ACB,∴\\frac{CD}{BC}=\\frac{BC}{AC},∴\\frac{CD}{3}=\\frac{3}{6}∴CD=\\frac{3}{2},故选:C．", "dataset_name": "Geoqa", "ground_truth": "1.5", "org_choices": ["1", "2", "\\frac{3}{2}", "\\frac{5}{2}"], "choices": [1.0, 2.0, 1.5, 2.5], "label": 2}
+{"prob_id": 7802, "image_path": "images/7802.png", "question": "如图,DE∥BC,BD,CE相交于O,\\frac{EO}{OC}=\\frac{1}{3},AE=3,则EB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴△EOD∽△COB,△AED∽△ABC,∴\\frac{DE}{BC}=\\frac{EO}{OC}=\\frac{1}{3},\\frac{DE}{BC}=\\frac{AE}{AB},又∵AE=3,∴BE=6．故选:A．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["6", "9", "12", "15"], "choices": [6.0, 9.0, 12.0, 15.0], "label": 0}
+{"prob_id": 7806, "image_path": "images/7806.png", "question": "如图,一束光线从点A(-3,3)出发,经过y轴上的点C反射后经过点B(-1,0),则光线从点A到点B经过的路线长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图所示,延长AC交x轴于B′．则点B、B′关于y轴对称,CB=CB′．作AD⊥x轴于D点．则AD=3,DB′=3+1=4．∴AB′=AC+CB′=AC+CB=√{3²+4²}=5．即光线从点A到点B经过的路径长为5．故选:C．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["3", "\\frac{7}{2}", "5", "6"], "choices": [3.0, 3.5, 5.0, 6.0], "label": 2}
+{"prob_id": 7807, "image_path": "images/7807.png", "question": "如图,在△ABC中,若DE∥BC,\\frac{AD}{AB}=\\frac{1}{3},DE=4cm,则BC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴△ADE∽△ABC,∴\\frac{AD}{AB}=\\frac{DE}{BC},∴\\frac{4}{BC}=\\frac{1}{3},∴BC=12．故选:C．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["8cm", "10cm", "12cm", "11cm"], "choices": [8.0, 10.0, 12.0, 11.0], "label": 2}
+{"prob_id": 7828, "image_path": "images/7828.png", "question": "如图,已知D、E、F分别为等腰△ABC边BC、CA、AB上的点,如果AB=AC,∠FDE=∠B,BD=2,CD=3,CE=4,AE=1,那么AF的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB=AC,∴∠B=∠C；又∵∠FDE=∠B,∴∠BFD+∠BDF=∠BDF+∠CDE,∴∠BFD=∠CDE,而∠B=∠C,∴△BDF∽△CED,∴BD:CE=BF:DC,而BD=2,CD=3,CE=4,∴BF=1.5,∵AB=AC=1+4=5,∴AF=5-1.5=3.5．故选:A．", "dataset_name": "Geoqa", "ground_truth": "3.5", "org_choices": ["3.5", "4", "4.5", "5"], "choices": [3.5, 4.0, 4.5, 5.0], "label": 0}
+{"prob_id": 7842, "image_path": "images/7842.png", "question": "如图,一小型水库堤坝的横断面为直角梯形,坝顶BC宽6m,坝高14m,斜坡CD的坡度i=1:2,则坝底AD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过点C作CE⊥AD于点E,∵BC=6m,坝高为14m,∴AE=6m,CE=14m,∵斜坡CD的坡度i=1:2,∴CE:DE=1:2,∴DE=28m,则AD=AE+DE=6+28=34(m)．故选:B．", "dataset_name": "Geoqa", "ground_truth": "34.0", "org_choices": ["13m", "34m", "(6+14√{3})m", "40m"], "choices": [13.0, 34.0, 30.249, 40.0], "label": 1}
+{"prob_id": 7884, "image_path": "images/7884.png", "question": "如图,传送带和地面所成斜坡的坡度为1:2,它把物体从地面点A处送到离地面2米高的B处,则物体从A到B所经过的路程为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图:由已知得:BC=8,\\frac{BC}{AC}=\\frac{1}{2},∴AC=4,BC=2,∴AB=√{AC²+BC²}=2√{5},故选B．", "dataset_name": "Geoqa", "ground_truth": "4.47213595499958", "org_choices": ["4", "2√{5}", "√{5}", "2√{3}"], "choices": [4.0, 4.472, 2.236, 3.464], "label": 1}
+{"prob_id": 7898, "image_path": "images/7898.png", "question": "如图,△ABC中,AB=AC=18,BC=12,正方形DEFG的顶点E,F在△ABC内,顶点D,G分别在AB,AC上,AD=AG,DG=6,则点F到BC的距离为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过点A作AM⊥BC于点M,交DG于点N,延长GF交BC于点H,∵AB=AC,AD=AG,∴AD:AB=AG:AC,∵∠BAC=∠DAG,∴△ADG∽△ABC,∴∠ADG=∠B,∴DG∥BC,∵四边形DEFG是正方形,∴FG⊥DG,∴FH⊥BC,AN⊥DG,∵AB=AC=18,BC=12,∴BM=\\frac{1}{2}BC=6,∴AM=√{AB²-BM²}=12√{2},∴\\frac{AN}{AM}=\\frac{DG}{BC},∴\\frac{AN}{12√{2}}=\\frac{6}{12},∴AN=6√{2},∴MN=AM-AN=6√{2},∴FH=MN-GF=6√{2}-6．故选:D．", "dataset_name": "Geoqa", "ground_truth": "2.4852813742385704", "org_choices": ["1", "2", "12√{2}-6", "6√{2}-6"], "choices": [1.0, 2.0, 10.971, 2.485], "label": 3}
+{"prob_id": 7914, "image_path": "images/7914.png", "question": "如图,在边长为9的正方形ABCD中,F为AB上一点,连接CF．过点F作FE⊥CF,交AD于点E,若AF=3,则AE等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是正方形,∴AD=AB=BC=9,∠A=∠B=90°,∵FE⊥CF,∴∠EFC=90°,∴∠AEF+∠EFA=90°,∠AFE+∠CFB=90°,∴∠AEF=∠CFB,∴△AEF∽△BFC,∴\\frac{AE}{BF}=\\frac{AF}{BC},∴\\frac{AE}{9-3}=\\frac{3}{9},∴AE=2,故选:C．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["1", "1.5", "2", "2.5"], "choices": [1.0, 1.5, 2.0, 2.5], "label": 2}
+{"prob_id": 7924, "image_path": "images/7924.png", "question": "如图,在Rt△ABC中,∠BAC=90°,AB=2,AC=3,D为BC的中点,动点E,F分别在AB,AC上,分别过点EG∥AD∥FH,交BC于点G、H,若EF∥BC,则EF+EG+FH的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BAC=90°,AB=2,AC=3,∴BC=√{AB²+AC²}=√{13},∵∠BAC=90°,D为BC的中点,∴DA=DB=DC,∴∠B=∠DAB,∠C=∠DAC,∵EF∥BC,EG∥AD∥FH,∴∠BEG=∠DAB,∠CFH=∠DAC,EF=GH,∴∠B=∠BEG,∠C=∠CFH,∴BG=EG,FH=HC,∴EF+EG+FH=GH+BG+HC=BC=√{13}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "3.605551275463989", "org_choices": ["√{10}", "√{13}", "2√{10}", "2√{13}"], "choices": [3.162, 3.606, 6.325, 7.211], "label": 1}
+{"prob_id": 7926, "image_path": "images/7926.png", "question": "如图,在△ABC中,D、E分别是AB、AC上的点,且DE∥BC,若AD=5,DB=3,DE=4,则BC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴△ADE∽△ABC,∴\\frac{AD}{AB}=\\frac{DE}{BC},∵AD=5,DB=3,DE=4,∴AB=AD+DB=8,∴BC=\\frac{AB\\cdotDE}{AD}=\\frac{32}{5}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "6.4", "org_choices": ["\\frac{12}{5}", "\\frac{15}{4}", "\\frac{20}{3}", "\\frac{32}{5}"], "choices": [2.4, 3.75, 6.667, 6.4], "label": 3}
+{"prob_id": 7939, "image_path": "images/7939.png", "question": "如图,平行四边形ABCD中,E为DC的中点,△DEF的面积为2,则△ABF的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AB∥CD,AB=CD,∴△DEF∽△BAF,∴\\frac{S_{\\bigtriangleupDEF}}{S_{\\bigtriangleupBAF}}={(\\frac{DE}{AB})}²,∵E为DC的中点,∴DE=\\frac{1}{2}CD,∴DE:AB=1:2,∴\\frac{S_{\\bigtriangleupDEF}}{S_{\\bigtriangleupBAF}}={(\\frac{1}{2})}²,∵△DEF的面积为2,∴△ABF的面积为8．故选:D．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["2", "4", "6", "8"], "choices": [2.0, 4.0, 6.0, 8.0], "label": 3}
+{"prob_id": 7941, "image_path": "images/7941.png", "question": "如图,AB∥CD,\\frac{AO}{OD}=\\frac{2}{3},则△AOB的周长与△DOC的周长比是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB∥CD,∴∠A=∠D,∠B=∠C,∴△AOB∽△DOC,∴\\frac{C_{\\bigtriangleupAOB}}{C_{\\bigtriangleupDOC}}=\\frac{AO}{OD}=\\frac{2}{3},故选:D．", "dataset_name": "Geoqa", "ground_truth": "0.6666666666666666", "org_choices": ["\\frac{2}{5}", "\\frac{3}{2}", "\\frac{4}{9}", "\\frac{2}{3}"], "choices": [0.4, 1.5, 0.444, 0.667], "label": 3}
+{"prob_id": 7959, "image_path": "images/7959.png", "question": "如图,AB∥CD,AC、BD交于O,BO=6,DO=3,AC=12,则AO长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB∥CD,∴∠C=∠A,∠B=∠D,∴△DOC∽△BOA,∴\\frac{DO}{BO}=\\frac{OC}{AO},∴\\frac{3}{6}=\\frac{12-OA}{AO},∴AO=8．故选:C．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["4", "6", "8", "10"], "choices": [4.0, 6.0, 8.0, 10.0], "label": 2}
+{"prob_id": 7999, "image_path": "images/7999.png", "question": "如图,△ABC中,E、F分别是AB,AC的中点,若△AEF的面积为1,则四边形EBCF的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵E、F分别是AB,AC的中点,∴EF∥BC,∴△AEF∽△ABC,∴\\frac{S_{\\bigtriangleupAEF}}{S_{\\bigtriangleupABC}}={(\\frac{EF}{BC})}²={(\\frac{1}{2})}²=\\frac{1}{4},∵△AEF的面积为1,∴△ABC的面积是4,∴四边形EBCF的面积是4-1=3,故选:C．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["1", "2", "3", "4"], "choices": [1.0, 2.0, 3.0, 4.0], "label": 2}
+{"prob_id": 8019, "image_path": "images/8019.png", "question": "如图,梯形ABCD中,AD∥BC,对角线AC、BD相交于O点,若S~△AOD~:S~△OCD~=1:2,则S~△AOD~:S~△BOC~=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设点D到AC边的距离为h,则S~△AOD~:S~△OCD~=(\\frac{1}{2}×OA×h):(\\frac{1}{2}×OC×h)=OA:OC=1:2．∵AD∥BC,∴∠DAO=∠BCO,∠ADO=∠CBO,∴△AOD∽△COB,∴S~△AOD~:S~△BOC~=(OA:OC)²=1:4．故选:C．", "dataset_name": "Geoqa", "ground_truth": "0.25", "org_choices": ["\\frac{1}{6}", "\\frac{1}{3}", "\\frac{1}{4}", "\\frac{√{6}}{6}"], "choices": [0.167, 0.333, 0.25, 0.408], "label": 2}
+{"prob_id": 8121, "image_path": "images/8121.png", "question": "如图所示,在山坡上种树,已知∠A=30°,AC=3m,相邻两株树的坡面距离AB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:AB=\\frac{AC}{cosA}=\\frac{3}{cos30{^°}}=2√{3}．故选C．", "dataset_name": "Geoqa", "ground_truth": "3.4641016151377544", "org_choices": ["6m", "√{3}m", "2√{3}m", "2√{2}m"], "choices": [6.0, 1.732, 3.464, 2.828], "label": 2}
+{"prob_id": 8203, "image_path": "images/8203.png", "question": "如图,热气球从空中的A处看一栋楼的顶部仰角为30°,看这栋楼的俯角为60°．热气球与楼的水平距离为120m．这栋楼的高度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意可得,∠BAD=30°,∠DAC=60°,AD=120m,∴tan30°=\\frac{BD}{120},tan60°=\\frac{CD}{120},解得,BD=40√{3},CD=120√{3},∴BC=BD+CD=160√{3},故选:B．", "dataset_name": "Geoqa", "ground_truth": "277.1281292110204", "org_choices": ["160m", "160√{3}m", "(160-160√{3})m", "360m"], "choices": [160.0, 277.128, -117.128, 360.0], "label": 1}
+{"prob_id": 8236, "image_path": "images/8236.png", "question": "如图,某教学兴趣小组想测量一棵树CD的高度,他们先在点A处测得树顶C的仰角为30°,然后沿AD方向前行10m,到达B点,在B处测得树顶C的仰角高度为60°(A、B、D三点在同一直线上)则这棵树CD的高度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠CBD=60°,∠CBD=∠A+∠ACB,∴∠ACB=∠CBD-∠A=60°-30°=30°,∵∠A=30°,∴∠A=∠ACB,∵AB=10,∴BC=AB=10,在R△BCD中,CD=BC•sin∠CBD=10×\\frac{√{3}}{2}=5√{3}．故选:C．", "dataset_name": "Geoqa", "ground_truth": "8.660254037844387", "org_choices": ["10m", "5m", "5√{3}m", "10√{3}m"], "choices": [10.0, 5.0, 8.66, 17.321], "label": 2}
+{"prob_id": 8240, "image_path": "images/8240.png", "question": "如图,为了测得电视塔的高度AB,在D处用高为1米的测角仪CD,测得电视塔顶端A的仰角为30°,再向电视塔方向前进120米达到F处,又测得电视塔顶端A的仰角为60°,则这个电视塔的高度AB(单位:米)为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意得,CE=DF=120m,∠EAC=∠AEG-∠ACE=30°,∴∠EAC=∠ECA,∴AE=DF=120m,∴AG=AE×sin∠AEG=60√{3}m,∴AB=AG+GB=(60√{3}+1)m．故选:C．", "dataset_name": "Geoqa", "ground_truth": "104.92304845413264", "org_choices": ["60√{3}", "61", "60√{3}+1", "121"], "choices": [103.923, 61.0, 104.923, 121.0], "label": 2}
+{"prob_id": 8243, "image_path": "images/8243.png", "question": "如图,在一次数学课外实践活动中,小文在点C处测得树的顶端A的仰角为37°,BC=20m,则树的高度AB为()(参考数据:sin37°≈0.60,cos37°≈0.80,tan37°≈0.75). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:tanC=\\frac{AB}{BC},∴AB=BC•tanC=20×0.75=15m,∴树的高度AB为15m,故选:B．", "dataset_name": "Geoqa", "ground_truth": "15.0", "org_choices": ["20m", "15m", "12m", "16m"], "choices": [20.0, 15.0, 12.0, 16.0], "label": 1}
+{"prob_id": 8258, "image_path": "images/8258.png", "question": "如图,某地修建高速公路,要从B地向C地修一座隧道(B、C在同一水平面上)．为了测量B、C两地之间的距离,某工程师乘坐热气球从C地出发,垂直上升100m到达A处,在A处观察B地的俯角为30°,则B、C两地之间的距离为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:根据题意得:∠ABC=30°,AC⊥BC,AC=100m,在Rt△ABC中,BC=\\frac{AC}{tan∠ABC}=\\frac{100}{\\frac{√{3}}{3}}=100√{3}(m)．故选:A．", "dataset_name": "Geoqa", "ground_truth": "173.20508075688772", "org_choices": ["100√{3}m", "50√{2}m", "50√{3}m", "\\frac{100√{3}}{3}m"], "choices": [173.205, 70.711, 86.603, 57.735], "label": 0}
+{"prob_id": 8273, "image_path": "images/8273.png", "question": "数学实践探究课中,老师布置同学们测量学校旗杆的高度．如图所示,小明所在的学习小组在距离旗杆底部10米的地方,用测角仪测得旗杆顶端的仰角为60°,则旗杆的高度是()米．. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,根据题意得:AC=10米,∠ACB=60°,∵∠A=90°,∴在Rt△ABC中,AB=AC•tan∠ACB=10×tan60°=10×√{3}=10√{3}(米)．故选:D．", "dataset_name": "Geoqa", "ground_truth": "17.320508075688775", "org_choices": ["10√{2}", "20", "\\frac{10√{3}}{3}", "10√{3}"], "choices": [14.142, 20.0, 5.774, 17.321], "label": 3}
+{"prob_id": 8336, "image_path": "images/8336.png", "question": "如图,要测量底部不能到达的一座塔的高度AB,甲、乙两名同学分别在C,D两处进行了测量．已知点B,C,D在同一直线上,且AB⊥BD,CD=12米,∠ACB=60°,∠ADB=30°,则塔的高度AB为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:根据题意得:∠ABC=90°,∵∠ACB=60°,∠ADB=30°,∴∠CAD=∠ACB-∠ADB=30°,∴∠CAD=∠ADB,∴AC=CD=12米,在Rt△ABC中,AB=AC•sin60°=12$×\\frac{√{3}}{2}=$6$√{3}$(米),故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.392304845413264", "org_choices": ["12√{3}米", "6√{3}米", "12米", "6米"], "choices": [20.785, 10.392, 12.0, 6.0], "label": 1}
+{"prob_id": 8368, "image_path": "images/8368.png", "question": "如图1表示一个时钟的钟面垂直固定于水平桌面上,其中分针上有一点A,且当钟面显示3点30分时,分针垂直于桌面,A点距桌面的高度为10公分．如图2,若此钟面显示3点45分时,A点距桌面的高度为16公分,则钟面显示3点50分时,A点距桌面的高度为多少公分(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作A″M⊥OA′,垂足为点M,∵当钟面显示3点30分时,分针垂直于桌面,A点距桌面的高度为10公分．∴AD=10,∵钟面显示3点45分时,A点距桌面的高度为16公分,∴A′C=16,∴AO=A″O=6,则钟面显示3点50分时,∠A″OA′=30°,∴MA″=3,∴A点距桌面的高度为:16+3=19公分．故选:D．", "dataset_name": "Geoqa", "ground_truth": "19.0", "org_choices": ["22-3√{3}", "16+π", "18", "19"], "choices": [16.804, 19.142, 18.0, 19.0], "label": 3}
+{"prob_id": 8398, "image_path": "images/8398.png", "question": "如图,PA、PB是⊙O的切线,AC是⊙O的直径,∠P=50°,则∠BOC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA、PB是⊙O的切线,∴∠OAP=∠OBP=90°,而∠P=50°,∴∠AOB=360°-90°-90°-50°=130°,又∵AC是⊙O的直径,∴∠BOC=180°-130°=50°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["50°", "25°", "40°", "60°"], "choices": [50.0, 25.0, 40.0, 60.0], "label": 0}
+{"prob_id": 8406, "image_path": "images/8406.png", "question": "如图,在Rt△ABC中,AD⊥BC于D,DE⊥AB于E,若AD=3,DE=2,则AC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在Rt△ABC中,AD⊥BC于D,DE⊥AB于E,∴∠ADC=∠AED=∠BAC=90°,∴∠EAD+∠DAC=90°,∠C+∠CAD=90°,∴∠C=∠EAD,∴sin∠EAD=sin∠C=\\frac{DE}{AD}=\\frac{AD}{AC}∵AD=3,DE=2,∴\\frac{2}{3}=\\frac{3}{AC},解得:AC=\\frac{9}{2}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "4.5", "org_choices": ["\\frac{21}{2}", "\\frac{√{15}}{2}", "√{15}", "\\frac{9}{2}"], "choices": [10.5, 1.936, 3.873, 4.5], "label": 3}
+{"prob_id": 8422, "image_path": "images/8422.png", "question": "如图,在△ABC中,AB=BC=2,以AB为直径的⊙O与BC相切于点B,则AC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BC是⊙O的切线,且切点为B,∴∠ABC=90°,故△ABC是等腰直角三角形；由勾股定理,得:AC=√{AB²+BC²}=√{2BC²}=2√{2}；故选C．", "dataset_name": "Geoqa", "ground_truth": "2.8284271247461903", "org_choices": ["√{2}", "√{3}", "2√{2}", "2√{3}"], "choices": [1.414, 1.732, 2.828, 3.464], "label": 2}
+{"prob_id": 8423, "image_path": "images/8423.png", "question": "定义:定点A与⊙O上任意一点之间的距离的最小值称为点A与⊙O之间的距离．现有一矩形ABCD(如图),AB=14cm,BC=12cm,⊙K与矩形的边AB,BC,CD分别切于点E,F,G,则点A与⊙K的距离为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接KE,KF,KG、AK,交⊙K于H点,∵ABCD是矩形,⊙K与矩形的边AB,BC,CD分别切于点E,F,G,∴EK=FK=KG,∴四边形BEKF、四边形FKGC均为正方形,∴BF=FC=EK=6cm；∵AB=14cm,∴AE=8cm,AK=10cm,∴AH=AK-KH=10-6=4cm,∴点A与⊙K的距离为4cm．故选:A．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["4cm", "8cm", "10cm", "12cm"], "choices": [4.0, 8.0, 10.0, 12.0], "label": 0}
+{"prob_id": 8434, "image_path": "images/8434.png", "question": "如图,⊙O是△ABC的外接圆,∠BOC=3∠AOB,若∠ACB=20°,则∠BAC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ACB=20°,∴∠AOB=2∠ACB=40°,∵∠BOC=3∠AOB,∴∠BOC=120°,∴∠BAC=\\frac{1}{2}∠BOC=60°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["120°", "80°", "60°", "30°"], "choices": [120.0, 80.0, 60.0, 30.0], "label": 2}
+{"prob_id": 8437, "image_path": "images/8437.png", "question": "如图,AB是⊙O的直径,C、D是⊙O上两点,CD⊥AB,若∠DAB=70°,则∠BOC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵CD⊥AB．∠DAB=70°,∴∠ADC=90°-∠DAB=20°,∴∠AOC=2∠ADC=40°,∴∠BOC=180°-∠AOC=140°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["70°", "130°", "140°", "160°"], "choices": [70.0, 130.0, 140.0, 160.0], "label": 2}
+{"prob_id": 8452, "image_path": "images/8452.png", "question": "如图,A,B,C都是⊙O上的点,若∠ABC=110°,则∠AOC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∠1=2∠ABC=2×110°=220°,则∠AOC=360°-∠1=360°-220°=140°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["70°", "110°", "135°", "140°"], "choices": [70.0, 110.0, 135.0, 140.0], "label": 3}
+{"prob_id": 8456, "image_path": "images/8456.png", "question": "点B在⊙O上,点C是⊙O上异于A、B的一点,若∠AOB=50°,则∠ACB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,∵∠AOB=50°,∴∠ACB=\\frac{1}{2}∠AOB=25°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["25°", "65°", "30°", "25°、155°"], "choices": [25.0, 65.0, 30.0, 155.0], "label": 0}
+{"prob_id": 8474, "image_path": "images/8474.png", "question": "如图,已知点A、B、C在⊙O上,∠AOB=100°,则∠ACB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠AOB和∠ACB是弧AB所对的角,∴∠AOB=2∠ACB,∵∠AOB=100°,∴∠ACB=50°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["50°", "80°", "100°", "200°"], "choices": [50.0, 80.0, 100.0, 200.0], "label": 0}
+{"prob_id": 8476, "image_path": "images/8476.png", "question": "如图,AB是⊙O的直径,CD是⊙O的弦,∠ABD=59°,则∠C等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB是⊙O的直径,∴∠ADB=90°,∵∠ABD=59°,∴∠A=90°-∠ABD=31°,∴∠C=∠A=31°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "31.0", "org_choices": ["29°", "31°", "59°", "62°"], "choices": [29.0, 31.0, 59.0, 62.0], "label": 1}
+{"prob_id": 9059, "image_path": "images/9059.png", "question": "如图,正方形ABCD中,AB=8,Q是CD的中点,设∠DAQ=α,在CD上取一点P,使∠BAP=2α,则CP的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:取BC的中点E,连接AE,作EF⊥AP,则△ABE≌△ADQ,得EB=EC=4,由≥ft\\{\\begin{matrix}AE=AE\\\\∠EFA=∠EBA\\\\∠BAE=∠FAE\\\\\\end{matrix}\\right.\\得:△ABE≌△AFE,∴∠AEB=∠AEF,得EF=EB=EC,∵PE=PE,∴∠ECP=∠EFP=90°,∴△EPC≌△EPF,∴∠FEP=∠PEC,∴∠AEP=∠AEF+∠FEP=90°,∴∠PEF=∠PEC=∠EAP=∠EAB,∴△CEP∽△BAE,∴\\frac{PC}{EC}=\\frac{BE}{AB}=\\frac{4}{8}=\\frac{1}{2},即PC=2,故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.0", "org_choices": ["1", "2", "3", "√{3}"], "choices": [1.0, 2.0, 3.0, 1.732], "label": 1}
+{"prob_id": 9088, "image_path": "images/9088.png", "question": "如图,矩形的两条对角线的一个交角为60°,AC+BD=20cm,则AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是矩形,∴AC=BD,OA=OC=OD=OB,∵AC+BD=20,∴OA=OB=5,∵∠AOB=60°,∴△AOB是等边三角形,∴AB=OA=5,故选:D．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["10cm", "8cm", "6cm", "5cm"], "choices": [10.0, 8.0, 6.0, 5.0], "label": 3}
+{"prob_id": 9119, "image_path": "images/9119.png", "question": "如图,在菱形ABCD中,∠BAD=120°,对角线AC的长为3,则菱形ABCD的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图所示,∵四边形ABCD是菱形,AC是对角线,∴AB=BC=CD=AD,∠BAC=∠CAD=\\frac{1}{2}∠BAD,∴∠BAC=60°,∴△ABC是等边三角形,∴AB=BC=3,∴AB=BC=CD=AD=3,∴菱形ABCD的周长是12．故选:D．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["3", "6", "9", "12"], "choices": [3.0, 6.0, 9.0, 12.0], "label": 3}
+{"prob_id": 9124, "image_path": "images/9124.png", "question": "如图,∠MON=90°,动点A、B分别位于射线OM、ON上,矩形ABCD的边AB=6,BC=4,则线段OC长的最大值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:取AB中点E,连接OE、CE,如图所示:则BE=\\frac{1}{2}AB=3,∵∠MON=90°,∴OE=\\frac{1}{2}AB=3．在Rt△BCE中,利用勾股定理可得CE=√{3²+4²}=5．在△OCE中,根据三角形三边关系可知CE+OE＞OC,∴当O、E、C三点共线时,OC最大为OE+CE=3+5=8．故选:B．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["10", "8", "6", "5"], "choices": [10.0, 8.0, 6.0, 5.0], "label": 1}
+{"prob_id": 9145, "image_path": "images/9145.png", "question": "如图,菱形ABCD中,∠BAD=120°,BC=10,则对角线AC的长等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是菱形,且∠BAD=120°,∴AB=BC,∠BAC=∠DAC=\\frac{1}{2}∠BAD=60°,∴△ABC是等边三角形,∴AC=BC=10．故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["5", "10", "15", "20"], "choices": [5.0, 10.0, 15.0, 20.0], "label": 1}
+{"prob_id": 9155, "image_path": "images/9155.png", "question": "如图,菱形ABCD的周长是16,∠A=60°,则对角线BD的长度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵菱形ABCD的周长是16,∴AB=AD=CD=BC=4,∵∠A=60°,∴△ABD是等边三角形,∴AB=AD=BD=4．∴对角线BD的长度为4．故选:C．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["2", "2√{3}", "4", "4√{3}"], "choices": [2.0, 3.464, 4.0, 6.928], "label": 2}
+{"prob_id": 9165, "image_path": "images/9165.png", "question": "如图,在菱形ABCD中,AB=5,∠B=60°,则对角线AC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB=BC,∠B=60°,∴△ABC为等边三角形∴AC=AB=5．故选:D．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["20", "15", "10", "5"], "choices": [20.0, 15.0, 10.0, 5.0], "label": 3}
+{"prob_id": 9171, "image_path": "images/9171.png", "question": "如图,菱形ABCD中,AB=15,∠ADC=120°,则B、D两点之间的距离为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BD,∵∠ADC=120°,∴∠A=180°-120°=60°,∵AB=AD,∴△ABD是等边三角形,∴BD=AB=15．故选:A．", "dataset_name": "Geoqa", "ground_truth": "15.0", "org_choices": ["15", "\\frac{15}{2}√{3}", "7.5", "15√{3}"], "choices": [15.0, 12.99, 7.5, 25.981], "label": 0}
+{"prob_id": 9175, "image_path": "images/9175.png", "question": "如图,在菱形ABCD中,两条对角线AC=12,BD=16,则此菱形的边长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是菱形,∴OA=\\frac{1}{2}AC=\\frac{1}{2}×12=6,OB=\\frac{1}{2}BD=\\frac{1}{2}×16=8,AC⊥BD,∴AB=√{OA²{+OB}²}=10．∴此菱形的边长为10．故选:A．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["10", "8", "6", "5"], "choices": [10.0, 8.0, 6.0, 5.0], "label": 0}
+{"prob_id": 9188, "image_path": "images/9188.png", "question": "如图,在菱形ABCD中,∠BAD=80°,AB的垂直平分线交对角线AC于点F,E为垂足,连接DF,则∠CDF等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BD,BF,∵∠BAD=80°,∴∠ADC=100°,又∵EF垂直平分AB,AC垂直平分BD,∴AF=BF,BF=DF,∴AF=DF,∴∠FAD=∠FDA=40°,∴∠CDF=100°-40°=60°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["60°", "65°", "70°", "80°"], "choices": [60.0, 65.0, 70.0, 80.0], "label": 0}
+{"prob_id": 9198, "image_path": "images/9198.png", "question": "如图,菱形ABCD中,∠B=60°,AB=2cm,E、F分别是BC、CD的中点,连接AE、EF、AF,则△AEF的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是菱形,∴AB=AD=BC=CD,∠B=∠D,∵E、F分别是BC、CD的中点,∴BE=DF,在△ABE和△ADF中,≥ft\\{\\begin{matrix}AB=AD\\\\∠B=∠D\\\\BE=DF\\\\\\end{matrix}\\right.\\∴△ABE≌△ADF(SAS),∴AE=AF,∠BAE=∠DAF．连接AC,∵∠B=∠D=60°,∴△ABC与△ACD是等边三角形,∴AE⊥BC,AF⊥CD(等腰三角形底边上的中线与底边上的高线重合),∴∠BAE=∠DAF=30°,∴∠EAF=60°,∴△AEF是等边三角形．∴AE=√{3}cm,∴周长是3√{3}cm．故选:B．", "dataset_name": "Geoqa", "ground_truth": "5.196152422706632", "org_choices": ["2√{3}cm", "3√{3}cm", "4√{3}cm", "3cm"], "choices": [3.464, 5.196, 6.928, 3.0], "label": 1}
+{"prob_id": 9230, "image_path": "images/9230.png", "question": "如图,在▱ABCD中,BC=BD,∠C=65°,则∠ADB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BC=BD,∠C=65°,∴∠BDC=∠C=65°,∴∠DBC=180°-∠C-∠BDC=50°,∵四边形ABCD是平行四边形,∴AD∥BC,∴∠ADB=∠DBC=50°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["25°", "35°", "50°", "60°"], "choices": [25.0, 35.0, 50.0, 60.0], "label": 2}
+{"prob_id": 9239, "image_path": "images/9239.png", "question": "如图,在▱ABCD中,AB=6,BC=8,∠C的平分线交AD于E,交BA的延长线于F,则AE+AF的值等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AB∥CD,AD=BC=8,CD=AB=6,∴∠F=∠DCF,∵CF平分∠BCD,∴∠FCB=∠DCF,∴∠F=∠FCB,∴BF=BC=8,同理:DE=CD=6,∴AF=BF-AB=2,AE=AD-DE=2,∴AE+AF=4；故选:C．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["2", "3", "4", "6"], "choices": [2.0, 3.0, 4.0, 6.0], "label": 2}
+{"prob_id": 9268, "image_path": "images/9268.png", "question": "如图,在▱ABCD中,AE⊥BC于E,AF⊥DC交DC的延长线于点F,且∠EAF=60°,则∠B等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在▱ABCD中,AF⊥CD,∴BA⊥AF,∴∠BAF=90°,∵∠EAF=60°,∴∠BAE=30°,∵AE⊥BC,∴∠B=90°-30°=60°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["60°", "50°", "70°", "65°"], "choices": [60.0, 50.0, 70.0, 65.0], "label": 0}
+{"prob_id": 9270, "image_path": "images/9270.png", "question": "如图,▱ABCD中,AE平分∠BAD,若CE=3cm,AB=4cm,则▱ABCD的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AD=BC=10,AB=DC,AD∥BC,∴∠DAE=∠BEA,∵AE平分∠BCD,∴∠BAE=∠DAE,∴∠BEA=∠BAE,∴BE=AB=4cm,∴BC=BE+CE=7cm,∴▱ABCD的周长=2(DC+BC)=2(4+7)=22cm；故选:C．", "dataset_name": "Geoqa", "ground_truth": "22.0", "org_choices": ["20cm", "21cm", "22cm", "23cm"], "choices": [20.0, 21.0, 22.0, 23.0], "label": 2}
+{"prob_id": 9272, "image_path": "images/9272.png", "question": "如图,在▱ABCD中,AE平分∠BAD,已知∠AEB=63°,则∠D的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:四边形ABCD是平行四边形,∴AD∥BC,∴∠DAB+∠B=180°,∠B=∠D,∴∠AEB=∠DAE=63°,∵AE平分∠BAD,∴∠DAB=2∠DAE=2×63°=126°,∴∠B=180°-126°=54°∴∠D=∠B=54°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "54.0", "org_choices": ["63°", "72°", "54°", "60°"], "choices": [63.0, 72.0, 54.0, 60.0], "label": 2}
+{"prob_id": 9276, "image_path": "images/9276.png", "question": "如图,在▱ABCD中,对角线AC、BD相交于点O,AC=10,BD=6,AD=4,则▱ABCD的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,且AC=10,BD=6,∴OA=OC=\\frac{1}{2}AC=5,OB=OD=\\frac{1}{2}BD=3,∵AD=4,∴AD²+DO²=OA²,∴△ADO是直角三角形,且∠BDA=90°,即AD⊥BD,∴▱ABCD面积为:AD•BD=4×6=24．故选:C．", "dataset_name": "Geoqa", "ground_truth": "24.0", "org_choices": ["12", "12√{3}", "24", "30"], "choices": [12.0, 20.785, 24.0, 30.0], "label": 2}
+{"prob_id": 9303, "image_path": "images/9303.png", "question": "如图,平行四边形ABCD的对角线交于点O,且AB=6,△OCD的周长为19,则▱ABCD的两条对角线的和是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AB=CD=6,∵△OCD的周长为19,∴OD+OC=19-6=13,∵BD=2DO,AC=2OC,∴平行四边形ABCD的两条对角线的和=BD+AC=2(DO+OC)=26,故选:C．", "dataset_name": "Geoqa", "ground_truth": "26.0", "org_choices": ["13", "25", "26", "38"], "choices": [13.0, 25.0, 26.0, 38.0], "label": 2}
+{"prob_id": 9308, "image_path": "images/9308.png", "question": "如图,在平行四边形ABCD中,若∠B=60°,则∠D等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴∠D=∠B=60°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["30°", "45°", "60°", "90°"], "choices": [30.0, 45.0, 60.0, 90.0], "label": 2}
+{"prob_id": 9311, "image_path": "images/9311.png", "question": "如图,平行四边形ABCD中,已知∠AOB=90°,AC=8cm,AD=5cm,则BD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴OA=\\frac{1}{2}AC=\\frac{1}{2}×8=4(cm),∵∠AOB=90°,∴∠AOD=180°-∠AOB=90°,∴OD=√{AD²-OA²}=√{5²-4²}=3(cm),∴BD=2OD=6cm．故选:C．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["3cm", "4cm", "6cm", "8cm"], "choices": [3.0, 4.0, 6.0, 8.0], "label": 2}
+{"prob_id": 9313, "image_path": "images/9313.png", "question": "如图,▱ABCD中,CE⊥AB,垂足为E,如果∠A=115°,则∠BCE等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AD∥BC,∴∠A+∠B=180°,∴∠B=180°-115°=65°,∵CE⊥AB,∴∠BEC=90°,∴∠BCE=90°-∠B=90°-65°=25°；故选:B．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["65°", "25°", "30°", "15°"], "choices": [65.0, 25.0, 30.0, 15.0], "label": 1}
+{"prob_id": 9328, "image_path": "images/9328.png", "question": "如图,在平行四边形ABCD中,CE平分∠BCD交AD边于点E,且DE=3,则AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AB=DC,AD∥BC,∴∠DEC=∠BCE,∵CE平分∠DCB,∴∠DCE=∠BCE,∴∠DEC=∠DCE,∴DE=DC=AB=3,故选:C．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["1", "2", "3", "6"], "choices": [1.0, 2.0, 3.0, 6.0], "label": 2}
+{"prob_id": 9333, "image_path": "images/9333.png", "question": "▱ABCD中,对角线AC与BD交于点O,∠DAC=42°,∠CBD=23°,则∠COD是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AD∥BC,∴∠DAC=∠BCA=42°,∴∠COD=∠CBD+∠BCA=65°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["61°", "63°", "65°", "67°"], "choices": [61.0, 63.0, 65.0, 67.0], "label": 2}
+{"prob_id": 9336, "image_path": "images/9336.png", "question": "如图,平行四边形ABCD的对角线AC、BD相交于点O,点E是CD的中点,△ABD的周长为16cm,则△DOE的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴O是BD中点,△ABD≌△CDB,又∵E是CD中点,∴OE是△BCD的中位线,∴OE=\\frac{1}{2}BC,即△DOE的周长=\\frac{1}{2}△BCD的周长,∴△DOE的周长=\\frac{1}{2}△DAB的周长．∴△DOE的周长=\\frac{1}{2}×16=8cm．故选:A．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["8cm", "10cm", "12cm", "16cm"], "choices": [8.0, 10.0, 12.0, 16.0], "label": 0}
+{"prob_id": 9338, "image_path": "images/9338.png", "question": "如图,在▱ABCD中,BM是∠ABC的平分线交CD于点M,且MC=2,▱ABCD的周长是14,则DM等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BM是∠ABC的平分线,∴∠ABM=∠CBM,∵AB∥CD,∴∠ABM=∠BMC,∴∠BMC=∠CBM,∴BC=MC=2,∵▱ABCD的周长是14,∴BC+CD=7,∴CD=5,则DM=CD-MC=3,故选:C．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["1", "2", "3", "4"], "choices": [1.0, 2.0, 3.0, 4.0], "label": 2}
+{"prob_id": 9341, "image_path": "images/9341.png", "question": "如图,P是▱ABCD上一点．已知S~△ABP~=3,S~△PDC~=2,那么平行四边形ABCD的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵P是▱ABCD上一点,∴S~△PBC~=\\frac{1}{2}S~平行四边形ABCD~,∴S~△ABP~+S~△PDC~═\\frac{1}{2}S~平行四边形ABCD~,∵S~△ABP~=3,S~△PDC~=2,∴S~平行四边形ABCD~=(3+2)×2=10,故选:C．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["6", "8", "10", "无法确定"], "choices": [6.0, 8.0, 10.0], "label": 2}
+{"prob_id": 9356, "image_path": "images/9356.png", "question": "如图,在▱ABCD中,AE平分∠BAD交边BC于点E,若AD=8,EC=2,则AB的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AD∥BC,AD=BC=8,∵AE平分∠BAD交边BC于点E,∴∠BAE=∠DAE,∵AD∥BC,∴∠DAE=∠BEA,∴∠BAE=∠BEA,∴AB=BE,∴AB=BE=BC-CE=6,故选:C．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["10", "8", "6", "4"], "choices": [10.0, 8.0, 6.0, 4.0], "label": 2}
+{"prob_id": 9358, "image_path": "images/9358.png", "question": "如图,在平行四边形ABCD中,过点C的直线CE⊥AB,垂足为E,若∠EAD=54°,则∠BCE的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵CE⊥AB,∴∠E=90°,∵∠EAD=54°,∴∠2=90°-54°=36°,∵四边形ABCD是平行四边形,∴AD∥BC,∴∠ECB=∠2=36°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "36.0", "org_choices": ["54°", "36°", "46°", "126°"], "choices": [54.0, 36.0, 46.0, 126.0], "label": 1}
+{"prob_id": 9359, "image_path": "images/9359.png", "question": "如图,在▱ABCD中,BD=CD,∠C=70°,AE⊥BD于点E,则∠BAE的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在△DBC中,∵BD=CD,∠C=70°,∴∠DBC=∠C=70°,又∵在▱ABCD中,AD∥BC,∴∠ADB=∠DBC=70°,又∵AE⊥BD,∴∠DAE=90°-∠ADB=90°-70°=20°．故选:AD．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["20°", "30°", "40°", "50°"], "choices": [20.0, 30.0, 40.0, 50.0], "label": 0}
+{"prob_id": 9363, "image_path": "images/9363.png", "question": "如图,P为平行四边形ABCD内一点,过点P分别作AB、AD的平行线交平行四边形于E、F、G、H四点,若S~AHPE~=3,S~PFCG~=5,则S~△PBD~为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:显然EPGD、GPFC、EPHA、PHBF均为平行四边形,∴S~△DEP~=S~△DGP~=\\frac{1}{2}S~平行四边形DEPG~,∴S~△PHB~=S~△PBF~=\\frac{1}{2}S~平行四边形PHBF~,又S~△ADB~=S~△EPD~+S~平行四边形AHPE~+S~△PHB~+S~△PDB~①S~△BCD~=S~△PDG~+S~平行四边形PFCG~+S~△PFB~-S~△PDB~②①-②得0=S~平行四边形AHPE~-S~平行四边形PFCG~+2S~△PDB~,即2S~△PBD~=5-3=2∴S~△PBD~=1．故选:B．", "dataset_name": "Geoqa", "ground_truth": "1.0", "org_choices": ["1.5", "1", "2.5", "3"], "choices": [1.5, 1.0, 2.5, 3.0], "label": 1}
+{"prob_id": 9368, "image_path": "images/9368.png", "question": "如图,▱ABCD中,∠A=120°,则∠1=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴∠BCD=∠A=120°,∴∠1=180°-∠BCD=60°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["80°", "60°", "45°", "30°"], "choices": [80.0, 60.0, 45.0, 30.0], "label": 1}
+{"prob_id": 9369, "image_path": "images/9369.png", "question": "如图,在▱ABCD中,CE⊥AB,点E为垂足,如果∠D=55°,则∠BCE=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴∠B=∠D=55°,∵CE⊥AB,∴∠BEC=90°,∴∠BCE=90°-∠B=35°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["55°", "35°", "25°", "30°"], "choices": [55.0, 35.0, 25.0, 30.0], "label": 1}
+{"prob_id": 9386, "image_path": "images/9386.png", "question": "如图,在▱ABCD中,∠ABC=60°,AB=BC=4cm,点M,N分别在边BC,CD上,且∠MAN=60°,则四边形AMCN的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接AC,∵∠B=60°,∴∠BAD=120°,∵∠MAN=60°,∴∠BAM=∠CAN,∴△ABC为等边三角形,∴AB=AC,∴△ABM≌△ACN,∴四边形AMCN的面积等于平行四边形面积的一半．∵AB=4cm,∴BC边上的高为2√{3},S~菱形ABCD~=4×2√{3}=8√{3}∴四边形AMCN的面积等于\\frac{1}{2}×8√{3}=4√{3}．故选:A．", "dataset_name": "Geoqa", "ground_truth": "6.928203230275509", "org_choices": ["4√{3}cm²", "2√{3}cm²", "8√{3}cm²", "8cm²"], "choices": [6.928, 3.464, 13.856, 8.0], "label": 0}
+{"prob_id": 9387, "image_path": "images/9387.png", "question": "如图,在平行四边形ABCD中,AB=4,BC=6,AC的垂直平分线交AD于点E,则△CDE的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AC的垂直平分线交AD于E,∴AE=EC,∵四边形ABCD是平行四边形,∴DC=AB=4,AD=BC=6,∴△CDE的周长为:EC+CD+ED=AD+CD=6+4=10,故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["7", "10", "11", "12"], "choices": [7.0, 10.0, 11.0, 12.0], "label": 1}
+{"prob_id": 9402, "image_path": "images/9402.png", "question": "如图,在▱ABCD中,AD=3,DC=5,BD的垂直平分线交BD于点E,则△BCE的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴BC=AD=3,∵BD的垂直平分线交BD于点E,∴DE=BE,∴EB+CE=DC=5,∴△BCE的周长是:5+3=8,故选:B．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["6", "8", "9", "10"], "choices": [6.0, 8.0, 9.0, 10.0], "label": 1}
+{"prob_id": 9415, "image_path": "images/9415.png", "question": "如图,▱ABCD的周长为10cm,AC、BD相交于点O,OE⊥AC交AD于E,则△DCE的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵▱ABCD的周长为10cm,∴AD+DC=5cm,∵四边形ABCD是平行四边形,∴AO=CO,∵OE⊥AC交AD于E,∴AE=EC,∴EC+ED+CD=5cm,故选:D．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["4cm", "6cm", "8cm", "5cm"], "choices": [4.0, 6.0, 8.0, 5.0], "label": 3}
+{"prob_id": 9421, "image_path": "images/9421.png", "question": "如图,在平行四边形ABCD中,已知AB=6,BC=9,∠B=30°,则平行四边形ABCD的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过点A作AE⊥BC于E,∴∠AEB=90°,∵AB=6,∠B=30°,∴AE=3；又∵BC=9,∴S~平行四边形ABCD~=9×3=27．故选:C．", "dataset_name": "Geoqa", "ground_truth": "27.0", "org_choices": ["12", "18", "27", "54"], "choices": [12.0, 18.0, 27.0, 54.0], "label": 2}
+{"prob_id": 9438, "image_path": "images/9438.png", "question": "如图,▱ABCD中,∠AEB=36°,BE平分∠ABC,则∠C等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AD∥BC,∴∠AEB=∠EBC；∵BE平分∠ABC,∠AEB=36°,∴∠ABC=2∠EBC=2∠AEB=72°,又∵AB∥CD,∴∠C+∠ABC=180°,∴∠C=108°；故选:C．", "dataset_name": "Geoqa", "ground_truth": "108.0", "org_choices": ["36°", "72°", "108°", "144°"], "choices": [36.0, 72.0, 108.0, 144.0], "label": 2}
+{"prob_id": 9445, "image_path": "images/9445.png", "question": "如图,平行四边形ABCD的对角线交于点O,且AB=5,△OCD的周长为23,则平行四边形ABCD的两条对角线的和是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AB=CD=5,∵△OCD的周长为23,∴OD+OC=23-5=18,∵BD=2DO,AC=2OC,∴平行四边形ABCD的两条对角线的和=BD+AC=2(DO+OC)=36,故选:C．", "dataset_name": "Geoqa", "ground_truth": "36.0", "org_choices": ["18", "28", "36", "46"], "choices": [18.0, 28.0, 36.0, 46.0], "label": 2}
+{"prob_id": 9449, "image_path": "images/9449.png", "question": "如图,在▱ABCD中,对角线AC、BD相交于点O,如果AC=12,BD=8,AB=7,那么△OAB的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵▱ABCD,∴OA=OC,OD=OB,∵AC=12,BD=8,∴OA=6,OB=4,∵AB=7,∴△OAB的周长=OA+OB+AB=6+4+7=17．故选:B．", "dataset_name": "Geoqa", "ground_truth": "17.0", "org_choices": ["15", "17", "21", "27"], "choices": [15.0, 17.0, 21.0, 27.0], "label": 1}
+{"prob_id": 9452, "image_path": "images/9452.png", "question": "平行四边形ABCD的周长是28cm,AC与BD相交于点O,△AOB的周长比△OBC的周长大4cm,那么AB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵平行四边形ABCD,∴OA=OC,OB=OD,∵平行四边形ABCD的周长是28cm,∴AB=CD,AD=BC,∴AB+BC+CD+AD=2(AB+BC)=28cm,∴AB+BC=14cm,∵△AOB的周长比△OBC的周长大4cm,∴AB+OA+OB-(BC+OB+OC)=AB-BC=4cm,∴AB=9cm．故选:B．", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["8cm", "9cm", "10cm", "11cm"], "choices": [8.0, 9.0, 10.0, 11.0], "label": 1}
+{"prob_id": 9459, "image_path": "images/9459.png", "question": "如图,平行四边形ABCD中,对角线AC和BD交于O点,过O点作OE∥BC交DC于点E,若OE=2.5,则AD的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴AD=BC,DO=BO,∵OE∥BC,∴DE=CE,∴BC=2OE=2×2.5=5,∴AD=5,故选:B．", "dataset_name": "Geoqa", "ground_truth": "5.0", "org_choices": ["2.5", "5", "10", "15"], "choices": [2.5, 5.0, 10.0, 15.0], "label": 1}
+{"prob_id": 9465, "image_path": "images/9465.png", "question": "如图平行四边形ABCD的对角线AC与BD相交于点O,AB=7,AC=10,△ABO周长为16,那么对角线BD的长等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB=7,AC=10,△ABO周长为16,∴AB+OA+0B=16,∴OA+OB=9,∵平行四边形ABCD,∴AC=2OA=10,BD=2OB,∴OA=5,∴OB=4,∴BD=8,故选:D．", "dataset_name": "Geoqa", "ground_truth": "8.0", "org_choices": ["4", "5", "6", "8"], "choices": [4.0, 5.0, 6.0, 8.0], "label": 3}
+{"prob_id": 9466, "image_path": "images/9466.png", "question": "如图所示,E是▱ABCD内任一点,若S~四边形ABCD~=6,则图中阴影部分的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设两个阴影部分三角形的底为AB,CD,高分别为h~1~,h~2~,则h~1~+h~2~为平行四边形的高,∴S~△EAB~+S~△ECD~=\\frac{1}{2}AB•h~1~+\\frac{1}{2}CD•h~2~=\\frac{1}{2}AB(h~1~+h~2~)=\\frac{1}{2}S~四边形ABCD~=\\frac{1}{2}×6=3．故选B．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["2", "3", "4", "5"], "choices": [2.0, 3.0, 4.0, 5.0], "label": 1}
+{"prob_id": 9467, "image_path": "images/9467.png", "question": "如图,在平行四边形ABCD中,AB=4,∠BAD的平分线与BC的延长线交于点E,与DC交于点F,且点F为边DC的中点,DG⊥AE,垂足为G,若DG=1,则AE的边长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AE为∠DAB的平分线,∴∠DAE=∠BAE,∵DC∥AB,∴∠BAE=∠DFA,∴∠DAE=∠DFA,∴AD=FD,又F为DC的中点,∴DF=CF,∴AD=DF=\\frac{1}{2}DC=\\frac{1}{2}AB=2,在Rt△ADG中,根据勾股定理得:AG=√{3},则AF=2AG=2√{3},∵平行四边形ABCD,∴AD∥BC,∴∠DAF=∠E,∠ADF=∠ECF,在△ADF和△ECF中,≥ft\\{\\begin{matrix}∠DAF=∠E\\\\∠ADF=∠ECF\\\\DF=CF\\\\\\end{matrix}\\right.\\,∴△ADF≌△ECF(AAS),∴AF=EF,则AE=2AF=4√{3}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "6.928203230275509", "org_choices": ["2√{3}", "4√{3}", "4", "8"], "choices": [3.464, 6.928, 4.0, 8.0], "label": 1}
+{"prob_id": 9481, "image_path": "images/9481.png", "question": "如图,AB是⊙O的弦,过点A作⊙O的切线AC．如果∠BAC=55°,那么∠AOB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AC为圆O的切线,∴OA⊥AC,∴∠OAC=90°,∵∠BAC=55°,∴∠OAB=∠OAC-∠BAC=35°,∵OA=OB,∴∠OAB=∠OBA=35°,则∠AOB=180°-2×35°=110°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "110.0", "org_choices": ["55°", "90°", "110°", "120°"], "choices": [55.0, 90.0, 110.0, 120.0], "label": 2}
+{"prob_id": 9482, "image_path": "images/9482.png", "question": "如图,线段AB过圆心O,交⊙O于点A、C,∠B=30°,直线BD与⊙O切于点D,则∠ADB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OD,∵BD切⊙O于D,∴∠ODB=90°,∵∠B=30°,∴∠DOB=60°,∴∠A=\\frac{1}{2}∠DOB=30°,∴∠ADB=180°-∠B-∠A=180°-30°-30°=120°,故选:C．", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["150°", "135°", "120°", "100°"], "choices": [150.0, 135.0, 120.0, 100.0], "label": 2}
+{"prob_id": 9530, "image_path": "images/9530.png", "question": "如图,在平行四边形ABCD中,AC,BD为对角线,BC=6,BC边上的高为4,则图中阴影部分的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:通过观察结合平行四边形性质得:S_{阴影}=\\frac{1}{2}×6×4=12．故选:C．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["3", "6", "12", "24"], "choices": [3.0, 6.0, 12.0, 24.0], "label": 2}
+{"prob_id": 9538, "image_path": "images/9538.png", "question": "如图,把平行四边形ABCD分成4个平行四边形,已知其中三个面积分别为8、10、30,则第四个平行四边形的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵平行四边形ABCD被分成4个平行四边形,∴AB∥EF∥CD,AD∥MN∥BC,∴四边形AMOE与四边形MBFO同高,底分别为OE与OF,四边形EOND与四边形OFCN同高,底分别为OE与OF,∴\\frac{S_{四边形AEMO}}{S_{四边形MBFO}}=\\frac{OE}{OF}=\\frac{8}{10}=\\frac{4}{5},∴\\frac{S_{四边形EOND}}{S_{四边形OFCN}}=\\frac{OE}{OF},即:\\frac{S_{四边形EOND}}{30}=\\frac{4}{5},∴S~四边形EOND~=24．故选:C．", "dataset_name": "Geoqa", "ground_truth": "24.0", "org_choices": ["28", "26", "24", "22"], "choices": [28.0, 26.0, 24.0, 22.0], "label": 2}
+{"prob_id": 9540, "image_path": "images/9540.png", "question": "如图,▱ABCD的对角线AC、BD相交于点O,若AC+BD=10,BC=4,则△BOC的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵ABCD是平行四边形,∴BD=AC,BO=OD,AO=OC,又∵AC+BD=10,∴BO+OC=5,∴△BOC的周长为5+4=9．故选:B．", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["8", "9", "10", "14"], "choices": [8.0, 9.0, 10.0, 14.0], "label": 1}
+{"prob_id": 9549, "image_path": "images/9549.png", "question": "如图,在▱ABCD中,AC、BD相交于点O,点E、F分别在边AD、BC上,EF经过点O．如果AB=3,BC=5,EF=AB,那么四边形CDEF的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∴CD=AB=3,AD=BC=5,OA=OC,AD∥BC,∴∠EAO=∠FCO,∠AEO=∠CFO,在△AOE和△COF中,≥ft\\{\\begin{matrix}∠EAO=∠FCO&\\\\AEO=∠CFO&\\\\OA=OC&\\\\\\end{matrix}\\right.\\,∴△AOE≌△COF(AAS)．∴OF=OE,CF=AE．∴四边形CDEF的周长=CD+DE+EF+CF=CD+AB+DE+AE=CD+AB+AD=3+3+5=11；故选:D．", "dataset_name": "Geoqa", "ground_truth": "11.0", "org_choices": ["8", "9", "10", "11"], "choices": [8.0, 9.0, 10.0, 11.0], "label": 3}
+{"prob_id": 9556, "image_path": "images/9556.png", "question": "如图,平行四边形ABCD的对角线AC的垂直平分线与边BC、DA分别交于E、F,连接CF,若平行四边形ABCD的周长等于18cm,则△CDF的周长等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵EF垂直平分AC,∴AF=CF,∴△CDF的周长=AD+DC=9cm,故选:C．", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["6cm", "8cm", "9cm", "10cm"], "choices": [6.0, 8.0, 9.0, 10.0], "label": 2}
+{"prob_id": 9568, "image_path": "images/9568.png", "question": "如图,在△ABC中,AB=AC,∠A=40°,以C为圆心,CB的长为半径画弧,交AB于点D,连接CD,则∠ACD等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB=AC,∠A=40°,∴∠B=∠ACB=70°,∵BC=CD,∴∠CDB=∠B=70°,∴∠BCD=40°,∴∠ACD=30°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["20°", "30°", "40°", "50°"], "choices": [20.0, 30.0, 40.0, 50.0], "label": 1}
+{"prob_id": 9582, "image_path": "images/9582.png", "question": "如图,在⊙O中,已知∠AOB=110°,C是圆周上的一点,则∠ACB为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在优弧AB上取点D,连接AD,BD,∵∠D=\\frac{1}{2}∠AOB=\\frac{1}{2}×110°=55°,∴∠ACB=180°-∠D=125°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "125.0", "org_choices": ["130°", "125°", "80°", "50°"], "choices": [130.0, 125.0, 80.0, 50.0], "label": 1}
+{"prob_id": 9591, "image_path": "images/9591.png", "question": "如图,CD是⊙O的直径,弦DE∥OA,若∠D的度数是50°,则∠C的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥OA,∴∠AOD=∠D=50°,∴∠C=\\frac{1}{2}∠AOD=25°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["25°", "30°", "40°", "50°"], "choices": [25.0, 30.0, 40.0, 50.0], "label": 0}
+{"prob_id": 9620, "image_path": "images/9620.png", "question": "如图,BD是⊙O的直径,点A、C在⊙O上,且BD⊥AC,若⁀{AB}的度数为60°,则∠BDC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC,∵BD是⊙O的直径,BD⊥AC,∴⁀{AB}=⁀{BC},∴∠BOC=∠AOB=60°,∴∠BDC=\\frac{1}{2}∠BOC=30°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["60°", "30°", "35°", "45°"], "choices": [60.0, 30.0, 35.0, 45.0], "label": 1}
+{"prob_id": 9632, "image_path": "images/9632.png", "question": "如图,已知AB、AD是⊙O的弦,∠B=20°,点C在弦AB上,连接CO并延长CO交于⊙O于点D,∠D=15°,则∠BAD的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OA,∵OA=OB,∠B=20°,∴∠OAB=∠B=20°．∵OA=OD,∠D=15°,∴∠OAD=∠D=15°,∴∠BAD=∠OAB+∠OAD=20°+15°=35°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["30°", "45°", "20°", "35°"], "choices": [30.0, 45.0, 20.0, 35.0], "label": 3}
+{"prob_id": 9655, "image_path": "images/9655.png", "question": "如图,⊙O是△ABC的外接圆,已知∠C=60°,则∠BAO的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OB,由圆周角定理得,∠AOB=2∠C=120°,又OA=OB,∴∠BAO=\\frac{1}{2}(180°-120°)=30°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["15°", "30°", "60°", "120°"], "choices": [15.0, 30.0, 60.0, 120.0], "label": 1}
+{"prob_id": 9658, "image_path": "images/9658.png", "question": "如图,AB是半圆的直径,∠ABC=50°,点D是⁀{AC}的中点,则∠DAB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连结BD,如图,∵点D是⁀{AC}的中点,即弧CD=弧AD,∴∠ABD=∠CBD,∵∠ABC=50°,∴∠ABD=\\frac{1}{2}×50°=25°,∵AB是半圆的直径,∴∠ADB=90°,∴∠DAB=90°-25°=65°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["40°", "50°", "65°", "70°"], "choices": [40.0, 50.0, 65.0, 70.0], "label": 2}
+{"prob_id": 9676, "image_path": "images/9676.png", "question": "如图,AB是⊙O的直径,弦CD与AB相交,且∠ABC=32°,则∠CDB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵线段AB为⊙O的直径,∴∠ACB=90°,∴∠BAC=180°-∠ACB-∠ABC=58°．∵∠CDB与∠BAC均为弦BC的圆周角,∴∠CDB=∠BAC=58°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "58.0", "org_choices": ["58°", "32°", "80°", "64°"], "choices": [58.0, 32.0, 80.0, 64.0], "label": 0}
+{"prob_id": 9677, "image_path": "images/9677.png", "question": "如图,⁀{AB}是半圆,连接AB,点O为AB的中点,点C、D在⁀{AB}上,连接AD、CO、BC、BD、OD．若∠COD=62°,且AD∥OC,则∠ABD的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB是半圆的直径,∴∠ADB=90°,∵AD∥OC,∴∠A=∠COD=62°,∴∠ABD=90°-∠A=28°；故选:B．", "dataset_name": "Geoqa", "ground_truth": "28.0", "org_choices": ["26°", "28°", "30°", "32°"], "choices": [26.0, 28.0, 30.0, 32.0], "label": 1}
+{"prob_id": 9716, "image_path": "images/9716.png", "question": "如图,AB是⊙O的直径,点C、点D在⊙O上,连结AC、BC、AD、CD,若∠BAC=50°,则∠ADC的度数等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB是⊙O的直径,∴∠ACB=90°,∵∠BAC=50°,∴∠B=40°,∴∠ADC=∠B=40°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["30°", "35°", "40°", "45°"], "choices": [30.0, 35.0, 40.0, 45.0], "label": 2}
+{"prob_id": 9728, "image_path": "images/9728.png", "question": "如图,AB是⊙O直径,∠AOC=140°,则∠D为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠AOC=140°,∴∠BOC=180°-140°=40°,∴∠D=\\frac{1}{2}∠BOC=\\frac{1}{2}×40°=20°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["40°", "30°", "20°", "70°"], "choices": [40.0, 30.0, 20.0, 70.0], "label": 2}
+{"prob_id": 9729, "image_path": "images/9729.png", "question": "如图,在⊙O中,直径AB⊥弦CD于点H,E是⊙O上的点,若∠BEC=25°,则∠BAD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接AC,∵直径AB⊥弦CD于点H,∴⁀{BC}=⁀{BD}∴∠CAB=∠DAB∵∠BAC=∠BEC=25°,∴∠BAD=∠BAC=25°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["65°", "50°", "25°", "12.5°"], "choices": [65.0, 50.0, 25.0, 12.5], "label": 2}
+{"prob_id": 9736, "image_path": "images/9736.png", "question": "如图,AB为⊙O的直径,CD为⊙O的弦,∠ABD=53°,则∠BCD为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接AC,∵AB是圆的直径,∴∠BCA=90°,又∠ACD=∠ABD=53°,∴∠BCD=∠ACB-∠ACD=90°-53°=37°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "37.0", "org_choices": ["37°", "47°", "45°", "53°"], "choices": [37.0, 47.0, 45.0, 53.0], "label": 0}
+{"prob_id": 9760, "image_path": "images/9760.png", "question": "如图,⊙O是△ABC的外接圆,∠AOB=60°,则∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵⊙O是△ABC的外接圆,∠AOB=60°,∴∠C=\\frac{1}{2}∠AOB=\\frac{1}{2}×60°=30°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["25°", "30°", "35°", "40°"], "choices": [25.0, 30.0, 35.0, 40.0], "label": 1}
+{"prob_id": 9761, "image_path": "images/9761.png", "question": "如图,点A,B,C是⊙O上的三点,∠AOC=110°,则∠ABC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠AOC与∠ABC是同弧所对的圆心角与圆周角,∠AOC=110°,∴∠ABC=\\frac{1}{2}∠AOC=55°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["70°", "65°", "55°", "50°"], "choices": [70.0, 65.0, 55.0, 50.0], "label": 2}
+{"prob_id": 9768, "image_path": "images/9768.png", "question": "如图,AB是⊙O的直径,CD为弦,且AB⊥CD,垂足是点E,已知∠COB=60°,则∠DAB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB⊥CD,AB是⊙O的直径,∴⁀{CB}=⁀{BD},∴∠DAB=\\frac{1}{2}∠COB,∵∠COB=60°,∴∠DAB=30°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["60°", "30°", "25°", "35°"], "choices": [60.0, 30.0, 25.0, 35.0], "label": 1}
+{"prob_id": 9773, "image_path": "images/9773.png", "question": "如图,已知AB为⊙O的直径,若∠BOC的度数是50°,则∠A的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由圆周角定理得,∠A=\\frac{1}{2}∠BOC=25°,故选:D．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["50°", "40°", "30°", "25°"], "choices": [50.0, 40.0, 30.0, 25.0], "label": 3}
+{"prob_id": 9779, "image_path": "images/9779.png", "question": "如图,点A、B、C在⊙O上,∠AOB=140°,∠ACB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在优弧AB上任意找一点D,连接AD,BD．∵∠D=\\frac{1}{2}∠AOB=70°∴∠ACB=180°-40°=110°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "110.0", "org_choices": ["140°", "110°", "70°", "120"], "choices": [140.0, 110.0, 70.0, 120.0], "label": 1}
+{"prob_id": 9798, "image_path": "images/9798.png", "question": "如图,AB是⊙O的直径,CD是⊙O的一条弦,且CD⊥AB于E,分别连接AD、BC,已知∠D=65°,则∠OCD=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠B=∠D=65°,CD⊥AB,∴∠BCE=90°-65°=25°,∵OB=OC,∴∠OCB=∠B=65°,∴∠OCD=65°-25°=40°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["30°", "35°", "40°", "45°"], "choices": [30.0, 35.0, 40.0, 45.0], "label": 2}
+{"prob_id": 9803, "image_path": "images/9803.png", "question": "如图,AB为⊙O的直径,CD为⊙O的弦,∠ACD=42°,则∠BAD=()°．. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BD,∵∠ACD=42°,∴∠ABD=42°,∵AB为直径,∴∠ADB=90°,∴∠BAD=890°-∠ABD=48°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "48.0", "org_choices": ["42", "48", "60", "45"], "choices": [42.0, 48.0, 60.0, 45.0], "label": 1}
+{"prob_id": 9814, "image_path": "images/9814.png", "question": "如图,AB是O的直径,∠AOC=110°,则∠D=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "】解:∵∠AOC=110°,∴∠BOC=180°-110°=70°,∴∠D=\\frac{1}{2}∠BOC=35°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["24°", "22°", "20°", "35°"], "choices": [24.0, 22.0, 20.0, 35.0], "label": 3}
+{"prob_id": 9829, "image_path": "images/9829.png", "question": "如图,AB是⊙O的直径,点C在⊙O上,若∠ABC=30°,则∠CAB为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连结BE,如图,∵AB为直径,∴∠ACB=90°,∴∠CAB=90°-∠ABC=90°-30°=60°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["30°", "45°", "60°", "75°"], "choices": [30.0, 45.0, 60.0, 75.0], "label": 2}
+{"prob_id": 9832, "image_path": "images/9832.png", "question": "如图,P是⊙O外一点,PA、PB分别交⊙O于C、D两点,已知⁀{AB}和⁀{CD}所对的圆心角分别为90°和50°,则∠P=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵⁀{AB}和⁀{CD}所对的圆心角分别为90°和50°,∴∠A=25°,∠ADB=45°,∵∠P+∠A=∠ADB,∴∠P=∠ADB-∠P=45°-25°=20°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["45°", "40°", "25°", "20°"], "choices": [45.0, 40.0, 25.0, 20.0], "label": 3}
+{"prob_id": 9868, "image_path": "images/9868.png", "question": "如图,已知A、B、C三点在⊙O上,AC⊥BO于D,∠B=50°,则∠BOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AC⊥BO,∴∠ADB=90°,∴∠A=90°-∠B=90°-50°=40°,∴∠BOC=2∠A=80°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["80°", "60°", "50°", "40°"], "choices": [80.0, 60.0, 50.0, 40.0], "label": 0}
+{"prob_id": 9874, "image_path": "images/9874.png", "question": "如图,⊙O中,弦AB的长为2,OC⊥AB于C,OC=1,若从⊙O外一点P作⊙O的两条切线,切点分别为A、B,则∠APB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连OA,OB．PA,PB是切线,则∠OAP=∠OBP=90°．OC⊥AB⇒AC=BC=1=OC⇒△ACO,△BCO是等腰直角三角形⇒∠AOB=90°⇒四边形AOBP是正方形⇒∠APB=90°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "90.0", "org_choices": ["120°", "90°", "60°", "45°"], "choices": [120.0, 90.0, 60.0, 45.0], "label": 1}
+{"prob_id": 9893, "image_path": "images/9893.png", "question": "如图,在△ABC中,AB=10,AC=8,BC=6,经过点C且与边AB相切的动圆与CA、CB分别相交于点P、Q,则线段PQ长度的最小值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,设QP的中点为F,圆F与AB的切点为D,连接FD、CF、CD,则FD⊥AB．∵AB=10,AC=8,BC=6,∴∠ACB=90°,FC+FD=PQ,∴FC+FD＞CD,∵当点F在直角三角形ABC的斜边AB的高CD上时,PQ=CD有最小值,∴CD=BC•AC÷AB=4.8．故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.8", "org_choices": ["4.75", "4.8", "5", "4√{2}"], "choices": [4.75, 4.8, 5.0, 5.657], "label": 1}
+{"prob_id": 9894, "image_path": "images/9894.png", "question": "如图,在△ABC中,AB=2,AC=1,以AB为直径的圆与AC相切,与边BC交于点D,则AD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB为直径的圆与AC相切,∴∠CAB=∠ADB=90°,∵AB=2,AC=1,∴BC=√{5},∵AD•BC=AC•AB,∴AD=\\frac{AC\\cdotAB}{BC}=\\frac{2}{5}√{5}．故选:A．", "dataset_name": "Geoqa", "ground_truth": "0.8944271909999159", "org_choices": ["\\frac{2}{5}√{5}", "\\frac{4}{5}√{5}", "\\frac{2}{5}√{3}", "\\frac{4}{5}√{3}"], "choices": [0.894, 1.789, 0.693, 1.386], "label": 0}
+{"prob_id": 9901, "image_path": "images/9901.png", "question": "如图,AB是⊙O的直径,点C在AB的延长线上,CD与⊙O相切,切点为D．如果∠A=35°,那么∠C等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BD,AB是⊙O的直径,则∠ADB=90°,∠ABD=90°-∠A=55°∴BDC=∠A=35°,∴∠C=∠ABD-∠BDC=20°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["20°", "30°", "35°", "55°"], "choices": [20.0, 30.0, 35.0, 55.0], "label": 0}
+{"prob_id": 9918, "image_path": "images/9918.png", "question": "如图,Rt△ABC中,∠ACB=90°,AC=4,BC=3,以AC为直径的圆交AB于D,则AD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接CD,∵Rt△ABC中,∠ACB=90°,AC=4,BC=3,∴根据勾股定理得:AB=√{AC²+BC²}=5,∵AC为直径,∴CD⊥AB,∴CD=\\frac{AC\\cdotBC}{AB}=\\frac{12}{5},∴AD=√{AC²-CD²}=\\frac{16}{5}．故选:C．", "dataset_name": "Geoqa", "ground_truth": "3.2", "org_choices": ["\\frac{9}{5}", "\\frac{12}{5}", "\\frac{16}{5}", "4"], "choices": [1.8, 2.4, 3.2, 4.0], "label": 2}
+{"prob_id": 1019, "image_path": "images/1019.png", "question": "如图,已知AD与BC相交于点O,AB∥CD,如果∠B=40°,∠D=30°,则∠AOC的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB//CD,∴∠A=∠D=30°由三角形的外角的性质得∠AOC=∠A+∠B=70°故选:B.", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["60°", "70°", "80°", "120°"], "choices": [60.0, 70.0, 80.0, 120.0], "label": 1}
+{"prob_id": 1031, "image_path": "images/1031.png", "question": "如图,在△ABC中,AB=AC,D是BC的中点,∠B=40°,则∠BAD=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB=AC,D是BC的中点,∴AD⊥BC,∵∠B=40°,∴∠BAD=90°-40°=50°故选C", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["100°", "80°", "50°", "40°"], "choices": [100.0, 80.0, 50.0, 40.0], "label": 2}
+{"prob_id": 1042, "image_path": "images/1042.png", "question": "如图,∠A=70°,∠2=130°,则∠1=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图,∵∠2=130°,∴∠3=180°-∠2=180°-130°=50°,∴∠1=∠A+∠3=70°+50°=120°.故选B", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["130°", "120°", "140°", "110°"], "choices": [130.0, 120.0, 140.0, 110.0], "label": 1}
+{"prob_id": 1053, "image_path": "images/1053.png", "question": "如图所示,在四边ABCD中,∠BAD=120°,∠B=∠D=90°,若在BC和CD上分别找一点M,使得△AMN的周长最小,则此时∠AMN+∠ANM的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "作A关于BC和CD的对称点A'\",A\",连接A'A\",交BC于M,交CD于N,则A'A\"即为△AMN的周长最小值.∵∠DAB=120°∴∠AA′M+∠A\"=180^{°}-120^{°}=60^{°},∵∠MA'A=∠MAA',∠NAD=∠A\",且∠MA'A+∠MAA'=∠AMN,∠NAD+∠A\"=∠ANMr∴∠AMN+∠ANM=∠MA'A+∠MAA'+∠NAD+∠A\"=2(∠AA'M+∠A\")=2×60°=120°,故选B.", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["110°", "120°", "140°", "150°"], "choices": [110.0, 120.0, 140.0, 150.0], "label": 1}
+{"prob_id": 1060, "image_path": "images/1060.png", "question": "如图,将长方形ABCD沿线段OG折叠到OB'C'G的位置,∠OGC'等于100°,则∠DGC'的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵将长方形ABCD沿线段OG折叠到OB'C'G的位置,∠OGC'等于100°,∴∠OGC=∠OGC'=100°,∴∠OGD=180°-∠OGC=80°,∴∠DGC'=∠OGC-∠OGD=20°故选A.", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["20°", "25°", "30°", "40°"], "choices": [20.0, 25.0, 30.0, 40.0], "label": 0}
+{"prob_id": 1064, "image_path": "images/1064.png", "question": "如图,AB是⊙O的直径,若∠BDC=40°,则∠BOC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∠BOC=2∠BDC=80°故选:B.", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["40°", "80°", "14°", "无法确定"], "choices": [40.0, 80.0, 14.0], "label": 1}
+{"prob_id": 1073, "image_path": "images/1073.png", "question": "如图,将△ABC折叠,使点A与BC边中点D重合,折痕为MN,若AB=9,BC=6,则△DNB的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵D是BC的中点,BC=6∴BD=3,由折叠的性质可知DN=AN,∴△DNB的周长=DN+BN+BD=AN+BN+BD=AB+BD=9+3=12.故选A.", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["12", "13", "14", "15"], "choices": [12.0, 13.0, 14.0, 15.0], "label": 0}
+{"prob_id": 1076, "image_path": "images/1076.png", "question": "如图,▱ABCD的周长为36,对角线AC、BD相交于点O,点E是CD的中点,BD=12,则△DOE的周长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵\\sqsubsetABCD的周长为36,∴2(BC+CD)=36,则BC+CD=18∵四边形ABCD是平行四边形,对角线AC,BD相交于点O,BD=12又∵点E是CD的中点,DE=\\frac{1}{2}CD,∴OE是△BCD的中位线,∴OE=\\frac{1}{2}BC,∴△DOE的周长=OD+OE+DE=\\frac{1}{2}BD+\\frac{1}{2}(BC+CD)=6+9=15,即△DOE的周长为15.故选A", "dataset_name": "Geoqa", "ground_truth": "15.0", "org_choices": ["15", "18", "21", "24"], "choices": [15.0, 18.0, 21.0, 24.0], "label": 0}
+{"prob_id": 1087, "image_path": "images/1087.png", "question": "如图,点A、B、C、D在⊙O上,∠AOC=140°,点B是弧AC的中点,则∠D的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "连接OB,∵点B是弧AC的中点,∴∠AOB=\\frac{1}{2}∠AOC=70^{°},由圆周角定理得,∠D=\\frac{1}{2}∠AOB=35^{°}故答案选:D.", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["70°", "55°", "35.5°", "35°"], "choices": [70.0, 55.0, 35.5, 35.0], "label": 3}
+{"prob_id": 1092, "image_path": "images/1092.png", "question": "如图,AB是⊙O的直径,点C,D在⊙O上．若∠ABD=50°,则∠BCD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "连接AD,∵AB是⊙O的直径,∴∠ADB=90°.∠ABD=50°∴∠∠DAB=90^{°}-50^{°}=40^{°}∴∠BCD=∠DAB=40°.故选C.", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["30°", "35°", "40°", "45°"], "choices": [30.0, 35.0, 40.0, 45.0], "label": 2}
+{"prob_id": 1108, "image_path": "images/1108.png", "question": "如图,在△ABC中,∠CAB=30°,将△ABC在平面内绕点A逆时针旋转到△AB'C'的位置,且CC'∥AB,则旋转角的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵△ABC在平面内绕点A逆时针旋转到△AB'C'的位置,∴AC=AC,∠CAC为旋转角,∵CC'//AB,∴∠ACC'=∠CAB=30°∵AC=AC'∴∠AC'C=∠ACC'=30°,∴∠CAC'=180°-30°-30°=120°∴旋转角的度数为120°,故选B.", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["100°", "120°", "110°", "130°"], "choices": [100.0, 120.0, 110.0, 130.0], "label": 1}
+{"prob_id": 1128, "image_path": "images/1128.png", "question": "如图,O是直线AB上一点,∠1=40°,OD平分∠BOC,则∠2的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠1=40°,∴∠COB=180°-40°=140°.OD平分∠BOC,∴∠2=\\frac{1}{2}∠BOC=\\frac{1}{2}×140^{°}=70^{°}故选:D.", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["20°", "30°", "50°", "70°"], "choices": [20.0, 30.0, 50.0, 70.0], "label": 3}
+{"prob_id": 1131, "image_path": "images/1131.png", "question": "如图所示,是一株美丽的勾股树,其中所有的四边形都是正方形,所有的三角形都是直角三角形,若正方形A．B、C、D的面积分别为2,5,1,2．则最大的正方形E的面积是().. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "根据勾股定理,可知,以直角边为边长的正方形的面积和等于以斜边为边的正方形的面积.即S_{A}+S_{B}+S_{C}+S_{D}=S_{E}=2+5+1+2=10故选B", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": [".9", "10", "11", "12"], "choices": [0.9, 10.0, 11.0, 12.0], "label": 1}
+{"prob_id": 1147, "image_path": "images/1147.png", "question": "如图,直线AB,CD被BC所截,若AB∥CD,∠1=45°,∠2=35°,则∠3=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB//CD,∠1=45°,∴∠C=∠1=45°∵∠2=35°,∴∠3=∠2+∠C=35°+45°=80°.故选A.", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["80°", "70°", "60°", "90°"], "choices": [80.0, 70.0, 60.0, 90.0], "label": 0}
+{"prob_id": 1150, "image_path": "images/1150.png", "question": "如图,在Rt△ABC中,∠BAC=90°,将△ABC绕点A顺时针旋转90°后得到△AB′C′(点B的对应点是点B′,点C的对应点是点C′),连接CC′.若∠CC′B′=32°,则∠AC′B′的大小是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵△ABC绕点A顺时针旋转90°后得到△AB'C',∴AC=AC',∠B=∠AB'C,∠CAC'=90°,∴△ACC为等腰直角三角形,∴∠ACC'=∠AC'C=45°,∵∠CC'B'=32°∴∠AC'B'=∠AC'C-∠CC'B'=45°-32°=13°,∴∠B=13°故答案选:C.", "dataset_name": "Geoqa", "ground_truth": "13.0", "org_choices": ["32°", "45°", "13°", "30°"], "choices": [32.0, 45.0, 13.0, 30.0], "label": 2}
+{"prob_id": 1167, "image_path": "images/1167.png", "question": "已知:如图,AB∥CD,BC平分∠ABD,且∠C=40°,则∠D的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵AB∥CD∴∠ABC=∠C=40°又∵BC平分∠ABD,∴∠DBC=∠ABC=40°∴△BCD中,∠D=180°-40°-40°=100°,故选D.", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["40°", "80°", "90°", "100°"], "choices": [40.0, 80.0, 90.0, 100.0], "label": 3}
+{"prob_id": 1191, "image_path": "images/1191.png", "question": "已知直线a∥b,∠1和∠2互余,∠3=121°,那么∠4等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图:∵a∥b,∴∠2+∠5=180°,∵∠3=∠5=121°,∴∠2=59°,∵∠2和∠1互余,∴∠1=90°59°=31°,∵a∥b,∴∠1+∠4=180°,∴∠4=149°,故选B", "dataset_name": "Geoqa", "ground_truth": "149.0", "org_choices": ["159°", "149°", "139°", "21°"], "choices": [159.0, 149.0, 139.0, 21.0], "label": 1}
+{"prob_id": 1215, "image_path": "images/1215.png", "question": "在△ABC中,AB=AC,D、E分别在BC、AC上,AD=AE,∠CDE=20°,则∠BAD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵∠ADC是三角形ABD的外角,∠AED是三角形DEC的一个外角,∠CDE=20°,∴∠ADC=∠BAD+∠B=∠ADE+∠EDC,∠AED=∠EDC+∠C,∠B+∠BAD=∠ADE+20°,∠AED=∠C+20°.∵AB=AC,AD=AE,∠CDE=20°,∴∠B=∠C,∠ADE=∠AED=∠C+20°,∴∠C+∠BAD=∠C+20°+20°,∴∠BAD=40°故选B.", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["36°", "40°", "45°", "50°"], "choices": [36.0, 40.0, 45.0, 50.0], "label": 1}
+{"prob_id": 1228, "image_path": "images/1228.png", "question": "如图,直线m∥n,Rt△ABC的顶点A在直线n上,∠C=90°,AB,CB分别交直线m于点D和点E,且DB=DE,若∠B=25°,则∠1的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,∵DB=DE,∠B=25°,∴∠2=25°∴∠3=25°+25°=50°,∵m\\vertn,∴∠4=50°∵∠C=90°∴∠5=65°,∴∠1=180°-50°-65°=65°.故选B.", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["60°", "65°", "70°", "75°"], "choices": [60.0, 65.0, 70.0, 75.0], "label": 1}
+{"prob_id": 1229, "image_path": "images/1229.png", "question": "如图,直线a∥b,直线c与直线a,b分别相交于点A,B,AM⊥b,垂足为点M．如果∠1=58°,那么∠2=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵直线a∥b,∠1=58°,∴∠ABM=∠1=58°∵AM⊥b,垂足为点M,∴∠AMB=90°∴∠2=180°-∠1-∠ABM=180°-58°-90°=32°.故选A.", "dataset_name": "Geoqa", "ground_truth": "32.0", "org_choices": ["32°", "58°", "42°", "122°"], "choices": [32.0, 58.0, 42.0, 122.0], "label": 0}
+{"prob_id": 1247, "image_path": "images/1247.png", "question": "如图,把一块直角三角板的直角顶点放在直尺的一边上,若∠1=30°,则∠2是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图所示∵∠1+∠3=90°,且∠1=30°∴∠3=90°-∠1=60°∵直尺两边互相平行∴∠2=∠3=60°故选D.", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["45°", "50°", "55°", "60°"], "choices": [45.0, 50.0, 55.0, 60.0], "label": 3}
+{"prob_id": 1248, "image_path": "images/1248.png", "question": "如图,AB⊥CD于D,DE⊥DF,若∠BDE=60°,则∠CDF等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB⊥CD,DE⊥DF,∴∠BDC=∠EDF=90°,∴∠CDF+∠CDE=∠CDE+∠BDE=90°,∴∠CDF=∠BDE=60°,故选:C.", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["30°", "45°", "60°", "120°"], "choices": [30.0, 45.0, 60.0, 120.0], "label": 2}
+{"prob_id": 1264, "image_path": "images/1264.png", "question": "如图,测得BD=120m,DC=60m,EC=50m,则河宽AB为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ADB=∠EDC,∠ABC=∠ECD=90°,∴△ABD\\sim△ECD,∴\\frac{AB}{EC}=\\frac{BD}{CD},∴AB=\\frac{BD×EC}{CD}=\\frac{120×50}{60}=100(米).则两岸间的大致距离为100米.故选:B.", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["120m", "100m", "75m", "25m"], "choices": [120.0, 100.0, 75.0, 25.0], "label": 1}
+{"prob_id": 1280, "image_path": "images/1280.png", "question": "如图,在△ABE中,AE的垂直平分线MN交BE于点C,∠E=30°,且AB=CE,则∠BAE的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:已知在△ABE中,AE的垂直平分线MN交BE于点C,∠E=30°,且AB=CE,故CE=CA=AB,∠ACB=∠ABC=∠CEA+∠CAE=60°,故∠CAB=60°即∠BAE=∠CAB+∠CAE=60+30°=90°.故选C.", "dataset_name": "Geoqa", "ground_truth": "90.0", "org_choices": ["80°", "85°", "90°", "105°"], "choices": [80.0, 85.0, 90.0, 105.0], "label": 2}
+{"prob_id": 1293, "image_path": "images/1293.png", "question": "如图,在△ABC中,D、E分别是AB、AC边上的点,DE∥BC,∠ADE=35°,∠C=120°,则∠A为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵DE//BC,∠C=120°,∴∠AED=∠C=120°∵∠ADE=35°,∠ADE+∠AED+∠A=180°,∴∠A=180°-∠AED-∠ADE=180°-120°-35°=25°.故选D.", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["60°", "45°", "35°", "25°"], "choices": [60.0, 45.0, 35.0, 25.0], "label": 3}
+{"prob_id": 1315, "image_path": "images/1315.png", "question": "如图,点A,B,C在⊙O上,∠AOB=72°,则∠ACB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "根据圆周角定理可知,∠AOB=2∠ACB=72°,则∠ACB=36°,故选A.", "dataset_name": "Geoqa", "ground_truth": "36.0", "org_choices": ["36°", "54°", "18°", "28°"], "choices": [36.0, 54.0, 18.0, 28.0], "label": 0}
+{"prob_id": 1342, "image_path": "images/1342.png", "question": "将一张长方形纸片按如图所示折叠后,再展开．如果∠1=56°,那么∠2等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "根据题意知:折叠所重合的两个角相等.再根据两条直线平行,同旁内角互补,得:2∠1+∠2=180°,解得:∠2=180°-2∠1=68°.故选D.", "dataset_name": "Geoqa", "ground_truth": "68.0", "org_choices": ["56°", "62°", "66°", "68°"], "choices": [56.0, 62.0, 66.0, 68.0], "label": 3}
+{"prob_id": 1346, "image_path": "images/1346.png", "question": "如图,直线a∥b,∠1=72°,则∠2的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "∵直线a//b,∴∠2=∠3,∵∠1=72°∴∠3=108°,∴∠2=108°故选:B.", "dataset_name": "Geoqa", "ground_truth": "108.0", "org_choices": ["118°", "108°", "98°", "72°"], "choices": [118.0, 108.0, 98.0, 72.0], "label": 1}
+{"prob_id": 1354, "image_path": "images/1354.png", "question": "如图,一个含有30°角的直角三角板的两个顶点放在一个矩形的对边上,如果∠1=25°,那么∠2的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "如图,∵四边形ABCD是矩形,∴AD//BC,∴∠2=∠DEF,∵∠1=25^{°},∠GEF=90^{°},∴∠2=25^{°}+90^{°}=115^{°},故选C.", "dataset_name": "Geoqa", "ground_truth": "115.0", "org_choices": ["130°", "105°", "115°", "125°"], "choices": [130.0, 105.0, 115.0, 125.0], "label": 2}
+{"prob_id": 1368, "image_path": "images/1368.png", "question": "如图,已知AB、AD是圆O的弦,∠ABO=30°,∠ADO=20°,则∠BAD=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接AO,则AO=BO=DO∠ABO=∠BAO;∠ADO=∠DAO∵∠ABO=30°,∠ADO=20°∴∠BAD=∠BAO+∠DAO=20^{°}+30^{°}=50^{°}.故选C.", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["30°", "40°", "50°", "60°"], "choices": [30.0, 40.0, 50.0, 60.0], "label": 2}
+{"prob_id": 1377, "image_path": "images/1377.png", "question": "如图,C、D是线段AB上两点,若CB=4cm,DB=7cm,且D是AC的中点,则AB的长等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BD=7cm,BC=4cm,∴CD=BD-BC=3cm,∵D是AC的中点,∴AC=2CD=6cm,∴AB=AC+BC=10cm,故选:B.", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["9cm", "10cm", "12cm", "14cm"], "choices": [9.0, 10.0, 12.0, 14.0], "label": 1}
+{"prob_id": 1398, "image_path": "images/1398.png", "question": "如图所示,C、D是线段AB上两点,若AC=3cm,C为AD中点且AB=10cm,则DB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵点C为AD的中点,AC=3cm,∴CD=3cm.∵AB=10cm,AC+CD+DB=AB,∴BD=10-3-3=4cm.故答案选:A.", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["4cm", "5cm", "6cm", "7cm"], "choices": [4.0, 5.0, 6.0, 7.0], "label": 0}
+{"prob_id": 1417, "image_path": "images/1417.png", "question": "如图,⊙O中,AC为直径,MA,MB分别切⊙O于点A,B,∠BAC=25°,则∠AMB的大小为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵MA切⊙O于点A,AC为直径,∴∠MAC=90°,又∠BAC=25°,∠MAB=∠MAC-∠BAC=65°∵MA、MB分别切⊙O于点A、B,∴MA=MB,∴∠MAB=∠MBA=65°,∴∠AMB=180-(∠MAB+∠MBA)=50°故选:D.", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["25°", "30°", "45°", "50°"], "choices": [25.0, 30.0, 45.0, 50.0], "label": 3}
+{"prob_id": 1444, "image_path": "images/1444.png", "question": "已知:AB∥CD,∠ABE=120°,∠C=25°,则∠α度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "过点E作EF//CD∴∠C=∠FEC(两直线平行,内错角相等),∴∠FEC=25°∵AB//CD(已知),∴EF//AB(平行于同一直线的两直线平行),∴∠B+∠BEF=180°(两直线平行1同旁内角互补)∴∠BEF=60°∴∠α=∠BEF+∠FEC=85°.故选:C.", "dataset_name": "Geoqa", "ground_truth": "85.0", "org_choices": ["60°", "75°", "85°", "80°"], "choices": [60.0, 75.0, 85.0, 80.0], "label": 2}
+{"prob_id": 1457, "image_path": "images/1457.png", "question": "如图,直线AB、CD相交于点O,OD平分∠AOE,∠BOC=50°,则∠EOB=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BOC=50°,∴∠AOD=50°,∴∠AOE=100°,∠EOB=180°-100°=80°,故选D.", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["50°", "60°", "70°", "80°"], "choices": [50.0, 60.0, 70.0, 80.0], "label": 3}
+{"prob_id": 1459, "image_path": "images/1459.png", "question": "如图一棵大树在离地面9米高的B处断裂,树顶A落在离树底部C的12米处,则大树断裂之前的高度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "由题意得BC=91AC=12,在直角三角形ABC中1根据勾股定理得:AB=√{9²+12²}=15米所以大树的高度是15+9=24米,故选D.", "dataset_name": "Geoqa", "ground_truth": "24.0", "org_choices": ["9米", "15米", "21米", "24米"], "choices": [9.0, 15.0, 21.0, 24.0], "label": 3}
+{"prob_id": 1468, "image_path": "images/1468.png", "question": "如图,过⊙O上一点A作⊙O的切线,交直径BC的延长线与点D,连接AB,若∠B=25°,则∠D的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OA∵∠B=25°.∴∠DOA=2∠B=50°.∵AD是⊙的切线,∴∠OAD=90°.∴∠D=180°-90°-50°=40°故选B.", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["25°", "40°", "45°", "50°"], "choices": [25.0, 40.0, 45.0, 50.0], "label": 1}
+{"prob_id": 1472, "image_path": "images/1472.png", "question": "如图所示,将含有30°角的三角板(∠A=30°)的直角顶点放在相互平行的两条直线其中一条上,若∠1=38°,则∠2的度数(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图1延长AB交CF于E,∵∠ACB=90°,∠A=30°∴∠ABC=60°,∵∠1=38°,∴∠AEC=∠ABC-∠1=22°,∵GH||EF,∴∠2=∠AEC=22°故选B.", "dataset_name": "Geoqa", "ground_truth": "22.0", "org_choices": ["28°", "22°", "32°", "38°"], "choices": [28.0, 22.0, 32.0, 38.0], "label": 1}
+{"prob_id": 1484, "image_path": "images/1484.png", "question": "如图,小明从点A向北偏东80°方向走到B点,又从B点向南偏西25°方向走到点C,则∠ABC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "|N_{2}B,如图,∠1=80°,∵N_{1}A||N_{2}A∴∠1=∠2+∠3=80^{°},∵∠3=25^{°},∴∠2=80^{°}-∠3=80^{°}-25^{°}=55^{°}即∠ABC=55°故选A.", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["55°", "50°", "45°", "40°"], "choices": [55.0, 50.0, 45.0, 40.0], "label": 0}
+{"prob_id": 1485, "image_path": "images/1485.png", "question": "如图,已知直线AB,CD相交于点O,OE⊥AB,∠EOC=30°,则∠BOD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:因为OE⊥AB,∠EOC=30°,所以∠COB=90°-30°=60°,因为∠COB+∠BOD=180°,所以∠BOD=180-60°=120°,故选C.", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["60°", "30°", "120°", "150°"], "choices": [60.0, 30.0, 120.0, 150.0], "label": 2}
+{"prob_id": 7034, "image_path": "images/7034.png", "question": "某几何体的三视图如图所示,其中主视图和左视图均为边长为2的等边三角形,则该几何体的表面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由三视图可知:该几何体是一个圆锥,其轴截面是一个边长为2的正三角形．S~表面积~=S~圆锥侧面积~+S~圆~=\\frac{1}{2}×2π×1×2+π×1²=3π．故选:B．", "dataset_name": "Geoqa", "ground_truth": "9.42477796076938", "org_choices": ["4π", "3π", "2π", "π"], "choices": [12.566, 9.425, 6.283, 3.142], "label": 1}
+{"prob_id": 7065, "image_path": "images/7065.png", "question": "如图,在直角三角形ABC中,∠C=90°,AB=5,AC=4,则sin∠B的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在直角三角形ABC中,∠C=90°,AB=5,AC=4,∴sin∠B=AC:AB=4:5．故选:B．", "dataset_name": "Geoqa", "ground_truth": "0.8", "org_choices": ["\\frac{3}{5}", "\\frac{4}{5}", "\\frac{3}{4}", "\\frac{4}{3}"], "choices": [0.6, 0.8, 0.75, 1.333], "label": 1}
+{"prob_id": 7100, "image_path": "images/7100.png", "question": "如图,在Rt△ABC中,∠C为直角,CD⊥AB于D,已知AC=3,AB=5,则tan∠BCD等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠C为直角,CD⊥AB,∴∠A+∠B=90°,∠BCD+∠B=90°,∴∠BCD=∠A,∵∠C为直角,AC=3,AB=5,∴BC=√{AB²-AC²}=4,∴tanA=\\frac{4}{3},∴tan∠BCD=\\frac{4}{3},故选:B．", "dataset_name": "Geoqa", "ground_truth": "1.3333333333333333", "org_choices": ["\\frac{3}{4}", "\\frac{4}{3}", "\\frac{3}{5}", "\\frac{4}{5}"], "choices": [0.75, 1.333, 0.6, 0.8], "label": 1}
+{"prob_id": 7124, "image_path": "images/7124.png", "question": "如图,在△ABC中,DE∥BC,若AD=3,DB=6,DE=2.5,则BC长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴△ADE∽△ABC．∴\\frac{AD}{AB}=\\frac{DE}{BC},即\\frac{3}{9}=\\frac{2.5}{BC},解得BC=7.5．故选:C．", "dataset_name": "Geoqa", "ground_truth": "7.5", "org_choices": ["5", "5.5", "7.5", "10"], "choices": [5.0, 5.5, 7.5, 10.0], "label": 2}
+{"prob_id": 7141, "image_path": "images/7141.png", "question": "如图,在Rt△ABC中,∠BAC=90°,AB=3,AC=4,点P为BC上任意一点,连接PA,以PA,PC为邻边作平行四边形PAQC,连接PQ,则PQ的最小值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BAC=90°,AB=3,AC=4,∴BC=√{AC²+AB²}=5,∵四边形APCQ是平行四边形,∴PO=QO,CO=AO,∵PQ最短也就是PO最短,∴过O作BC的垂线OP′,∵∠ACB=∠P′CO,∠CP′O=∠CAB=90°,∴△CAB∽△CP′O,∴\\frac{CO}{BC}=\\frac{OP'}{AB},∴\\frac{2}{5}=\\frac{OP'}{3},∴OP′=\\frac{6}{5},∴则PQ的最小值为2OP′=\\frac{12}{5},故选:B．", "dataset_name": "Geoqa", "ground_truth": "2.4", "org_choices": ["\\frac{6}{5}", "\\frac{12}{5}", "\\frac{5}{3}", "2"], "choices": [1.2, 2.4, 1.667, 2.0], "label": 1}
+{"prob_id": 7161, "image_path": "images/7161.png", "question": "如图,AB∥CD,AB=6,CD=9,AD=10,则OD的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB∥CD,∴△AOB∽△DOC,∴\\frac{AB}{CD}=\\frac{AO}{OD},∵AB=6,CD=9,AD=10,∴\\frac{6}{9}=\\frac{10-OD}{OD},∴OD=6,故选:C．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["4", "5", "6", "7"], "choices": [4.0, 5.0, 6.0, 7.0], "label": 2}
+{"prob_id": 7165, "image_path": "images/7165.png", "question": "如图,在△ABC中,DE∥BC,分别交AB,AC于点D,E．若AD=2,DB=3,BC=6,则DE的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AD=2,DB=3,∴AB=5,∵DE∥BC,∴△ADE∽△ABC,∴\\frac{AD}{AB}=\\frac{DE}{BC},∴\\frac{2}{5}=\\frac{DE}{6},∴DE=\\frac{12}{5},故选:C．．", "dataset_name": "Geoqa", "ground_truth": "2.4", "org_choices": ["4", "2.5", "\\frac{12}{5}", "10"], "choices": [4.0, 2.5, 2.4, 10.0], "label": 2}
+{"prob_id": 7185, "image_path": "images/7185.png", "question": "如图,AB为⊙O的直径,C为⊙O上一点,弦AD平分∠BAC,交BC于点E,AB=6,AD=5,则DE的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图1,连接BD、CD,∵AB为⊙O的直径,∴∠ADB=90°,∴BD=√{AB²-AD²}=√{6²-5²}=√{11},∵弦AD平分∠BAC,∴CD=BD=√{11},∴∠CBD=∠DAB,在△ABD和△BED中,≥ft\\{\\begin{matrix}∠BAD=∠EBD\\\\∠ADB=∠BDE\\\\\\end{matrix}\\right.\\∴△ABD∽△BED,∴\\frac{DE}{DB}=\\frac{DB}{AD},即\\frac{DE}{√{11}}=\\frac{√{11}}{5},解得DE=\\frac{11}{5}．故选:A．", "dataset_name": "Geoqa", "ground_truth": "2.2", "org_choices": ["2.2", "2.5", "2", "1.8"], "choices": [2.2, 2.5, 2.0, 1.8], "label": 0}
+{"prob_id": 7190, "image_path": "images/7190.png", "question": "如图,在△ABC中,DE∥BC,\\frac{AD}{DB}=\\frac{1}{2},DE=4,则BC的长(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴△ADE∽△ABC,∴\\frac{DE}{BC}=\\frac{AD}{AB},∵\\frac{AD}{DB}=\\frac{1}{2},∴\\frac{AD}{AB}=\\frac{1}{3},∴\\frac{DE}{BC}=\\frac{1}{3},∵DE=4,∴BC=12．故选:C．", "dataset_name": "Geoqa", "ground_truth": "12.0", "org_choices": ["8", "10", "12", "16"], "choices": [8.0, 10.0, 12.0, 16.0], "label": 2}
+{"prob_id": 7198, "image_path": "images/7198.png", "question": "如图,AD•AB=AE•AC,∠ADE=80°,∠A=60°,则∠B=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AD•AB=AE•AC,∴\\frac{AD}{AC}=\\frac{AE}{AB},且∠A为公共角,∴△ADE∽△ACB,∴∠C=∠ADE=80°,∴∠B=180°-∠A-∠C=180°-60°-80°=40°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["40°", "60°", "80°", "100°"], "choices": [40.0, 60.0, 80.0, 100.0], "label": 0}
+{"prob_id": 7217, "image_path": "images/7217.png", "question": "如图,DC∥EF∥AB,若\\frac{EG}{AB}=\\frac{1}{2},DC=6,则GF的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵EF∥AB,∴△DEG∽△DAB,∴\\frac{DG}{DB}=\\frac{EG}{AB}=\\frac{1}{2},即点G为DB的中点,∵DC∥EF,点G为DB的中点,∴GF=\\frac{1}{2}CD=3,故选:B．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["2", "3", "4", "1.5"], "choices": [2.0, 3.0, 4.0, 1.5], "label": 1}
+{"prob_id": 7219, "image_path": "images/7219.png", "question": "如右图,△ABC中,DE∥BC,\\frac{AD}{AB}=\\frac{2}{5},DE=3,则BC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥BC,∴△ADE∽△ABC,∴\\frac{DE}{BC}=\\frac{AD}{AB}=\\frac{2}{5},∴BC=\\frac{5}{2}DE=\\frac{5}{2}×3=\\frac{15}{2}．故选:A．", "dataset_name": "Geoqa", "ground_truth": "7.5", "org_choices": ["7.5", "4.5", "8", "6"], "choices": [7.5, 4.5, 8.0, 6.0], "label": 0}
+{"prob_id": 7220, "image_path": "images/7220.png", "question": "如图,在平行四边形ABCD中,E为BC的中点,AE、BD相交于点F．若△BFE的面积为3,则△ABF的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD为平行四边形,∴AD∥BC,AD=BC,∴△AFD∽△EFB,∴\\frac{AF}{EF}=\\frac{AD}{BE},而E为BC的中点,∴BE=\\frac{1}{2}BC=\\frac{1}{2}AD,∴\\frac{AF}{EF}=2,∴\\frac{S_{\\bigtriangleupBAF}}{S_{\\bigtriangleupBEF}}=\\frac{AF}{EF}=2,∴S~△ABF~=2S~△BFE~=6．故选:B．", "dataset_name": "Geoqa", "ground_truth": "6.0", "org_choices": ["3", "6", "9", "12"], "choices": [3.0, 6.0, 9.0, 12.0], "label": 1}
+{"prob_id": 7224, "image_path": "images/7224.png", "question": "如图,△ABC中,D、E分别为AB、AC的中点,已知△ADE的面积为1,那么△ABC的面积是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵D、E分别是AB、AC的中点,∴DE是△ABC的中位线,∴DE∥BC,\\frac{DE}{BC}=\\frac{1}{2},∴△ADE∽△ABC,∴\\frac{S_{\\bigtriangleupADE}}{S_{\\bigtriangleupABC}}=(\\frac{1}{2})²=\\frac{1}{4},∵△ADE的面积为1,∴S~△ABC~=4．故选:C．", "dataset_name": "Geoqa", "ground_truth": "4.0", "org_choices": ["2", "3", "4", "5"], "choices": [2.0, 3.0, 4.0, 5.0], "label": 2}
+{"prob_id": 7250, "image_path": "images/7250.png", "question": "如图,已知AB、CD、EF互相平行,且AB=1,CD=4,那么EF的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB、CD、EF都与BD垂直,∴AB∥CD∥EF,∴△DEF∽△DAB,△BEF∽△BCD,∴\\frac{EF}{AB}=\\frac{DF}{DB},\\frac{EF}{CD}=\\frac{BF}{BD},∴\\frac{EF}{AB}+\\frac{EF}{CD}=\\frac{DF}{DB}+\\frac{BF}{BD}=\\frac{BD}{BD}=1．∵AB=1,CD=4,∴\\frac{EF}{1}+\\frac{EF}{4}=1,∴EF=\\frac{4}{5}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "0.8", "org_choices": ["\\frac{1}{3}", "\\frac{2}{3}", "\\frac{3}{4}", "\\frac{4}{5}"], "choices": [0.333, 0.667, 0.75, 0.8], "label": 3}
+{"prob_id": 7251, "image_path": "images/7251.png", "question": "如图,在△ABC中,DE∥BC,分别交AB,AC于点D,E．若AE=3,EC=6,则\\frac{DE}{BC}的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵△ABC中,DE∥BC,∴\\frac{DE}{BC}=\\frac{AE}{AC}=\\frac{AE}{AE+EC}=\\frac{3}{3+6}=\\frac{1}{3},故选:D．", "dataset_name": "Geoqa", "ground_truth": "0.3333333333333333", "org_choices": ["\\frac{1}{9}", "\\frac{1}{6}", "\\frac{1}{4}", "\\frac{1}{3}"], "choices": [0.111, 0.167, 0.25, 0.333], "label": 3}
+{"prob_id": 7259, "image_path": "images/7259.png", "question": "如图,BE,CF为△ABC的两条高,若AB=6,BC=5,EF=3,则AE的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BE,CF为△ABC的两条高,∴∠AEB=∠AFC=90°,∵∠A=∠A,∴△AEB∽△AFC,∴\\frac{AE}{AF}=\\frac{AB}{AC},∵∠A=∠A,∴△AEF∽△ABC,∴\\frac{EF}{BC}=\\frac{AE}{AB},∵AB=6,BC=5,EF=3,∴\\frac{3}{5}=\\frac{AE}{6},∴AE=\\frac{18}{5},故选:A．", "dataset_name": "Geoqa", "ground_truth": "3.6", "org_choices": ["\\frac{18}{5}", "4", "\\frac{21}{5}", "\\frac{24}{5}"], "choices": [3.6, 4.0, 4.2, 4.8], "label": 0}
+{"prob_id": 7302, "image_path": "images/7302.png", "question": "如图,长4m的楼梯AB的倾斜角∠ABD为60°,为了改善楼梯的安全性能,准备重新建造楼梯,使其倾斜角∠ACD为45°,则调整后的楼梯AC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:在Rt△ABD中,∵sin∠ABD=\\frac{AD}{AB},∴AD=4sin60°=2√{3}(m),在Rt△ACD中,∵sin∠ACD=\\frac{AD}{AC},∴AC=\\frac{2√{3}}{sin45{^°}}=2√{6}(m)．故选:B．", "dataset_name": "Geoqa", "ground_truth": "4.898979485566356", "org_choices": ["2√{3}m", "2√{6}m", "(2√{3}-2)m", "(2√{6}-2)m"], "choices": [3.464, 4.899, 1.464, 2.899], "label": 1}
+{"prob_id": 7303, "image_path": "images/7303.png", "question": "如图是拦水坝的横断面,斜坡AB的水平宽度为12m,斜面坡度为1:2,则斜坡AB的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:由题意可得,AC=12m,BC:AC=1:2,∴BC=6m,又∵∠BCA=90°,∴AB=√{AC²+BC²}=√{12²+6²}=6√{5}m．故选:B．", "dataset_name": "Geoqa", "ground_truth": "13.416407864998739", "org_choices": ["4√{3}m", "6√{5}m", "12√{5}m", "24m"], "choices": [6.928, 13.416, 26.833, 24.0], "label": 1}
+{"prob_id": 7320, "image_path": "images/7320.png", "question": "如图,在离地面高度5m处引拉线固定电线杆,拉线和地面成60°角,则拉线AC的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵CD⊥AB且CD=5,∠A=∠B=60°,∴AC=\\frac{CD}{sinA}=\\frac{5}{sin60{^°}}=\\frac{10√{3}}{3}．故选:B．", "dataset_name": "Geoqa", "ground_truth": "5.773502691896257", "org_choices": ["10m", "\\frac{10√{3}}{3}m", "\\frac{5√{2}}{2}m", "5√{3}m"], "choices": [10.0, 5.774, 3.536, 8.66], "label": 1}
+{"prob_id": 7348, "image_path": "images/7348.png", "question": "如图,在△ABC中,点D、E分别是AB、AC的中点,若△ADE的面积为4,则△ABC的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在△ABC中,点D、E分别是AB、AC的中点,∴DE∥BC,DE=\\frac{1}{2}BC,∴△ADE∽△ABC,∵\\frac{DE}{BC}=\\frac{1}{2},∴\\frac{S_{\\bigtriangleupADE}}{S_{\\bigtriangleupABC}}=\\frac{1}{4},∵△ADE的面积为4,∴△ABC的面积为:16,故选:D．", "dataset_name": "Geoqa", "ground_truth": "16.0", "org_choices": ["8", "12", "14", "16"], "choices": [8.0, 12.0, 14.0, 16.0], "label": 3}
+{"prob_id": 7354, "image_path": "images/7354.png", "question": "如图,矩形ABCD中,AB=4,BC=2,点M在BC上,连接AM,作∠AMN=∠AMB,点N在直线AD上,MN交CD于点E,则BM•AN的最大值是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作NH⊥AM于点H,如右图所示,则∠NHM=90°,∵在矩形ABCD中,AB=4,BC=2,点M在BC上,∠AMN=∠AMB,∴AC=2√{5},AD∥BC,∴∠DAM=∠AMB,∴∠DAM=∠AMN,∴△AMN是等腰三角形,∴AN=MN,AH=MH,∵∠ABM=∠NHM=90°,∠AMB=∠NMH,∴△ABM∽△NHM,∴\\frac{BM}{HM}=\\frac{AM}{MN},∴BM•MN=AM•HM,∵点M在边BC上,AM=2HM,∴AM的最大值是AM=AC,此时AM=2√{5},∴BM•MN的最大值是:2√{5}\\cdot√{5}=10,∵MN=AN,∴BM•AN的最大值是10,故选:B．", "dataset_name": "Geoqa", "ground_truth": "10.0", "org_choices": ["\\frac{17}{2}", "10", "17", "20"], "choices": [8.5, 10.0, 17.0, 20.0], "label": 1}
+{"prob_id": 7398, "image_path": "images/7398.png", "question": "如图,△ABC中,∠ACB=90°,CD⊥AB于D,CD=4,BC=5,则AC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∠ACB=90°,CD⊥AB于D,CD=4,BC=5,由勾股定理得:BD=√{BC²-CD²}=√{5²-4²}=3,∵∠ACB=90°,CD⊥AB于D,∴∠B=90°-∠BCD=∠ACD,∠BDC=∠ADC,∴△BDC∽△CDA,∴\\frac{BC}{AC}=\\frac{BD}{CD},即\\frac{5}{AC}=\\frac{3}{4},解得:AC=\\frac{20}{3},故选:D．", "dataset_name": "Geoqa", "ground_truth": "6.666666666666667", "org_choices": ["3", "4", "\\frac{16}{3}", "\\frac{20}{3}"], "choices": [3.0, 4.0, 5.333, 6.667], "label": 3}
+{"prob_id": 7429, "image_path": "images/7429.png", "question": "如图,△ABC中有一正方形DEFG,其中D在AC上,E、F在AB上,直线AG分别交DE、BC于M、N两点．若∠B=90°,AB=8,BC=6,EF=2,则BN的长度为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形DEFG为正方形,∴∠AED=∠AFG=∠B=90°．∵∠DAE=∠CAB,∠GAF=∠NAB,∴△DAE∽△CAB,△GAF∽△NAB．∵AB=8,BC=6,EF=2,∴\\frac{AE}{AB}=\\frac{DE}{CB},即\\frac{AE}{8}=\\frac{2}{6},∴AE=\\frac{8}{3},∴AF=AE+EF=\\frac{14}{3}．∵△GAF∽△NAB,∴\\frac{BN}{GF}=\\frac{AB}{AF},即\\frac{BN}{2}=\\frac{8}{\\frac{14}{3}},∴BN=\\frac{24}{7}．故选:C．", "dataset_name": "Geoqa", "ground_truth": "3.4285714285714284", "org_choices": ["\\frac{8}{3}", "\\frac{16}{5}", "\\frac{24}{7}", "\\frac{7}{2}"], "choices": [2.667, 3.2, 3.429, 3.5], "label": 2}
+{"prob_id": 7462, "image_path": "images/7462.png", "question": "如图,在△ABC中,点D,E分别为边AB,AC上的点,且DE∥BC,若AD=5,BD=10,DE=3,则BC的长为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AD=5,BD=10,∴AB=15,∵DE∥BC,∴△ADE∽△ABC,∴\\frac{AD}{AB}=\\frac{DE}{BC},即\\frac{5}{15}=\\frac{3}{BC},∴BC=9,故选:C．", "dataset_name": "Geoqa", "ground_truth": "9.0", "org_choices": ["3", "6", "9", "12"], "choices": [3.0, 6.0, 9.0, 12.0], "label": 2}
+{"prob_id": 8501, "image_path": "images/8501.png", "question": "如图,△ABC内接于⊙O,∠BAC=120°,AB=AC,BD为⊙O的直径,AB=3,则AD的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BAC=120°,AB=AC,∴∠ACB=30°,∴∠ACB=∠ADB=30°,∵BD是⊙O的直径,∴∠BAD=90°,∵AB=3,∴AD=\\frac{AB}{tan30°}=\\frac{3}{\\frac{√{3}}{3}}=3√{3}．故选:D．", "dataset_name": "Geoqa", "ground_truth": "5.196152422706632", "org_choices": ["6", "3√{5}", "5", "3√{3}"], "choices": [6.0, 6.708, 5.0, 5.196], "label": 3}
+{"prob_id": 8505, "image_path": "images/8505.png", "question": "如图,在⊙O中,∠ABC=130°,则∠AOC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∠1=2∠ABC=2×130°=260°,则∠AOC=360°-∠1=360°-260°=100°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "100.0", "org_choices": ["50°", "80°", "90°", "100°"], "choices": [50.0, 80.0, 90.0, 100.0], "label": 3}
+{"prob_id": 8522, "image_path": "images/8522.png", "question": "如图,AC、BC是两个半圆的直径,∠ACP=30°,若AB=20cm,则PQ的值为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接BQ,AP,如图,∵AC,BC为直径,∴∠APC=90°,∠BQC=90°,∵∠ACP=30°,∴PC=\\frac{√{3}}{2}AC,CQ=\\frac{√{3}}{2}BC,∴PQ=PC-CQ=\\frac{√{3}}{2}(AC-BC)=\\frac{√{3}}{2}AB=\\frac{√{3}}{2}×20=10√{3}(cm)．故选:B．", "dataset_name": "Geoqa", "ground_truth": "17.320508075688775", "org_choices": ["10cm", "10√{3}cm", "12cm", "16cm"], "choices": [10.0, 17.321, 12.0, 16.0], "label": 1}
+{"prob_id": 8523, "image_path": "images/8523.png", "question": "如图,四边形ABCD中,AB=AC=AD,∠CBD=23°,则∠CAD为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD中,AB=AC=AD,∴B、C、D三点在以A为圆心,AD为半径的圆上．∵∠CBD=23°,∴∠CAD=2∠CBD=46°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "46.0", "org_choices": ["47°", "46°", "45°", "44°"], "choices": [47.0, 46.0, 45.0, 44.0], "label": 1}
+{"prob_id": 8524, "image_path": "images/8524.png", "question": "如图,⊙O是△ABC的外接圆,∠BCO=40°,则∠A的度数等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OC=OB,∠BCO=40°,∴∠OBC=40°,∴∠BOC=180°-40°-40°=100°,∴∠A=100°×\\frac{1}{2}=$50°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["60°", "50°", "45°", "40°"], "choices": [60.0, 50.0, 45.0, 40.0], "label": 1}
+{"prob_id": 8528, "image_path": "images/8528.png", "question": "如图,A、B、C是⊙O上的三个点,∠ABC=25°,则∠AOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ABC=25°,∠AOC=2∠ABC,∴∠AOC=50°,故选:D．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["25°", "30°", "40°", "50°"], "choices": [25.0, 30.0, 40.0, 50.0], "label": 3}
+{"prob_id": 8535, "image_path": "images/8535.png", "question": "如图,A、B、C是⊙O上的点,∠ACB=32°,则∠AOB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠AOB与∠ACB都对⁀{AB},∠ACB=32°,∴∠AOB=2∠ACB=64°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "64.0", "org_choices": ["16°", "64°", "148°", "32°"], "choices": [16.0, 64.0, 148.0, 32.0], "label": 1}
+{"prob_id": 8538, "image_path": "images/8538.png", "question": "如图,点A、B、C在⊙O上,若∠ABC=35°,则∠AOC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵点A、B、C在⊙O上,∠ABC=35°,∴∠AOC=2∠ABC=70°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["20°", "40°", "60°", "70°"], "choices": [20.0, 40.0, 60.0, 70.0], "label": 3}
+{"prob_id": 8579, "image_path": "images/8579.png", "question": "如图,点A,B,C在⊙O上,连接AB,AC,若∠BOC=100°,则∠B+∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:作直径AD,如图所示,∵OA=OB=OC,∴∠B=∠BAO,∠C=∠CAO,∵∠BOD=∠B+∠BAO∴∠BOD=2∠B,∵∠COD=∠C+∠CAO∴∠COD=2∠C,∵∠BOD+∠COD=∠BOC=100°,即2∠B+2∠C=100°,∴∠B+∠C=50°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["25°", "50°", "100°", "无法计算"], "choices": [25.0, 50.0, 100.0], "label": 1}
+{"prob_id": 8589, "image_path": "images/8589.png", "question": "如图,将直角三角板45°角的顶点放在圆心O上,斜边和一直角边分别与⊙O相交于A、B两点,C是优弧AB上任意一点(与A、B不重合),则∠ACB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠AOB=45°,∴∠ACB=\\frac{1}{2}∠AOB=22.5°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "22.5", "org_choices": ["30°", "22.5°", "90°", "15°"], "choices": [30.0, 22.5, 90.0, 15.0], "label": 1}
+{"prob_id": 8590, "image_path": "images/8590.png", "question": "如图,线段AB是⊙O的直径,弦CD丄AB,∠CAB=20°,则∠AOD等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵线段AB是⊙O的直径,弦CD丄AB,∴⁀{CB}=⁀{BD},∵∠CAB=20°,∴∠BOD=40°,∴∠AOD=140°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "140.0", "org_choices": ["160°", "150°", "140°", "120°"], "choices": [160.0, 150.0, 140.0, 120.0], "label": 2}
+{"prob_id": 8596, "image_path": "images/8596.png", "question": "如图,▱ABCD的顶点A、B、D在⊙O上,顶点C在⊙O的直径BE上,连接AE,∠E=36°,则∠ADC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵BE是直径,∴∠BAE=90°,∵四边形ABCD是平行四边形,∠E=36°,∴∠BEA=∠DAE=36°,∴∠BAD=126°,∴∠ADC=54°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "54.0", "org_choices": ["44°", "54°", "72°", "53°"], "choices": [44.0, 54.0, 72.0, 53.0], "label": 1}
+{"prob_id": 8625, "image_path": "images/8625.png", "question": "量角器的直径与直角三角板ABC的斜边AB重合,其中量角器O刻度线的端点N与点A重合,射线CP从CA处出发沿顺时针方向以每秒3度的速度旋转,CP与量角器的半圆弧交于点E,当第20秒时,点E在量角器上对应的读数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OE,∵射线CP从CA处出发沿顺时针方向以每秒3度的速度旋转,∴第20秒时,∠ACE=3°×20=60°,∵∠ACB=90°,∴点C在以AB为直径的圆上,即点C在⊙O上,∴∠EOA=2∠ECA=2×60°=120°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["150°", "120°", "75°", "60°"], "choices": [150.0, 120.0, 75.0, 60.0], "label": 1}
+{"prob_id": 8627, "image_path": "images/8627.png", "question": "如图,A、B、C三点在⊙O上,且∠ABO=50°,则∠ACB等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA=OB,∴∠BAO=∠ABO=50°,∴∠AOB=180°-50°-50°=80°,∴∠ACB=\\frac{1}{2}∠AOB=40°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["100°", "80°", "50°", "40°"], "choices": [100.0, 80.0, 50.0, 40.0], "label": 3}
+{"prob_id": 8640, "image_path": "images/8640.png", "question": "AB为⊙O的直径,点C在⊙O上,若∠C=15°,则∠BOC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OA=OC,∴∠A=∠C=15°；∴∠BOC=2∠A=30°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["60°", "45°", "30°", "15°"], "choices": [60.0, 45.0, 30.0, 15.0], "label": 2}
+{"prob_id": 8650, "image_path": "images/8650.png", "question": "如图,圆内的两条弦AB、CD相交于E,∠D=35°,∠AEC=105°,则∠C=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠D=35°,∠AEC=105°,∴∠A=∠AEC-∠D=70°,∴∠C=∠A=70°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["60°", "70°", "80°", "85°"], "choices": [60.0, 70.0, 80.0, 85.0], "label": 1}
+{"prob_id": 8651, "image_path": "images/8651.png", "question": "如图,AB、CD是⊙O的两条弦,连结AD、BC．若∠BCD=70°,则∠BAD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BCD=70°,∴∠BAD=∠BCD=70°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "70.0", "org_choices": ["40°", "50°", "60°", "70°"], "choices": [40.0, 50.0, 60.0, 70.0], "label": 3}
+{"prob_id": 8652, "image_path": "images/8652.png", "question": "如图,A、B、C在⊙O上,若∠BAC=24°,则∠BOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BAC=24°,∴∠BOC的=2∠BAC=48°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "48.0", "org_choices": ["12°", "24°", "48°", "84°"], "choices": [12.0, 24.0, 48.0, 84.0], "label": 2}
+{"prob_id": 8653, "image_path": "images/8653.png", "question": "如图,点A,B,C都在⊙O上,若∠C=34°,则∠AOB为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠C=34°,∴∠AOB=2∠C=68°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "68.0", "org_choices": ["34°", "56°", "60°", "68°"], "choices": [34.0, 56.0, 60.0, 68.0], "label": 3}
+{"prob_id": 8658, "image_path": "images/8658.png", "question": "如图,直径为10的⊙A经过点C(0,5)和点O(0,0),B是y轴右侧⊙A优弧上一点,则∠OBC的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:设⊙A与x轴交于另一点D,连接CD,∵∠COD=90°,∴CD是⊙A的直径,且CD=10,∵点C(0,5)和点O(0,0),∴OC=5,∴sin∠ODC=\\frac{OC}{CD}=\\frac{1}{2},∴∠ODC=30°,∴∠OBC=∠ODC=30°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["30°", "40°", "50°", "60°"], "choices": [30.0, 40.0, 50.0, 60.0], "label": 0}
+{"prob_id": 8662, "image_path": "images/8662.png", "question": "如图,△ABC内接于⊙O,∠A=15°,连接OB,则∠OBC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵连接OC,∵△ABC内接于⊙O,∠A=15°,∴∠BOC=2∠A=30°,∵OB=OC,∴∠OBC=∠OCB=\\frac{180°-∠BOC}{2}=75°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "75.0", "org_choices": ["30°", "60°", "65°", "75°"], "choices": [30.0, 60.0, 65.0, 75.0], "label": 3}
+{"prob_id": 8685, "image_path": "images/8685.png", "question": "如图,在⊙O中,∠ABC=40°,则∠AOC=()度．. Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵在⊙O中,∠ABC=40°,∴∠AOC=2∠ABC=80°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["40", "20", "80", "50"], "choices": [40.0, 20.0, 80.0, 50.0], "label": 2}
+{"prob_id": 8686, "image_path": "images/8686.png", "question": "如图,A、B、C、是⊙O上的三点,且∠CAO=25°,∠BCO=35°,则∠AOB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:延长CO交⊙O于点D,∵∠BCO=35°,∴∠BOD=70°．∵∠CAO=25°,CO=OA,∴∠ACO=∠CAO=25°,∴∠AOD=2∠ACO=50°,∴∠AOB=50°+70°=120°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "120.0", "org_choices": ["100°", "110°", "120°", "130°"], "choices": [100.0, 110.0, 120.0, 130.0], "label": 2}
+{"prob_id": 8688, "image_path": "images/8688.png", "question": "如图,AB为⊙O的直径,弦CD⊥AB,E为⁀{BC}上一点,若∠CEA=28°,则∠ABD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB为直径,弦CD⊥AB,∴⁀{AC}=⁀{AD},∴∠ABD=∠CEA=28°,故选:B．", "dataset_name": "Geoqa", "ground_truth": "28.0", "org_choices": ["14°", "28°", "56°", "无法确定"], "choices": [14.0, 28.0, 56.0], "label": 1}
+{"prob_id": 8692, "image_path": "images/8692.png", "question": "如图所示,⊙O是△ABC的外接圆,已知∠B=70°,则∠CAO的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:延长AO交圆于点D,连接CD,如图所示,∵AD是直径,∴∠ACD=90°,∵∠D=∠B,∠B=70°,∴∠D=70°,∵∠ACD+∠D+∠CAO=180°,∴∠CAO=180°-70°-90°=20°,故选:A．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["20°", "30°", "35°", "40°"], "choices": [20.0, 30.0, 35.0, 40.0], "label": 0}
+{"prob_id": 8706, "image_path": "images/8706.png", "question": "如图,⊙O是△ABC的外接圆,∠OCB=30°,则∠A的度数等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵OB=OC,∴∠OBC=∠OCB=30°,∴∠BOC=180°-30°-30°=120°,∴∠A=\\frac{1}{2}∠BOC=60°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "60.0", "org_choices": ["60°", "50°", "40°", "30°"], "choices": [60.0, 50.0, 40.0, 30.0], "label": 0}
+{"prob_id": 8711, "image_path": "images/8711.png", "question": "如图,⊙O是△ABC的外接圆,AB是直径,若∠BOC=70°,则∠A等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB是直径,∠BOC=70°,∴∠A=\\frac{1}{2}∠BOC=35°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["35°", "45°", "40°", "30°"], "choices": [35.0, 45.0, 40.0, 30.0], "label": 0}
+{"prob_id": 8712, "image_path": "images/8712.png", "question": "如图,在⊙O中,直径AB=5cm,弦AC=4cm,则点O到直线AC的距离为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,过点C作CD⊥AB于点D,连接BC．则AD=CD,即点D是AC的中点．∵AB是⊙O的直径,∴∠ACB=90°．∴BC=√{AB^{2}-AC^{2}}∵AB=5cm,弦AC=4cm,∴BC=3cm．∵点O是AB的中点,∴OD=\\frac{1}{2}BC=1.5cm．故选:A．", "dataset_name": "Geoqa", "ground_truth": "1.5", "org_choices": ["1.5cm", "2cm", "2.5cm", "3cm"], "choices": [1.5, 2.0, 2.5, 3.0], "label": 0}
+{"prob_id": 8718, "image_path": "images/8718.png", "question": "如图,AB是⊙O的直径,若∠BAC=35°,则∠ADC=(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB为⊙O直径,∴∠ACB=90°,∵∠BAC=35°,∴∠B=90°-35°=55°,∴∠D=∠B=55°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["110°", "70°", "55°", "35°"], "choices": [110.0, 70.0, 55.0, 35.0], "label": 2}
+{"prob_id": 8724, "image_path": "images/8724.png", "question": "一副直角三角板如图放置(∠ACB=∠ADB=90°),∠CAB=30°,∠BAD=45°,AB交CD于E,则∠CEB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠ADB=90°,∠DAB=45°,∴△DAB是等腰直角三角形,∴∠DAB=∠ABD=45°；由于∠ACB=∠ADB=90°,所以A、C、B、D四点共圆,且直径为AB；由圆周角定理知:∠ACD=∠ABD=45°；△ACE中,外角∠CEB=∠CAB+∠ACD=30°+45°=75°；故选:D．", "dataset_name": "Geoqa", "ground_truth": "75.0", "org_choices": ["30°", "45°", "60°", "75°"], "choices": [30.0, 45.0, 60.0, 75.0], "label": 3}
+{"prob_id": 8727, "image_path": "images/8727.png", "question": "如下图,点C在以AB为直径的半圆O上,∠BAC=20°,则∠BOC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:根据圆周角定理,得∠BOC=2∠BAC=40°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "40.0", "org_choices": ["20°", "30°", "40°", "50°"], "choices": [20.0, 30.0, 40.0, 50.0], "label": 2}
+{"prob_id": 8738, "image_path": "images/8738.png", "question": "如图,AB为⊙O直径,∠ABC=25°,则∠D的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB为⊙O直径,∴∠ACB=90°,∵∠ABC=25°,∴∠CAB=90°-25°=65°,∴∠D=∠CAB=65°．", "dataset_name": "Geoqa", "ground_truth": "65.0", "org_choices": ["70°", "75°", "60°", "65°"], "choices": [70.0, 75.0, 60.0, 65.0], "label": 3}
+{"prob_id": 8742, "image_path": "images/8742.png", "question": "如图,△ABC是⊙O的内接三角形,BD为直径,若∠DBC=18°,则∠A的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接OC．∵OB=OC,∴∠DBC=∠OCB=18°,∴∠BOC=180°-2∠DBC=144°,∴∠A=\\frac{1}{2}∠BOC=72°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "72.0", "org_choices": ["36°", "72°", "60°", "无法确定"], "choices": [36.0, 72.0, 60.0], "label": 1}
+{"prob_id": 8753, "image_path": "images/8753.png", "question": "如图,AB、CD是⊙O的弦,且AB∥CD,若∠BAD=36°,则∠AOC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB∥CD,∴∠ADC=∠BAD=36°,∴∠AOC=2∠ADC=2×36°=72°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "72.0", "org_choices": ["36°", "54°", "72°", "90°"], "choices": [36.0, 54.0, 72.0, 90.0], "label": 2}
+{"prob_id": 8754, "image_path": "images/8754.png", "question": "如图,A、B、C是⊙O上的三个点,若∠C=35°,则∠OAB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠AOB与∠C是同弧所对的圆心角与圆周角,∴∠AOB=2∠C=2×35°=70°,∵OA=OB,∴∠OAB=∠OBA=\\frac{180{^°}-∠AOB}{2}=\\frac{180{^°}-70{^°}}{2}=55°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["35°", "55°", "65°", "70°"], "choices": [35.0, 55.0, 65.0, 70.0], "label": 1}
+{"prob_id": 8779, "image_path": "images/8779.png", "question": "如图,▱ABCD的顶点A、B、D在⊙O上,顶点C在⊙O的直径BE上,∠ADC=54°,连接AE,则∠AEB的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是平行四边形,∠ADC=54°,∴∠B=∠ADC=54°,∵BE为⊙O的直径,∴∠BAE=90°,∴∠AEB=90°-∠B=90°-54°=36°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "36.0", "org_choices": ["36°", "46°", "27°", "63°"], "choices": [36.0, 46.0, 27.0, 63.0], "label": 0}
+{"prob_id": 8781, "image_path": "images/8781.png", "question": "如图,CD是⊙O的直径,弦DE∥OA,若∠D的度数是50°,则∠A的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵DE∥OA,∠D=50°,∴∠AOD=∠D=50°,∴∠C=\\frac{1}{2}∠AOD=25°,∵OA=OC,∴∠A=∠C=25°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["25°", "30°", "40°", "50°"], "choices": [25.0, 30.0, 40.0, 50.0], "label": 0}
+{"prob_id": 8789, "image_path": "images/8789.png", "question": "如图,已知⊙O是△ABC的外接圆,∠AOB=110°,则∠C的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵⊙O是△ABC的外接圆,∠AOB=110°,∴∠C=\\frac{1}{2}∠AOB=\\frac{1}{2}×110°=55°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "55.0", "org_choices": ["55°", "70°", "60°", "45°"], "choices": [55.0, 70.0, 60.0, 45.0], "label": 0}
+{"prob_id": 8812, "image_path": "images/8812.png", "question": "如图,AB是⊙O的直径,点C在⊙O上,若∠A=40°,则∠B的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵AB是⊙O的直径,∴∠C=90°,∵∠A=40°,∴∠B=90°-∠A=50°．故选:C．", "dataset_name": "Geoqa", "ground_truth": "50.0", "org_choices": ["80°", "60°", "50°", "40°"], "choices": [80.0, 60.0, 50.0, 40.0], "label": 2}
+{"prob_id": 8814, "image_path": "images/8814.png", "question": "如图,若AB是⊙O的直径,CD是⊙O的弦,∠ABD=55°,则∠BCD的度数为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接AD,∵AB是⊙O的直径,∴∠ADB=90°,∵∠ABD=55°,∴∠A=90°-∠ABD=35°,∴∠BCD=∠A=35°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "35.0", "org_choices": ["35°", "45°", "55°", "75°"], "choices": [35.0, 45.0, 55.0, 75.0], "label": 0}
+{"prob_id": 8830, "image_path": "images/8830.png", "question": "如图,点A、B、C是⊙O上的三点,∠BAC=40°,则∠BOC的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠BAC=40°,∴∠BOC=2∠BAC=80°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "80.0", "org_choices": ["80°", "40°", "50°", "20°"], "choices": [80.0, 40.0, 50.0, 20.0], "label": 0}
+{"prob_id": 8839, "image_path": "images/8839.png", "question": "如图,在半径为5的⊙O中,如果弦AB的长为8,那么它的弦心距OC等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OA,在Rt△OAC中,OA=5,AC=4,根据勾股定理可得,OC=√{OA²-AC²}=√{5²-4²}=3．故选:B．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["2", "3", "4", "6"], "choices": [2.0, 3.0, 4.0, 6.0], "label": 1}
+{"prob_id": 8841, "image_path": "images/8841.png", "question": "如图,点O是⊙O的圆心,点A、B、C在⊙O上,AO∥BC,∠AOB=40°,则∠OAC的度数等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵∠C=\\frac{1}{2}∠AOB=\\frac{1}{2}×40°=20°,又∵AO∥BC,∴∠OAC=∠C=20°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "20.0", "org_choices": ["40°", "60°", "50°", "20°"], "choices": [40.0, 60.0, 50.0, 20.0], "label": 3}
+{"prob_id": 8847, "image_path": "images/8847.png", "question": "已知:如图,⊙O中直径AB垂直于弦CD,垂足为E,若AB=10,CD=6,则BE的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接OC,∵AB=10,∴半径OC=10÷2=5,∵CD=6,∴CE=6÷2=3,根据勾股定理OE=√{OC²-CE²}=√{5²-3²}=4,∴BE=5-4=1．故选:A．", "dataset_name": "Geoqa", "ground_truth": "1.0", "org_choices": ["1", "2", "3", "4"], "choices": [1.0, 2.0, 3.0, 4.0], "label": 0}
+{"prob_id": 8867, "image_path": "images/8867.png", "question": "如图,⊙O的半径为10,AB为弦,OC⊥AB,垂足为E．如果CE=4,那么AB的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OA,∵半径OC⊥AB,∴AE=BE=\\frac{1}{2}AB,∵OC=10,CE=4,∴OE=6,在Rt△AOE中,AE=√{OA²-OE²}=√{10²-6²}=8,∴AB=2AE=16,故选:C．", "dataset_name": "Geoqa", "ground_truth": "16.0", "org_choices": ["8", "12", "16", "20"], "choices": [8.0, 12.0, 16.0, 20.0], "label": 2}
+{"prob_id": 8883, "image_path": "images/8883.png", "question": "如图,正方形ABCD的边长为3,以CD为一边向CD两侧作等边三角形PCD和等边三角形QCD,那么PQ的长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:根据题意可知△PDQ是等腰三角形,且DC垂直平分PQ,易得DE=1.5,DQ=3；在Rt△DEQ中QE=√{9-\\frac{9}{4}}=\\frac{3√{3}}{2},所以PQ=2QE=3√{3}；故选:C．", "dataset_name": "Geoqa", "ground_truth": "5.196152422706632", "org_choices": ["\\frac{3√{3}}{2}", "\\frac{2√{3}}{3}", "3√{3}", "6√{3}"], "choices": [2.598, 1.155, 5.196, 10.392], "label": 2}
+{"prob_id": 8893, "image_path": "images/8893.png", "question": "如图,在正方形ABCD中,E是DC上一点,F为BC延长线上一点,∠BEC=70°,且△BCE≌△DCF．连接EF,则∠EFD的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵四边形ABCD是正方形,∴∠BCE=∠DCF=90°；由旋转的性质知:CE=CF,∠BEC=∠DFC=70°；则△ECF是等腰直角三角形,得∠EFC=45°,∴∠EFD=∠DFC-∠EFC=25°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "25.0", "org_choices": ["10°", "15°", "20°", "25°"], "choices": [10.0, 15.0, 20.0, 25.0], "label": 3}
+{"prob_id": 8923, "image_path": "images/8923.png", "question": "如图,已知⊙O的半径为5mm,弦AB=8mm,则圆心O到AB的距离是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:过O作OC⊥AB于C,∵OC过O,∴AC=BC=\\frac{1}{2}AB=4cm,在Rt△AOC中,由勾股定理得:OC=√{5²-4²}=3(cm),故选:C．", "dataset_name": "Geoqa", "ground_truth": "3.0", "org_choices": ["1mm", "2mm", "3mm", "4mm"], "choices": [1.0, 2.0, 3.0, 4.0], "label": 2}
+{"prob_id": 8932, "image_path": "images/8932.png", "question": "如图,MN切⊙O于点A,∠AOB=60°,那么∠BAM等于(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵MN切⊙O于点A,∴∠MAO=90°．∵∠AOB=60°,OB=OA,∴∠OAB=60°,∴∠BAM=30°．故选:D．", "dataset_name": "Geoqa", "ground_truth": "30.0", "org_choices": ["120°", "90°", "60°", "30°"], "choices": [120.0, 90.0, 60.0, 30.0], "label": 3}
+{"prob_id": 8938, "image_path": "images/8938.png", "question": "如图,从⊙O外一点P引圆的切线PA和PB,切点分别是A和B,如果∠APB=70°,那么这两条切线所夹劣弧AB的度数是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA和PB是切线,∴∠A=∠B=90°,∵∠APB=70°,∴∠AOB=180°-∠P=110°,∴劣弧AB的度数是110°．故选:A．", "dataset_name": "Geoqa", "ground_truth": "110.0", "org_choices": ["110°", "70°", "55°", "35°"], "choices": [110.0, 70.0, 55.0, 35.0], "label": 0}
+{"prob_id": 8947, "image_path": "images/8947.png", "question": "如图,PB切⊙O于点B,PO交⊙O于点E,延长PO交⊙O于点A,连结AB,⊙O的半径OD⊥AB于点C,BP=6,∠P=30°,则CD的长度是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,连接OB,∵PB切⊙O于点B,∴∠OBP=90°,∵BP=6,∠P=30°,∴∠POB=60°,OD=OB=BPtan30°=6×\\frac{√{3}}{3}=2√{3},∵OA=OB,∴∠OAB=∠OBA=30°,∵OD⊥AB,∴∠OCB=90°,∴∠OBC=30°,则OC=\\frac{1}{2}OB=√{3},∴CD=√{3},故选:C．", "dataset_name": "Geoqa", "ground_truth": "1.7320508075688772", "org_choices": ["\\frac{√{3}}{3}", "\\frac{√{3}}{2}", "√{3}", "2√{3}"], "choices": [0.577, 0.866, 1.732, 3.464], "label": 2}
+{"prob_id": 8950, "image_path": "images/8950.png", "question": "如图,PA、PB分别切⊙O于A、B,点C和点D分别是线段PA、PB上的动点,并且CD始终保持与圆O相切,若PA=8cm,则△PCD的周长是(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:∵PA、PB分别切⊙O于A、B,∴PB=PA=8,∵CD切⊙O于E,∴CA=CE,DE=DB,∴△PCD的周长=PC+PD+CD=PC+PD+CE+DE=PA+PB=8+8=16(cm)．故选:C．", "dataset_name": "Geoqa", "ground_truth": "16.0", "org_choices": ["8", "12", "16", "不能确定"], "choices": [8.0, 12.0, 16.0], "label": 2}
+{"prob_id": 8952, "image_path": "images/8952.png", "question": "如图,两个同心圆中,大圆的弦AB切小圆于点C,若AB=6,则圆环的面积为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:连接OC,OA∵AB切小⊙O于C,∴OC⊥AB,∴AC=BC=\\frac{1}{2}AB=3,∠OCA=90°,由勾股定理得:OA²-OC²=AC²=9,∴圆环的面积是πOB²-πOC²=π(OA²-OC²)=9π,故选:A．", "dataset_name": "Geoqa", "ground_truth": "28.274333882308138", "org_choices": ["9π", "6π", "3π", "π"], "choices": [28.274, 18.85, 9.425, 3.142], "label": 0}
+{"prob_id": 8978, "image_path": "images/8978.png", "question": "如图,正方形P、Q夹在ABCD框架中,正方形P下边一条边与AB夹角为15°,正方形P、Q有两个相邻边夹角为150°,则∠1为(). Please first convert the diagram to sematic sequences. Then, solve the problem.", "rationale": "解:如图,延长正方形P、Q的边相交于点E,过E作BC的平行线,过E作EM∥AB,则∠AED=360°-150°-90°-90°=30°,∵∠AED=∠1+∠EAG,∴∠1=∠AED-∠EAG=30°-15°=15°．故选:B．", "dataset_name": "Geoqa", "ground_truth": "15.0", "org_choices": ["55°", "15°", "50°", "70°"], "choices": [55.0, 15.0, 50.0, 70.0], "label": 1}
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-{"prob_id": "prob_27", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_423.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.000", "choices": [24.0, 33.941125496954285, 41.569219381653056, 48.0]}
-{"prob_id": "prob_31", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2339.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [35.0, 70.0, 75.0, 82.0]}
-{"prob_id": "prob_46", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2654.png", "question": "If ABCD is a kite. Find m \\angle C. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [60.0, 70.0, 85.0, 120.0]}
-{"prob_id": "prob_55", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_794.png", "question": "Solve for m \\angle 2 in the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "33.500", "choices": [33.5, 56.5, 67.0, 113.0]}
-{"prob_id": "prob_59", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_169.png", "question": "Find the value of x in the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "100.000", "choices": [20.0, 80.0, 100.0, 160.0]}
-{"prob_id": "prob_60", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_662.png", "question": "For trapezoid ABDC, E and F are midpoints of the legs. Let XY be the median of ABFE. Find XY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.500", "choices": [8.0, 9.25, 10.5, 18.0]}
-{"prob_id": "prob_72", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1475.png", "question": "Find SP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.000", "choices": [5.0, 6.0, 7.0, 17.0]}
-{"prob_id": "prob_87", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_883.png", "question": "If AB \\parallel DC, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [32.5, 65.0, 105.0, 115.0]}
-{"prob_id": "prob_88", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2023.png", "question": "In \\odot X, WS, VR, and QT are diameters, m \\angle WXV = 25 and m \\angle VXU = 45. Find the measure of \\widehat WRV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "335.000", "choices": [180.0, 245.0, 270.0, 335.0]}
-{"prob_id": "prob_92", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1191.png", "question": "In \\triangle MIV, Z is the centroid, MZ = 6, YI = 18, and NZ = 12. What is the measure of ZV? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [12.0, 24.0, 36.0, 54.0]}
-{"prob_id": "prob_111", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_73.png", "question": "Use the diagram of \\parallelogram ABCD to find m \\angle A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "53.000", "choices": [26.5, 53.0, 90.0, 127.0]}
-{"prob_id": "prob_112", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3063.png", "question": "PRYZ is a rhombus. If RK = 5, RY = 13 and m \\angle YRZ = 67, what is m \\angle RYK? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.000", "choices": [23.0, 46.0, 90.0, 134.0]}
-{"prob_id": "prob_120", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_884.png", "question": "What is m \\angle W? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [22.0, 52.0, 73.6, 90.0]}
-{"prob_id": "prob_129", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1776.png", "question": "Find YZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [6.0, 7.0, 8.0, 9.0]}
-{"prob_id": "prob_132", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3361.png", "question": "What is m \\angle C? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "110.000", "choices": [40.0, 70.0, 82.0, 110.0]}
-{"prob_id": "prob_143", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3291.png", "question": "For \\parallelogram ABCD, what is perimeter of ABCD? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.800", "choices": [36.8, 44.0, 44.8, 52.0]}
-{"prob_id": "prob_152", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3063.png", "question": "PRYZ is a rhombus. If RK = 5, RY = 13 and m \\angle YRZ = 67, what is m \\angle PKR? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [23.0, 46.0, 90.0, 134.0]}
-{"prob_id": "prob_159", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1591.png", "question": "Find a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [12.0, 12.5, 15.0, 17.5]}
-{"prob_id": "prob_165", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3687.png", "question": "For isosceles trapezoid ABCD, X and Y are midpoints of the legs. Find m \\angle C if m \\angle ADY = 78. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "102.000", "choices": [51.0, 78.0, 90.0, 102.0]}
-{"prob_id": "prob_172", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3125.png", "question": "Find the measure of \\angle FJE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "62.000", "choices": [25.0, 62.0, 90.0, 118.0]}
-{"prob_id": "prob_173", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_535.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 4.0, 5.0, 6.0]}
-{"prob_id": "prob_175", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1655.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.200", "choices": [16.8, 19.2, 21.6, 22.7]}
-{"prob_id": "prob_180", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_408.png", "question": "Find m \\angle ABD, given that m \\angle ABC = 112. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "56.000", "choices": [34.0, 56.0, 112.0, 124.0]}
-{"prob_id": "prob_182", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_947.png", "question": "Find the scale from B to B'. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.333", "choices": [0.75, 0.8333333333333334, 1.2, 1.3333333333333333]}
-{"prob_id": "prob_184", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_422.png", "question": "Find the value of y if line p \\parallel line q. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "105.000", "choices": [75.0, 85.0, 95.0, 105.0]}
-{"prob_id": "prob_186", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3797.png", "question": "NPLM \\cong EFGH. Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [0.143, 9.0, 11.143, 14.429]}
-{"prob_id": "prob_187", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1746.png", "question": "What is the measure of \\angle M? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 139.149, 165.0, 201.818]}
-{"prob_id": "prob_193", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2502.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [20.0, 28.0, 36.0, 44.0]}
-{"prob_id": "prob_198", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1783.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.600", "choices": [9.0, 9.6, 12.0, 14.4]}
-{"prob_id": "prob_200", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2166.png", "question": "What is the measure of \\angle 3? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "52.000", "choices": [38.0, 52.0, 90.0, 128.0]}
-{"prob_id": "prob_218", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_597.png", "question": "Find the perimeter of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "41.569", "choices": [24.0, 41.569, 45.255, 64.0]}
-{"prob_id": "prob_247", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1676.png", "question": "What is the measure of \\angle 3? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "129.000", "choices": [51.0, 90.0, 129.0, 258.0]}
-{"prob_id": "prob_276", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1108.png", "question": "Find the value of variable w. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "104.000", "choices": [22.0, 44.0, 72.0, 104.0]}
-{"prob_id": "prob_300", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_763.png", "question": "Use parallelogram ABCD to find m \\angle FBC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "59.000", "choices": [20.0, 49.0, 59.0, 111.0]}
-{"prob_id": "prob_311", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3147.png", "question": "Find m \\angle 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [45.0, 60.0, 75.0, 120.0]}
-{"prob_id": "prob_312", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3068.png", "question": "Point S is the incenter of \\triangle JPL. Find QJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [4.0, 6.0, 8.0, 10.0]}
-{"prob_id": "prob_313", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2332.png", "question": "Find the area of the trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "500.000", "choices": [125.0, 250.0, 500.0, 1000.0]}
-{"prob_id": "prob_335", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1086.png", "question": "Find PX, if XZ = 18 and PY = 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 15.0, 18.0, 21.0]}
-{"prob_id": "prob_350", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2369.png", "question": "What is m \\angle 3 in the isosceles trapezoid? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "111.000", "choices": [34.5, 42.0, 69.0, 111.0]}
-{"prob_id": "prob_367", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1037.png", "question": "Find the value of n. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [-3.333, -1.818, -1.25, 5.0]}
-{"prob_id": "prob_371", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3302.png", "question": "If AC = 12 and AB = 25, what is the measure of \\angle B? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.685", "choices": [25.6, 28.7, 61.3, 64.4]}
-{"prob_id": "prob_375", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2576.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [52.0, 60.0, 105.0, 475.933]}
-{"prob_id": "prob_377", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_8.png", "question": "Find the area of the trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "132.000", "choices": [72.0, 132.0, 144.0, 192.0]}
-{"prob_id": "prob_387", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2262.png", "question": "Solve for the length of CD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [0.0, 1.0, 6.0, 11.0]}
-{"prob_id": "prob_396", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3185.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "42.000", "choices": [28.0, 32.286, 42.0, 53.0]}
-{"prob_id": "prob_413", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1152.png", "question": "Find m \\angle DAB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "125.000", "choices": [55.0, 110.0, 125.0, 135.0]}
-{"prob_id": "prob_419", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2010.png", "question": "Find the area of the shaded sector. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "167.133", "choices": [47.5, 167.1, 285.3, 452.4]}
-{"prob_id": "prob_425", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1488.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [2.222, 2.812, 6.0, 7.2]}
-{"prob_id": "prob_439", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3633.png", "question": "m \\angle RST = x+50, and m \\angle STU = 3x+20. Find m \\angle SRV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [65.0, 77.5, 102.5, 115.0]}
-{"prob_id": "prob_441", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2011.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [-1.0, 0.548, 0.646, 2.0]}
-{"prob_id": "prob_443", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_850.png", "question": "J is the incenter of \\angle ABC. Find BE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.343", "choices": [9.0, 13.343, 14.403, 16.984]}
-{"prob_id": "prob_445", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2224.png", "question": "A regular polygon is inscribed in a circle. What is the measure of \\angle SRL? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 36.0, 60.0, 90.0]}
-{"prob_id": "prob_448", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2240.png", "question": "Find the measure of \\angle KLG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [57.0, 70.0, 103.5, 123.0]}
-{"prob_id": "prob_472", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_30.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [3.111, 4.0, 65.0, 80.0]}
-{"prob_id": "prob_494", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2270.png", "question": "Find the variable of x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 7.0, 8.0, 9.0]}
-{"prob_id": "prob_495", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_695.png", "question": "Find BD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [5.0, 10.0, 13.0, 24.0]}
-{"prob_id": "prob_500", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2815.png", "question": "Find the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [34.0, 56.0, 68.0, 146.0]}
-{"prob_id": "prob_508", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_890.png", "question": "If AB = 60 and DE = 48, find DC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [24.0, 30.0, 54.991, 56.604]}
-{"prob_id": "prob_517", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_801.png", "question": "Find the area of the shaded sector. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.815", "choices": [0.9, 1.8, 10.8, 12.6]}
-{"prob_id": "prob_533", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3852.png", "question": "The diagonals of rectangle MNPQ intersect at S. If MN = 4.1 meters, MS = 2.35 meters, and MQ = 2.3 meters, what is the length of NQ? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.700", "choices": [2.35, 4.1, 4.7, 8.2]}
-{"prob_id": "prob_537", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1184.png", "question": "If QT = 11, what is QU? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [7.0, 8.0, 11.0, 16.0]}
-{"prob_id": "prob_538", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3448.png", "question": "Find the area of the polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [60.0, 92.0, 120.0, 172.5]}
-{"prob_id": "prob_547", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1457.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [3.5, 7.0, 14.0, 56.0]}
-{"prob_id": "prob_572", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2716.png", "question": "Find m \\angle JKL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 50.0, 60.0, 80.0]}
-{"prob_id": "prob_579", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1994.png", "question": "Find x so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [11.0, 25.0, 26.0, 33.0]}
-{"prob_id": "prob_584", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3350.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "280.000", "choices": [259.0, 280.0, 294.0, 336.0]}
-{"prob_id": "prob_587", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_532.png", "question": "E is between D and F. Find DF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [3.667, 9.333, 11.0, 24.0]}
-{"prob_id": "prob_617", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3286.png", "question": "Use the Law of Sines to find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.142", "choices": [2.142, 2.976, 3.598, 6.949]}
-{"prob_id": "prob_640", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_850.png", "question": "J is the incenter of \\angle ABC. Find DB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.343", "choices": [9.0, 13.343, 14.403, 16.984]}
-{"prob_id": "prob_667", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1490.png", "question": "What is x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "46.000", "choices": [2.0, 36.8, 46.0, 72.8]}
-{"prob_id": "prob_679", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_371.png", "question": "Find m \\angle 8. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.500", "choices": [28.0, 28.5, 56.0, 57.0]}
-{"prob_id": "prob_687", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2481.png", "question": "Find the value of variable a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.828, 3.0, 5.657, 6.0]}
-{"prob_id": "prob_689", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3738.png", "question": "RS and RT are tangent to \\odot Q. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.400", "choices": [5.457, 8.4, 12.6, 293.04]}
-{"prob_id": "prob_692", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_390.png", "question": "Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 4.0, 5.0, 6.0]}
-{"prob_id": "prob_694", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2054.png", "question": "AD = 6 and DE = 7.5. What is the length of DC? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 7.5, 12.0, 15.0]}
-{"prob_id": "prob_697", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_664.png", "question": "JKLM is a rectangle. MLPR is a rhombus. m \\angle JMK = m \\angle RMP, m \\angle JMK = 55, and m \\angle MRP = 70. Find m \\angle KML. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [35.0, 70.0, 110.0, 140.0]}
-{"prob_id": "prob_701", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2340.png", "question": "Find the value of variable x. Lines that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [50.0, 65.0, 115.0, 130.0]}
-{"prob_id": "prob_716", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2447.png", "question": "What is \\tan A? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.417", "choices": [0.38, 0.42, 0.92, 2.4]}
-{"prob_id": "prob_731", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3639.png", "question": "Find CB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 3.0, 4.0, 55.0]}
-{"prob_id": "prob_738", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1662.png", "question": "Find FH if \\triangle ABC \\sim \\triangle DEF, BG is an altitude of \\triangle ABC, EH is an altitude of \\triangle DEF, BG = 3, BF = 4, FC = 2, and CE = 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.598", "choices": [1.5, 2.0, 2.5, 2.598]}
-{"prob_id": "prob_756", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1148.png", "question": "UA and VA are angle bisectors of \\triangle UVW. Determine m \\angle WVA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.000", "choices": [20.0, 24.0, 37.0, 66.0]}
-{"prob_id": "prob_760", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1750.png", "question": "The segment is tangent to the circle. Find TR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.000", "choices": [9.5, 19.0, 26.87, 38.0]}
-{"prob_id": "prob_761", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2689.png", "question": "Given that line t is the perpendicular bisector of JK and GK = 8.25, find GJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.250", "choices": [4.125, 8.25, 16.5, 90.0]}
-{"prob_id": "prob_765", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_65.png", "question": "Find m \\widehat BCD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "206.000", "choices": [52.0, 206.0, 283.0, 308.0]}
-{"prob_id": "prob_774", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2368.png", "question": "What is z? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [3.84, 15.0, 16.667, 37.5]}
-{"prob_id": "prob_782", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_293.png", "question": "Quadrilateral EFGH is a rectangle. If FK = 32 feet, find KG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.000", "choices": [16.0, 32.0, 45.255, 64.0]}
-{"prob_id": "prob_784", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3994.png", "question": "Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [6.0, 10.0, 28.0, 29.333]}
-{"prob_id": "prob_785", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3894.png", "question": "PM is a diameter of \\odot R. Find m \\widehat NMQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "155.000", "choices": [155.0, 205.0, 270.0, 295.0]}
-{"prob_id": "prob_799", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2733.png", "question": "Find TQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [6.0, 7.0, 12.0, 18.0]}
-{"prob_id": "prob_802", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2842.png", "question": "WXYZ is a rhombus. If m \\angle XYZ = 110, find m \\angle ZWY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [35.0, 55.0, 70.0, 110.0]}
-{"prob_id": "prob_812", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2295.png", "question": "Find the value of variable y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.928", "choices": [4.571, 6.928, 10.583, 24.5]}
-{"prob_id": "prob_815", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_163.png", "question": "ABCD \\sim QSRP. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "63.000", "choices": [34.0, 63.0, 82.0, 83.0]}
-{"prob_id": "prob_816", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_40.png", "question": "In kite WXYZ, m \\angle VXY = 58, and m \\angle ZWX = 50. What is m \\angle WZY? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "123.000", "choices": [40.0, 65.0, 90.0, 123.0]}
-{"prob_id": "prob_817", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3078.png", "question": "PQRS is a rhombus. Find the length of QR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [3.375, 6.75, 9.0, 18.0]}
-{"prob_id": "prob_818", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1259.png", "question": "Solve for y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "45.000", "choices": [30.0, 45.0, 67.5, 90.0]}
-{"prob_id": "prob_829", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2067.png", "question": "In \\odot P, m \\angle MPL = 65 and NP \\perp PL. Find m \\widehat JM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [25.0, 65.0, 90.0, 115.0]}
-{"prob_id": "prob_832", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1757.png", "question": "The square is circumscribed to the circle. Find the exact circumference of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.982", "choices": [21.991148575128552, 43.982297150257104, 65.97344572538566, 87.96459430051421]}
-{"prob_id": "prob_835", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2589.png", "question": "YZ is the midsegment of trapezoid TWRV. Determine the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.200", "choices": [1.2, 8.0, 14.8, 16.0]}
-{"prob_id": "prob_837", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_285.png", "question": "Find QP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 3.0, 5.0, 6.0]}
-{"prob_id": "prob_845", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3307.png", "question": "If m \\angle AFE = 14x+8 and m \\angle BFC = 8x-15, find the value of x so that \\angle AFC is a right angle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.167", "choices": [4.409, 8.5, 11.167, 19.0]}
-{"prob_id": "prob_866", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_334.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.400", "choices": [2.7, 5.4, 6.0, 9.0]}
-{"prob_id": "prob_872", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_424.png", "question": "Find the circumference of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.850", "choices": [9.4, 18.85, 28.3, 37.7]}
-{"prob_id": "prob_878", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2927.png", "question": "S is between R and T. Find RT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [14.0, 28.0, 42.0, 70.0]}
-{"prob_id": "prob_887", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3050.png", "question": "m \\angle 9 = 141+x, m \\angle 10 = 25+x, find m \\angle 10. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.000", "choices": [32.0, 103.0, 148.0, 206.0]}
-{"prob_id": "prob_888", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1509.png", "question": "ABCD is a square. Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [3.6, 9.0, 18.0, 90.0]}
-{"prob_id": "prob_889", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2782.png", "question": "In \\triangle TUV, Y is the centroid. If UZ = 13.5, find UY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [4.5, 6.75, 9.0, 40.5]}
-{"prob_id": "prob_891", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_220.png", "question": "Given isosceles \\triangle JKL with base JL. If JL = 5, find ML. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.500", "choices": [2.5, 4.33, 5.0, 10.0]}
-{"prob_id": "prob_908", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1871.png", "question": "Find the length of \\widehat AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.967", "choices": [19.967, 20.874, 39.933, 41.748]}
-{"prob_id": "prob_909", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_63.png", "question": "What is the measure of \\angle 4? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "75.000", "choices": [52.5, 75.0, 90.0, 105.0]}
-{"prob_id": "prob_919", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3652.png", "question": "In the diagram of the collinear points, PT = 20, QS = 6, and PQ = QR = RS. Find ST. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [3.0, 6.0, 9.0, 11.0]}
-{"prob_id": "prob_925", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1400.png", "question": "Find the area of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.018", "choices": [6.02, 7.54, 7.99, 9.42]}
-{"prob_id": "prob_927", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3646.png", "question": "If ABCD is a kite, find BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [2.5, 4.0, 5.0, 8.0]}
-{"prob_id": "prob_942", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2217.png", "question": "Use rhombus ABCD with AY = 6, DY = 3r+3, and BY = \\frac{10r-4}{2}. Find m \\angle CAB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.000", "choices": [29.745, 60.255, 90.0, 120.51]}
-{"prob_id": "prob_951", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1140.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 4.0, 5.0, 6.0]}
-{"prob_id": "prob_964", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2273.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [0.571, 2.25, 15.75, 28.0]}
-{"prob_id": "prob_969", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3483.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [32.5, 40.0, 72.5, 85.0]}
-{"prob_id": "prob_971", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3071.png", "question": "Find MK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.000", "choices": [2.0, 4.0, 9.0, 37.0]}
-{"prob_id": "prob_972", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2536.png", "question": "What is the length of \\widehat JL? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.499", "choices": [11.1, 15.499, 22.201, 46.496]}
-{"prob_id": "prob_987", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3870.png", "question": "Quadrilateral ABCD is inscribed in \\odot P. If m \\angle B = 80 and m \\angle C = 40, find m \\widehat DCB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "280.000", "choices": [180.0, 200.0, 240.0, 280.0]}
-{"prob_id": "prob_991", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3154.png", "question": "What is the area of the shaded region? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "113.097", "choices": [28.274, 84.823, 113.097, 169.646]}
-{"prob_id": "prob_995", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1008.png", "question": "Cut four congruent triangles off the corners of a rectangle to make an octagon. What is the area of the octagon? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "528.000", "choices": [456.0, 528.0, 552.0, 564.0]}
-{"prob_id": "prob_998", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_776.png", "question": "If \\triangle CAB \\sim \\triangle FDE, find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [12.0, 14.0, 16.0, 18.0]}
-{"prob_id": "prob_1010", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2290.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 5.733, 7.5, 10.444]}
-{"prob_id": "prob_1037", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3855.png", "question": "line a \\parallel line b, line c \\parallel line d, and m \\angle 4 = 57. Find the measure of \\angle 8. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "57.000", "choices": [57.0, 113.0, 123.0, 133.0]}
-{"prob_id": "prob_1040", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1353.png", "question": "Use parallelogram JKLM to find m \\angle MJK if JK = 2b+3 and JM = 3a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "100.000", "choices": [30.0, 70.0, 80.0, 100.0]}
-{"prob_id": "prob_1043", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3405.png", "question": "Find m \\angle B. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "79.000", "choices": [22.0, 39.5, 79.0, 101.0]}
-{"prob_id": "prob_1049", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_352.png", "question": "PQRS is a rhombus. Find m \\angle TQR, given that m \\angle QTR = 6y+6 and m \\angle SPR = 3y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.000", "choices": [42.0, 48.0, 84.0, 96.0]}
-{"prob_id": "prob_1053", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2955.png", "question": "Find c. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [0.258, 0.586, 2.0, 4.449]}
-{"prob_id": "prob_1091", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2834.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [15.0, 30.0, 60.0, 90.0]}
-{"prob_id": "prob_1097", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2017.png", "question": "Find m \\angle A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "81.000", "choices": [81.0, 89.0, 91.0, 99.0]}
-{"prob_id": "prob_1138", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1178.png", "question": "Find m \\angle B. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "76.000", "choices": [52.0, 76.0, 104.0, 128.0]}
-{"prob_id": "prob_1140", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_410.png", "question": "If PQ = UQ and m \\angle P = 32, find m \\angle PUQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.000", "choices": [32.0, 74.0, 79.0, 116.0]}
-{"prob_id": "prob_1142", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2580.png", "question": "If AB = DA = ED = CF, find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.400", "choices": [0.425, 2.4, 3.0, 8.0]}
-{"prob_id": "prob_1158", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3797.png", "question": "NPLM \\cong EFGH. Find m \\angle G. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "110.000", "choices": [21.0, 72.0, 87.0, 110.0]}
-{"prob_id": "prob_1166", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3894.png", "question": "PM is a diameter of \\odot R. Find m \\widehat NPQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "205.000", "choices": [180.0, 205.0, 270.0, 295.0]}
-{"prob_id": "prob_1169", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_277.png", "question": "\\triangle JKL \\sim \\triangle MNP. Find PM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [3.75, 6.0, 10.0, 16.0]}
-{"prob_id": "prob_1175", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3285.png", "question": "m \\angle 1 = 123. Find the measure of \\angle 14. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "57.000", "choices": [47.0, 57.0, 67.0, 123.0]}
-{"prob_id": "prob_1177", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_470.png", "question": "What is the value of b? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [18.0, 72.0, 108.0, 162.0]}
-{"prob_id": "prob_1187", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3830.png", "question": "Use parallelogram JKLM to find m \\angle KJL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 40.0, 50.0, 60.0]}
-{"prob_id": "prob_1190", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2708.png", "question": "Find m \\widehat MN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 67.5, 90.0, 180.0]}
-{"prob_id": "prob_1193", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1605.png", "question": "The angle bisectors of \\triangle XYZ meet at point W. Find AX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "72.284", "choices": [20.0, 72.284, 75.0, 144.568]}
-{"prob_id": "prob_1202", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2558.png", "question": "PR and QT are diameters of \\odot A. Solve for the measure of \\widehat PQR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "180.000", "choices": [140.0, 180.0, 230.0, 320.0]}
-{"prob_id": "prob_1224", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3192.png", "question": "What is the measure of \\angle DCE? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "79.000", "choices": [70.0, 79.0, 101.0, 110.0]}
-{"prob_id": "prob_1234", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2642.png", "question": "Find the value of variable x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.500", "choices": [2.571, 3.5, 14.0, 27.333]}
-{"prob_id": "prob_1238", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3664.png", "question": "If WXYZ is a kite, find XY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [4.0, 4.472, 6.0, 8.944]}
-{"prob_id": "prob_1242", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1372.png", "question": "For what value of y must ABCD be a parallelogram? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "39.000", "choices": [22.385, 25.5, 30.0, 39.0]}
-{"prob_id": "prob_1255", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1925.png", "question": "Find the area of the trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "84.000", "choices": [28.0, 42.0, 84.0, 168.0]}
-{"prob_id": "prob_1256", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2879.png", "question": "Find the value of variable a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [3.464, 4.899, 6.0, 8.0]}
-{"prob_id": "prob_1260", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3548.png", "question": "PR and PS are tangent to \\odot Q. What is m \\angle Q? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "138.000", "choices": [42.0, 48.0, 90.0, 138.0]}
-{"prob_id": "prob_1266", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2461.png", "question": "Square WXYZ is inscribed in \\odot R. Determine the measure of \\widehat ZY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 60.0, 72.0, 90.0]}
-{"prob_id": "prob_1324", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3176.png", "question": "Find m \\angle N. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.912", "choices": [35.889, 40.111, 48.912, 61.794]}
-{"prob_id": "prob_1333", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3536.png", "question": "What is the measure of \\angle 1? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [55.0, 62.5, 117.5, 235.0]}
-{"prob_id": "prob_1338", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3111.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [1.7320508075688772, 3.0, 5.196152422706632, 6.0]}
-{"prob_id": "prob_1350", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3255.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.785", "choices": [4.2, 4.8, 7.9, 16.9]}
-{"prob_id": "prob_1353", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1874.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 3.0, 4.0, 5.0]}
-{"prob_id": "prob_1355", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1370.png", "question": "CB is a tangent segment. Find the measure of \\angle BAC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 90.0, 720.0]}
-{"prob_id": "prob_1356", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1192.png", "question": "\\triangle LMN \\cong \\triangle PQR. What is LM? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 10.0, 12.0, 24.0]}
-{"prob_id": "prob_1358", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1792.png", "question": "Find b. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.622", "choices": [1.869, 1.947, 2.88, 4.622]}
-{"prob_id": "prob_1363", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1083.png", "question": "The HIJK is circumscribed about the circle. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.000", "choices": [1.923, 5.0, 13.0, 21.0]}
-{"prob_id": "prob_1364", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1819.png", "question": "The diameters of \\odot A, \\odot B, and \\odot C are 10, 30 and 10 units, respectively. Find ZX if AZ = CW and CW = 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 4.0, 5.0, 6.0]}
-{"prob_id": "prob_1366", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3565.png", "question": "AM bisects \\angle LAR, and AS bisects \\angle MAR. If m \\angle RAL = x+32 and m \\angle MAR = x-31, find m \\angle LAM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "63.000", "choices": [54.0, 63.0, 117.0, 126.0]}
-{"prob_id": "prob_1375", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2876.png", "question": "QRST is an isosceles trapezoid with median XY. Find TS if QR = 22 and XY = 15. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [2.0, 4.0, 8.0, 16.0]}
-{"prob_id": "prob_1380", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_969.png", "question": "Quadrilateral RSTU is a rectangle. If RZ = 3x+8 and ZS = 6x-28, find UZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.000", "choices": [14.667, 29.333, 44.0, 88.0]}
-{"prob_id": "prob_1394", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2461.png", "question": "Square WXYZ is inscribed in \\odot R. Solve for m \\angle YRS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "45.000", "choices": [30.0, 36.0, 45.0, 90.0]}
-{"prob_id": "prob_1399", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_603.png", "question": "Find the area of triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.004", "choices": [2.928, 16.004, 32.009, 142.684]}
-{"prob_id": "prob_1400", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_198.png", "question": "VWXY is a rhombus. Find m \\angle VWX if m \\angle WVY = 4b+10 and m \\angle XZW = 10b-5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "132.000", "choices": [24.0, 45.0, 90.0, 132.0]}
-{"prob_id": "prob_1401", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3122.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.142", "choices": [1.4, 7.1, 14.1, 15.6]}
-{"prob_id": "prob_1425", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3690.png", "question": "Find the area of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "127.306", "choices": [84.303, 116.504, 127.306, 169.741]}
-{"prob_id": "prob_1460", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3999.png", "question": "For isosceles trapezoid XYZW, find m \\angle W. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "110.000", "choices": [15.0, 70.0, 110.0, 250.0]}
-{"prob_id": "prob_1463", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2579.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 3.0, 6.0, 9.0]}
-{"prob_id": "prob_1469", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3249.png", "question": "Find the area of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1122.369", "choices": [770.356, 841.777, 916.41, 1122.369]}
-{"prob_id": "prob_1479", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1390.png", "question": "Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "39.000", "choices": [33.0, 39.0, 51.0, 108.0]}
-{"prob_id": "prob_1488", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_338.png", "question": "Find the length of CB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [2.857, 5.0, 6.0, 13.62]}
-{"prob_id": "prob_1494", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_714.png", "question": "Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.100", "choices": [3.5, 4.1, 4.5, 5.1]}
-{"prob_id": "prob_1496", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2485.png", "question": "ED is tangent to \\odot F at point E. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 4.0, 5.0, 6.0]}
-{"prob_id": "prob_1498", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1525.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "144.000", "choices": [36.0, 72.0, 136.0, 144.0]}
-{"prob_id": "prob_1501", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_532.png", "question": "E is between D and F. Find ED. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [3.667, 9.333, 11.0, 24.0]}
-{"prob_id": "prob_1508", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1261.png", "question": "Find the area of the figure. Perimeter = 90 centimeters. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "584.567", "choices": [387.107, 540.0, 584.567, 21044.419]}
-{"prob_id": "prob_1511", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_759.png", "question": "Assume the segments that appear to be tangent are tangent. Find the length of AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "41.000", "choices": [18.0, 23.0, 41.0, 46.0]}
-{"prob_id": "prob_1517", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3835.png", "question": "Find m \\angle 2 in the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "58.000", "choices": [32.0, 58.0, 74.0, 90.0]}
-{"prob_id": "prob_1543", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2170.png", "question": "If GK = 30, what is HJ? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 15.0, 21.0, 30.0]}
-{"prob_id": "prob_1551", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1031.png", "question": "Express the ratio of \\cos Q. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.882", "choices": [0.47, 0.53, 0.88, 1.88]}
-{"prob_id": "prob_1554", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3432.png", "question": "Find m \\angle KLM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "100.000", "choices": [80.0, 88.125, 91.875, 100.0]}
-{"prob_id": "prob_1572", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2306.png", "question": "Find the perimeter of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [12.0, 18.0, 31.177, 37.699]}
-{"prob_id": "prob_1573", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3721.png", "question": "Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "113.000", "choices": [46.0, 67.0, 90.0, 113.0]}
-{"prob_id": "prob_1589", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2491.png", "question": "a = 8, b = 15, and c = 17, find \\tan B. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.875", "choices": [1.23, 1.67, 1.88, 2.43]}
-{"prob_id": "prob_1594", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3783.png", "question": "TV is tangent to the circle, and R and S are points on the circle. What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.658", "choices": [4.8, 5.7, 6.4, 7.6]}
-{"prob_id": "prob_1613", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3523.png", "question": "Find the area of the quadrilateral. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "561.185", "choices": [162.0, 187.061, 280.592, 561.185]}
-{"prob_id": "prob_1618", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2152.png", "question": "Find the measure of \\widehat TBD in \\odot P. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "180.000", "choices": [180.0, 218.0, 270.0, 308.0]}
-{"prob_id": "prob_1628", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1065.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "46.000", "choices": [26.857, 38.889, 46.0, 54.0]}
-{"prob_id": "prob_1632", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2047.png", "question": "If m \\angle DEG is 6\\frac{1}{2} times m \\angle FEG, what is m \\angle DEG? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "156.000", "choices": [24.0, 78.0, 156.0, 173.5]}
-{"prob_id": "prob_1644", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3511.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 37.667, 54.0, 68.2]}
-{"prob_id": "prob_1657", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1538.png", "question": "Circle W has a radius of 4 units, \\odot Z has a radius of 7 units, and XY = 2. Find IC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [5.0, 10.0, 15.0, 20.0]}
-{"prob_id": "prob_1693", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3894.png", "question": "PM is a diameter of \\odot R. Find m \\widehat NMP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "270.000", "choices": [180.0, 205.0, 270.0, 295.0]}
-{"prob_id": "prob_1695", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3470.png", "question": "Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [40.0, 80.0, 110.0, 150.0]}
-{"prob_id": "prob_1706", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_96.png", "question": "Use \\odot D to find the length of \\widehat KL if JD = 7 centimeters. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.330", "choices": [6.109, 7.33, 9.774, 12.217]}
-{"prob_id": "prob_1729", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3402.png", "question": "Use parallelogram to find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "79.000", "choices": [39.0, 79.0, 101.0, 180.0]}
-{"prob_id": "prob_1730", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3863.png", "question": "Find the length of UR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [10.0, 14.0, 17.0, 27.0]}
-{"prob_id": "prob_1742", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_100.png", "question": "GHJK is a square with diagonals intersecting at L. Given that GH = 2 and GL = \\sqrt{2}, find the perimeter of \\triangle HJK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.828", "choices": [2.0, 2.828, 6.828, 8.828]}
-{"prob_id": "prob_1747", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1147.png", "question": "Find the perimeter of the trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.325", "choices": [44.325, 50.53, 56.601, 57.235]}
-{"prob_id": "prob_1750", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_947.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 4.0, 6.0, 8.0]}
-{"prob_id": "prob_1766", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3993.png", "question": "Find the measure of \\angle 1 in the isosceles trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "77.000", "choices": [26.0, 60.0, 77.0, 103.0]}
-{"prob_id": "prob_1769", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_559.png", "question": "Quadrilateral ABCD is a rhombus. If m \\angle BCD = 120, find m \\angle CDP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_1770", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2267.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 6.928203230275509, 8.0, 10.392304845413264]}
-{"prob_id": "prob_1790", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2750.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "42.000", "choices": [42.0, 69.0, 96.0, 138.0]}
-{"prob_id": "prob_1791", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2045.png", "question": "WX = YZ. What is the length of YX? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "59.000", "choices": [25.0, 50.0, 59.0, 84.0]}
-{"prob_id": "prob_1794", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3288.png", "question": "For the pair of similar figures, the area of the blue figure is 400 mm^{2} and the green figure is 64 mm^{2}, find the scale factor of the blue to the green figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.500", "choices": [0.16, 0.4, 2.5, 6.25]}
-{"prob_id": "prob_1822", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3745.png", "question": "What is the measure of \\angle 1? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "127.000", "choices": [26.5, 53.0, 74.0, 127.0]}
-{"prob_id": "prob_1835", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_62.png", "question": "For what value of y must EFGH be a parallelogram? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.000", "choices": [6.0, 30.667, 43.0, 50.4]}
-{"prob_id": "prob_1842", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3740.png", "question": "Find the radius of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.100", "choices": [1.55, 3.1, 6.2, 12.4]}
-{"prob_id": "prob_1850", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_758.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "21.000", "choices": [13.5, 21.0, 28.5, 43.5]}
-{"prob_id": "prob_1857", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_52.png", "question": "Polygon BCDE \\cong polygon RSTU. Find TS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [11.0, 12.0, 33.0, 49.0]}
-{"prob_id": "prob_1860", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_29.png", "question": "Q is the midpoint of RP. What is PQ? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "41.000", "choices": [6.833, 41.0, 82.0, 123.0]}
-{"prob_id": "prob_1871", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3112.png", "question": "Find x of isosceles \\triangle XYZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [0.75, 1.167, 2.0, 5.333]}
-{"prob_id": "prob_1876", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3954.png", "question": "In \\odot B, m \\angle LBM = 3x and m \\angle LBQ = 4x+61. What is the measure of \\angle PBQ? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "51.000", "choices": [17.0, 34.0, 51.0, 61.0]}
-{"prob_id": "prob_1877", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3919.png", "question": "Quadrilateral DEFG is a kite. Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [38.0, 52.0, 64.0, 90.0]}
-{"prob_id": "prob_1890", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_220.png", "question": "Given isosceles \\triangle JKL with base JL. If m \\angle L = 58, what is m \\angle LKJ? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "64.000", "choices": [29.0, 32.0, 64.0, 90.0]}
-{"prob_id": "prob_1933", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_912.png", "question": "What is f? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.619", "choices": [4.0, 4.619, 6.928, 9.238]}
-{"prob_id": "prob_1934", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3991.png", "question": "Quadrilateral ABCD is a rectangle. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [5.0, 12.0, 24.0, 25.0]}
-{"prob_id": "prob_1947", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1129.png", "question": "Find the measure of \\widehat AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [53.13, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_1970", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3515.png", "question": "Triangle RST is circumscribed about the circle. What is x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 6.0, 9.0, 11.0]}
-{"prob_id": "prob_1973", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2671.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [5.0, 80.0, 85.0, 100.0]}
-{"prob_id": "prob_1980", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2393.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [1.5, 1.854, 3.0, 6.0]}
-{"prob_id": "prob_1996", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2149.png", "question": "WX = ZY, and m \\widehat ZW = 120. Find the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_2015", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1926.png", "question": "Given that UT = TV and m \\angle PQS = 42, find m \\angle VTS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "132.000", "choices": [42.0, 48.0, 96.0, 132.0]}
-{"prob_id": "prob_2031", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3169.png", "question": "What is the area of \\odot K? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "201.062", "choices": [50.265, 110.851, 201.062, 804.248]}
-{"prob_id": "prob_2043", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3513.png", "question": "What is the measure of \\angle 1 in rhombus PQRS? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [38.0, 52.0, 76.0, 104.0]}
-{"prob_id": "prob_2053", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3729.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.854", "choices": [3.9, 5.2, 7.9, 20.4]}
-{"prob_id": "prob_2057", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2664.png", "question": "AB, BC, CD, and AD are tangent to a circle. If AB = 19, DC = 14, and AD = 27, find BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 22.0, 27.0, 32.0]}
-{"prob_id": "prob_2070", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_527.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.748", "choices": [11.0, 15.556349186104047, 17.74823934929885, 25.553864678361276]}
-{"prob_id": "prob_2071", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_925.png", "question": "Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [4.0, 6.0, 10.0, 11.0]}
-{"prob_id": "prob_2091", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3690.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "26.632", "choices": [26.632, 37.434, 55.938, 127.306]}
-{"prob_id": "prob_2095", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2404.png", "question": "Find the area of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "665.108", "choices": [456.507, 498.831, 665.108, 697.481]}
-{"prob_id": "prob_2099", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3464.png", "question": "If TR = 12 what is CP? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [4.0, 8.0, 24.0, 36.0]}
-{"prob_id": "prob_2117", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_503.png", "question": "In \\triangle JKL, points Q, R, and S are midpoints of the sides. If QR = 6, determine the length of JL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [1.5, 3.0, 6.0, 12.0]}
-{"prob_id": "prob_2130", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1900.png", "question": "Quadrilateral ABCD is a rectangle. If m \\angle ADB = 4x+8 and m \\angle DBA = 6x+12, find \\angle DBC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "36.000", "choices": [36.0, 54.0, 72.0, 108.0]}
-{"prob_id": "prob_2137", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_643.png", "question": "Find m \\angle UWT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "139.000", "choices": [20.5, 41.0, 98.0, 139.0]}
-{"prob_id": "prob_2141", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_566.png", "question": "Use parallelogram MNPR to find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [8.0, 20.0, 24.0, 32.0]}
-{"prob_id": "prob_2142", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_414.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 3.0, 4.0, 8.0]}
-{"prob_id": "prob_2146", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2541.png", "question": "Find the value of variable y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "150.000", "choices": [30.0, 75.0, 105.0, 150.0]}
-{"prob_id": "prob_2173", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1775.png", "question": "Polygon ABCD \\cong polygon PQRS. Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.000", "choices": [4.0, 8.0, 38.0, 48.0]}
-{"prob_id": "prob_2197", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_688.png", "question": "Find the value of variable z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_2200", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1869.png", "question": "GHJK is a rhombus. Find m \\angle GKJ if m \\angle JLH = 4b-6 and m \\angle JKH = 2b+11. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "118.000", "choices": [31.0, 59.0, 90.0, 118.0]}
-{"prob_id": "prob_2202", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_425.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 7.5, 10.0, 12.5]}
-{"prob_id": "prob_2206", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2129.png", "question": "In \\odot S, HJ = 22, LG = 18, m \\widehat IJ = 35, and m \\widehat LM = 30. Solve for the measure of HR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [9.0, 11.0, 22.0, 44.0]}
-{"prob_id": "prob_2209", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_48.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.402", "choices": [5.657, 6.364, 11.402, 12.728]}
-{"prob_id": "prob_2239", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2307.png", "question": "In the triangle, what is the measure of \\angle X? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "72.000", "choices": [18.0, 72.0, 90.0, 120.0]}
-{"prob_id": "prob_2253", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1772.png", "question": "Find AD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [5.4, 11.619, 16.0, 25.0]}
-{"prob_id": "prob_2254", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2635.png", "question": "Use rhombus XYZW with m \\angle WYZ = 53, VW = 3, XV = 2a-2, and ZV = \\frac{5a+1}{4}. Find XZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.000", "choices": [2.0, 4.0, 8.0, 16.0]}
-{"prob_id": "prob_2259", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2489.png", "question": "If a = 10\\sqrt{3}, find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.981", "choices": [10.0, 15.0, 17.32050807568877, 25.980762113533157]}
-{"prob_id": "prob_2264", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1487.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.726", "choices": [7.1, 7.7, 21.9, 28.9]}
-{"prob_id": "prob_2273", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_499.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [20.0, 30.0, 40.0, 50.0]}
-{"prob_id": "prob_2281", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_973.png", "question": "In \\odot D, DE = EC, m \\widehat CF = 60, and DE \\perp EC. Find m \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [30.0, 45.0, 60.0, 90.0]}
-{"prob_id": "prob_2287", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3110.png", "question": "Find AB if \\triangle ABC is an isosceles triangle with AB = BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [3.0, 4.0, 7.0, 11.0]}
-{"prob_id": "prob_2297", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_259.png", "question": "Find the diameter of \\odot P. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [5.0, 10.0, 20.0, 40.0]}
-{"prob_id": "prob_2325", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3218.png", "question": "What is the value of e? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [32.0, 35.0, 58.0, 90.0]}
-{"prob_id": "prob_2330", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_907.png", "question": "Find RT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [6.667, 9.6, 14.667, 15.0]}
-{"prob_id": "prob_2331", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1829.png", "question": "Use parallelogram NQRM to find QR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [13.0, 14.0, 15.0, 16.0]}
-{"prob_id": "prob_2349", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3938.png", "question": "Find the value of variable d. Lines that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "124.000", "choices": [28.0, 60.0, 124.0, 184.0]}
-{"prob_id": "prob_2351", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1749.png", "question": "Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "105.000", "choices": [75.0, 90.0, 105.0, 210.0]}
-{"prob_id": "prob_2363", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1789.png", "question": "Find the length of RU if \\triangle RUW \\sim \\triangle STV, ST = 24, VS = 12, VT = 18 and UW = 21. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [20.571, 28.0, 36.0, 42.0]}
-{"prob_id": "prob_2366", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1268.png", "question": "PT = 4x-6 and QT = 3x+4, find the length of TP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [6.8, 13.6, 34.0, 68.0]}
-{"prob_id": "prob_2385", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_810.png", "question": "For the pair of similar figures, the area of the blue figure is 36 yd^{2}, find the area of the green figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [9.0, 18.0, 72.0, 144.0]}
-{"prob_id": "prob_2386", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1778.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [17.083, 17.899, 21.083, 22.0]}
-{"prob_id": "prob_2403", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_559.png", "question": "Quadrilateral ABCD is a rhombus. If m \\angle ABC = 2x-7 and m \\angle BCD = 2x+3, find m \\angle DAB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "95.000", "choices": [33.0, 50.0, 95.0, 120.0]}
-{"prob_id": "prob_2405", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1136.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.000", "choices": [42.0, 48.0, 69.0, 90.0]}
-{"prob_id": "prob_2420", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1723.png", "question": "What is the length of RS? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.773", "choices": [9.773, 18.0, 25.357, 35.097]}
-{"prob_id": "prob_2423", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_265.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "36.000", "choices": [30.0, 36.0, 45.0, 72.0]}
-{"prob_id": "prob_2427", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1949.png", "question": "Find m \\angle C. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_2449", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1795.png", "question": "In ABCD, m \\angle ABC = 79, BC = 62.4, and BD = 75. Find the measurement of \\angle DAB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "101.000", "choices": [11.0, 79.0, 101.0, 158.0]}
-{"prob_id": "prob_2450", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1456.png", "question": "In \\odot R, SU = YW = 20, and m \\widehat YX = 45. Find m \\widehat SU. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [20.0, 30.0, 45.0, 90.0]}
-{"prob_id": "prob_2455", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3223.png", "question": "Find the measure of \\angle Q. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "64.500", "choices": [2.5, 59.831, 64.5, 123.5]}
-{"prob_id": "prob_2457", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3024.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "471.934", "choices": [332.3, 396.0, 471.9, 616.1]}
-{"prob_id": "prob_2460", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1402.png", "question": "Quadrilateral WXZY is a rectangle. Find the measure of \\angle 7 if m \\angle 1 = 30. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 75.0, 120.0]}
-{"prob_id": "prob_2482", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3526.png", "question": "\\triangle MHJ \\cong \\triangle PQJ. Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 4.0, 5.0, 6.0]}
-{"prob_id": "prob_2487", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3561.png", "question": "What is the value of y? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.392", "choices": [2.133, 8.485, 10.392, 12.5]}
-{"prob_id": "prob_2495", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3946.png", "question": "In \\odot R, m \\widehat MN = 120. Solve for m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 60.0, 120.0, 150.0]}
-{"prob_id": "prob_2504", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3909.png", "question": "In \\triangle QRS, T, U, and B are midpoints. Find the perimeter of \\triangle UTB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "75.000", "choices": [75.0, 190.0, 200.0, 240.0]}
-{"prob_id": "prob_2505", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3977.png", "question": "The polygons are similar. Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 4.8, 13.333, 16.0]}
-{"prob_id": "prob_2507", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_584.png", "question": "\\triangle JKL \\sim \\triangle WYZ. Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [44.0, 56.0, 65.0, 71.0]}
-{"prob_id": "prob_2550", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3051.png", "question": "Find m \\angle W. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "76.000", "choices": [38.0, 38.0, 76.0, 152.0]}
-{"prob_id": "prob_2553", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1105.png", "question": "\\triangle DFG \\sim \\triangle HKM. Determine the length of GD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [9.818, 13.75, 16.364, 25.0]}
-{"prob_id": "prob_2573", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3860.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [0.75, 1.5, 3.0, 4.5]}
-{"prob_id": "prob_2580", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1498.png", "question": "HJ is the perpendicular bisector of KL. HJ bisects \\angle KHL. Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [4.8, 12.0, 16.5, 48.0]}
-{"prob_id": "prob_2585", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1969.png", "question": "What is the measure of \\angle 1 in the kite? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [22.5, 45.0, 67.5, 90.0]}
-{"prob_id": "prob_2602", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_953.png", "question": "\\triangle KLM is the midsegment triangle of \\triangle GHJ. What is the perimeter of \\triangle KLM? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.000", "choices": [17.0, 34.0, 39.0, 46.0]}
-{"prob_id": "prob_2627", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3878.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [12.0, 14.0, 16.0, 18.0]}
-{"prob_id": "prob_2636", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2084.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "39.961", "choices": [30.0, 35.0, 40.0, 45.0]}
-{"prob_id": "prob_2639", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2131.png", "question": "ZA = 9. What is the length of ZC? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.500", "choices": [3.0, 4.5, 6.0, 13.5]}
-{"prob_id": "prob_2649", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2152.png", "question": "Find the measure of \\widehat TC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "128.000", "choices": [52.0, 90.0, 128.0, 142.0]}
-{"prob_id": "prob_2656", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1019.png", "question": "If CW = WF and ED = 30, what is AB? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [15.0, 30.0, 42.426, 60.0]}
-{"prob_id": "prob_2663", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1253.png", "question": "m \\widehat AB = 176, and m \\widehat BC = 42. Solve for the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "21.000", "choices": [21.0, 71.0, 88.0, 109.0]}
-{"prob_id": "prob_2670", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3928.png", "question": "Find the measure of \\angle S. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "135.000", "choices": [45.0, 49.091, 67.5, 135.0]}
-{"prob_id": "prob_2672", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1238.png", "question": "Find y if P is between Q and R. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [1.0, 4.0, 5.25, 20.0]}
-{"prob_id": "prob_2673", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2979.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "83.235", "choices": [48.0, 58.0, 68.0, 83.235]}
-{"prob_id": "prob_2675", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3377.png", "question": "In \\triangle CDF, K is the centroid and DK = 16. Find GK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 8.0, 18.0, 24.0]}
-{"prob_id": "prob_2686", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2217.png", "question": "Use rhombus ABCD with AY = 6, DY = 3r+3, and BY = \\frac{10r-4}{2}. Find m \\angle ADY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.745", "choices": [29.745, 60.255, 90.0, 120.51]}
-{"prob_id": "prob_2695", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_397.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [5.0, 36.0, 74.0, 115.0]}
-{"prob_id": "prob_2699", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_720.png", "question": "WXYZ is a kite. If m \\angle WXY = 13x+24, m \\angle WZY = 35, and m \\angle ZWX = 13x+14, find m \\angle ZYX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "105.000", "choices": [13.0, 24.0, 105.0, 210.0]}
-{"prob_id": "prob_2706", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2491.png", "question": "a = 8, b = 15, and c = 17, find \\cos A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.882", "choices": [0.12, 0.22, 0.44, 0.88]}
-{"prob_id": "prob_2708", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1480.png", "question": "Find WB if \\triangle RST \\sim \\triangle UVW, TA and WB are medians, TA = 8, RA = 3, WB = 3x-6, and UB = x+2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "96.000", "choices": [4.571, 36.0, 72.0, 96.0]}
-{"prob_id": "prob_2718", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3613.png", "question": "What is x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 14.142, 17.321, 40.0]}
-{"prob_id": "prob_2726", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2342.png", "question": "Find m \\angle PQM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "92.000", "choices": [44.0, 46.0, 88.0, 92.0]}
-{"prob_id": "prob_2736", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_256.png", "question": "m \\angle 3 = 43. Find the measure of \\angle 13. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.000", "choices": [33.0, 43.0, 53.0, 63.0]}
-{"prob_id": "prob_2747", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3877.png", "question": "Find the area of the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "73.901", "choices": [64.0, 73.901, 110.851, 221.702]}
-{"prob_id": "prob_2782", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1117.png", "question": "Find the value of variable y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.697", "choices": [8.485, 10.392, 13.416, 14.697]}
-{"prob_id": "prob_2802", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3738.png", "question": "RS and RT are tangent to \\odot Q. Find RS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.100", "choices": [1.05, 2.1, 4.2, 286.74]}
-{"prob_id": "prob_2805", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3407.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [36.0, 60.0, 80.0, 100.0]}
-{"prob_id": "prob_2808", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1375.png", "question": "What is the measure of \\angle TSR? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "56.000", "choices": [34.0, 42.0, 56.0, 82.0]}
-{"prob_id": "prob_2811", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3980.png", "question": "Find m \\widehat AD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [35.0, 65.0, 80.0, 145.0]}
-{"prob_id": "prob_2845", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3402.png", "question": "Use parallelogram to find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "101.000", "choices": [79.0, 101.0, 180.0, 360.0]}
-{"prob_id": "prob_2871", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1663.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "91.924", "choices": [65.0, 91.9, 112.6, 130.0]}
-{"prob_id": "prob_2875", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_826.png", "question": "Find the measure of \\angle A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "53.000", "choices": [46.0, 53.0, 81.0, 127.0]}
-{"prob_id": "prob_2878", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_978.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "74.000", "choices": [74.0, 81.456, 97.196, 112.0]}
-{"prob_id": "prob_2880", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3687.png", "question": "For isosceles trapezoid ABCD, X and Y are midpoints of the legs. Find m \\angle CYX if m \\angle ADY = 78. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "78.000", "choices": [39.0, 51.0, 78.0, 102.0]}
-{"prob_id": "prob_2881", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2311.png", "question": "\\triangle BTW \\sim \\triangle ETC. Find m \\angle TEC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "79.000", "choices": [34.0, 79.0, 101.0, 146.0]}
-{"prob_id": "prob_2887", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1898.png", "question": "What is m \\angle APD? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 90.0, 120.0, 150.0]}
-{"prob_id": "prob_2898", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1928.png", "question": "Find DF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.500", "choices": [1.15, 1.25, 2.3, 2.5]}
-{"prob_id": "prob_2899", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2490.png", "question": "Find the measure of QR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.400", "choices": [3.8, 4.0, 4.1, 4.4]}
-{"prob_id": "prob_2908", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2994.png", "question": "Find m \\angle DBC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "135.000", "choices": [45.0, 90.0, 135.0, 180.0]}
-{"prob_id": "prob_2920", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_167.png", "question": "Use parallelogram to find a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [7.0, 21.0, 27.0, 28.0]}
-{"prob_id": "prob_2927", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_56.png", "question": "What is the value of variable w? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "250.000", "choices": [110.0, 140.0, 210.0, 250.0]}
-{"prob_id": "prob_2934", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_456.png", "question": "Find h. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.849", "choices": [10.5, 14.849242404917499, 18.186533479473212, 21.0]}
-{"prob_id": "prob_2938", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_135.png", "question": "Find the area of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.383", "choices": [3.9, 11.7, 23.4, 46.8]}
-{"prob_id": "prob_2945", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2709.png", "question": "Find the measure of \\angle 2 for the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.000", "choices": [32.0, 38.0, 70.0, 110.0]}
-{"prob_id": "prob_2951", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3451.png", "question": "Find the area of sector LKJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.425", "choices": [5.188, 10.053, 80.425, 723.823]}
-{"prob_id": "prob_2953", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3161.png", "question": "Parallelogram MNPQ is shown. Solve for m \\angle M. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "102.000", "choices": [78.0, 90.0, 102.0, 246.0]}
-{"prob_id": "prob_2963", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_696.png", "question": "Quadrilateral KLMN is a rectangle. If PL = x^{2}-1 and PM = 4x+11, find KP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [17.5, 35.0, 51.98, 70.0]}
-{"prob_id": "prob_2964", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_732.png", "question": "Find x so that line m \\parallel line n. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [9.0, 10.0, 11.0, 12.0]}
-{"prob_id": "prob_2970", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2211.png", "question": "JH, JP, and PH are midsegments of \\triangle KLM. Find m \\angle JPM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "123.000", "choices": [28.5, 57.0, 66.0, 123.0]}
-{"prob_id": "prob_2976", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1313.png", "question": "Find the area of the regular polygon. Assume that the triangle is equilateral. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.785", "choices": [20.785, 32.0, 50.265, 83.138]}
-{"prob_id": "prob_2989", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2723.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [7.5, 13.125, 18.75, 30.0]}
-{"prob_id": "prob_2996", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1183.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "452.389", "choices": [113.097, 226.195, 437.31, 452.389]}
-{"prob_id": "prob_2997", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_685.png", "question": "The segment is tangent to the circle. Find m \\angle J. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "53.130", "choices": [36.87, 38.66, 51.34, 53.13]}
-{"prob_id": "prob_3008", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3215.png", "question": "Find the measure of \\angle DAC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [28.0, 62.0, 118.0, 152.0]}
-{"prob_id": "prob_3012", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3802.png", "question": "Use \\odot P to find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "36.000", "choices": [18.0, 22.5, 30.0, 36.0]}
-{"prob_id": "prob_3016", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2453.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "259.808", "choices": [86.6, 129.9, 150.0, 259.8]}
-{"prob_id": "prob_3024", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_415.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [20.0, 40.0, 80.0, 140.0]}
-{"prob_id": "prob_3028", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_398.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "58.000", "choices": [25.0, 37.0, 39.0, 58.0]}
-{"prob_id": "prob_3032", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2740.png", "question": "Express the ratio of \\sin J. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.923", "choices": [0.385, 0.923, 1.083, 2.4]}
-{"prob_id": "prob_3036", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_912.png", "question": "What is h? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.238", "choices": [4.0, 4.619, 6.928, 9.238]}
-{"prob_id": "prob_3037", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2445.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.809", "choices": [18.8, 23.2, 25.9, 44.0]}
-{"prob_id": "prob_3048", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2275.png", "question": "Find m \\widehat CD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [40.0, 50.0, 80.0, 140.0]}
-{"prob_id": "prob_3050", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2580.png", "question": "If AB = DA = ED = CF, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.625", "choices": [0.5, 0.559, 0.571, 0.625]}
-{"prob_id": "prob_3074", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2531.png", "question": "If PR \\parallel KL, KN = 9, LN = 16, and PM = 2 KP, find ML. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [15.0, 16.0, 20.0, 24.0]}
-{"prob_id": "prob_3092", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1756.png", "question": "m \\angle 19 = 100+20x, m \\angle 20 = 20x. Find the measure of \\angle 20. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [20.0, 40.0, 60.0, 80.0]}
-{"prob_id": "prob_3093", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_104.png", "question": "Each pair of polygons is similar. Find AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.600", "choices": [7.0, 7.6, 12.0, 19.0]}
-{"prob_id": "prob_3107", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2841.png", "question": "Find the perimeter of \\triangle DEF, if \\triangle DEF \\sim \\triangle CBF, perimeter of \\triangle CBF = 27, DF = 6, and FC = 8. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.250", "choices": [16.0, 17.25, 20.25, 27.0]}
-{"prob_id": "prob_3144", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2803.png", "question": "Find ML. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "39.000", "choices": [24.0, 32.726, 36.0, 39.0]}
-{"prob_id": "prob_3152", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_308.png", "question": "JKLM is a rhombus. If CK = 8, JK = 10 and \\angle JKM = 37. What is m \\angle MKL? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.000", "choices": [37.0, 53.0, 74.0, 106.0]}
-{"prob_id": "prob_3182", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3879.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "45.000", "choices": [30.0, 45.0, 60.0, 90.0]}
-{"prob_id": "prob_3187", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1811.png", "question": "\\triangle ABC \\sim \\triangle XYZ. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.500", "choices": [1.5, 2.667, 3.0, 6.0]}
-{"prob_id": "prob_3237", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2639.png", "question": "In \\triangle ABC, AF = 9, and GE = 2.4. Find the length of AG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [3.6, 6.0, 7.2, 27.0]}
-{"prob_id": "prob_3247", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2451.png", "question": "What is the length of GC? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "21.213", "choices": [15.0, 17.321, 21.213, 30.0]}
-{"prob_id": "prob_3255", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3278.png", "question": "Find the exact area of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "157.080", "choices": [20.0, 44.429, 157.08, 628.319]}
-{"prob_id": "prob_3269", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2474.png", "question": "In \\odot Y the radius is 34, AB = 60, and m \\widehat AC = 71. Find the length of YD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [16.0, 18.0, 30.0, 57.541]}
-{"prob_id": "prob_3272", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3759.png", "question": "Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.946", "choices": [8.319, 9.239, 17.96, 19.946]}
-{"prob_id": "prob_3290", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_874.png", "question": "\\odot A and \\odot B are congruent. CD is a chord of both circles. If a radius = 13 ft and CD = 10 ft, how long is AB? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [10.0, 12.0, 15.199, 24.0]}
-{"prob_id": "prob_3371", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1989.png", "question": "Find the measure of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [25.0, 30.0, 35.0, 40.0]}
-{"prob_id": "prob_3384", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3967.png", "question": "If QR = 2, XW = 12, QW = 15, and ST = 5, find QS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [4.167, 7.5, 8.0, 10.0]}
-{"prob_id": "prob_3399", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1653.png", "question": "What must the value of x if \\triangle EFG \\cong \\triangle EHG? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.500", "choices": [4.25, 4.667, 5.5, 24.0]}
-{"prob_id": "prob_3400", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_215.png", "question": "Given that \\angle PQR \\cong \\angle XYZ. Determine m \\angle Z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [35.0, 55.0, 70.0, 90.0]}
-{"prob_id": "prob_3421", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1242.png", "question": "AD and BE are diameters. Find m \\angle AQE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "145.000", "choices": [35.0, 55.0, 125.0, 145.0]}
-{"prob_id": "prob_3424", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_845.png", "question": "TUWY is a rhombus. What is the length of UW? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.4, 3.0, 4.243, 6.0]}
-{"prob_id": "prob_3427", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_853.png", "question": "Assume that the segment is tangent, find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.644", "choices": [3.7416573867739413, 4.123105625617661, 9.643650760992955, 22.02271554554524]}
-{"prob_id": "prob_3428", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3770.png", "question": "What is PQ? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [1.333, 12.0, 19.238, 21.238]}
-{"prob_id": "prob_3450", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2677.png", "question": "What is the length of \\widehat AB? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.883", "choices": [10.973, 20.883, 21.945, 41.766]}
-{"prob_id": "prob_3455", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3355.png", "question": "The area of \\parallelogram ABCD is 150 square meters. The area of \\parallelogram FGHJ is 54 square meters. If \\parallelogram ABCD \\sim \\parallelogram FGHJ, find the scale factor of \\parallelogram FGHJ to \\parallelogram ABCD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.600", "choices": [0.36, 0.6, 1.6666666666666667, 2.7777777777777777]}
-{"prob_id": "prob_3459", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3382.png", "question": "Find the exact radius of circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.349", "choices": [9.192, 12.349, 24.698, 77.592]}
-{"prob_id": "prob_3462", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2951.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "135.000", "choices": [45.0, 90.0, 135.0, 180.0]}
-{"prob_id": "prob_3464", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2355.png", "question": "JKMN is a rectangle. If m \\angle NKM = x^{2}+4 and m \\angle KNM = x+30, find m \\angle QJK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.000", "choices": [37.0, 53.0, 74.0, 106.0]}
-{"prob_id": "prob_3468", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3311.png", "question": "\\triangle KLN and \\triangle LMN are isosceles and m \\angle JKN = 130. Find the measure of \\angle J. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "106.000", "choices": [105.0, 106.0, 108.0, 111.0]}
-{"prob_id": "prob_3470", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2925.png", "question": "m \\angle 1 = 94. Find the measure of \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "94.000", "choices": [76.0, 86.0, 94.0, 96.0]}
-{"prob_id": "prob_3475", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1575.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.500", "choices": [5.5, 7.778174593052023, 11.0, 15.556349186104047]}
-{"prob_id": "prob_3481", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3042.png", "question": "Find x so that line l \\parallel line m. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.000", "choices": [14.4, 19.0, 41.5, 67.0]}
-{"prob_id": "prob_3485", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3209.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.000", "choices": [-2.0, 0.0, 3.0, 6.0]}
-{"prob_id": "prob_3497", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_935.png", "question": "In quadrilateral PQRS, PQ = 721, QR = 547, RS = 593, PS = 756, and m \\angle P = 58. Find m \\angle PSQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "58.552", "choices": [40.333, 58.552, 77.793, 122.0]}
-{"prob_id": "prob_3509", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3049.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "61.726", "choices": [61.7, 71.2, 90.0, 118.3]}
-{"prob_id": "prob_3515", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3618.png", "question": "Find the measure of \\angle 6. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "86.000", "choices": [24.0, 74.0, 86.0, 104.0]}
-{"prob_id": "prob_3516", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2596.png", "question": "Solve for BA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "41.994", "choices": [11.885, 36.595, 41.994, 44.981]}
-{"prob_id": "prob_3517", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_848.png", "question": "Use parallelogram ABCD to find m \\angle BCD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [15.0, 65.0, 80.0, 115.0]}
-{"prob_id": "prob_3529", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_343.png", "question": "What is the measure of \\angle DEF? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "67.500", "choices": [67.5, 112.5, 202.5, 292.5]}
-{"prob_id": "prob_3569", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3805.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_3584", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3493.png", "question": "Find the measure of \\angle P. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "81.512", "choices": [33.762, 56.847, 64.725, 81.512]}
-{"prob_id": "prob_3589", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_355.png", "question": "The square is circumscribed to the circle. Find the exact circumference of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "78.540", "choices": [39.269908169872416, 78.53981633974483, 94.24777960769379, 157.07963267948966]}
-{"prob_id": "prob_3593", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3051.png", "question": "Find m \\angle Y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "68.000", "choices": [34.0, 68.0, 70.0, 136.0]}
-{"prob_id": "prob_3594", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2384.png", "question": "Q is the incenter of \\triangle JKL. Find LP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.755", "choices": [15.0, 27.061, 30.755, 34.218]}
-{"prob_id": "prob_3604", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_369.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "21.000", "choices": [7.0, 15.0, 21.0, 75.0]}
-{"prob_id": "prob_3616", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2386.png", "question": "Find the area of sector JHG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.686", "choices": [15.708, 40.841, 70.686, 183.783]}
-{"prob_id": "prob_3617", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3050.png", "question": "m \\angle 9 = 141+x, m \\angle 10 = 25+x, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [7.0, 65.0, 97.0, 148.0]}
-{"prob_id": "prob_3624", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3672.png", "question": "WXYZ is a parallelogram. What is the measure of \\angle W? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "99.000", "choices": [81.0, 90.0, 99.0, 126.0]}
-{"prob_id": "prob_3625", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3495.png", "question": "Find the length of YW. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.250", "choices": [2.25, 6.806, 7.2, 11.25]}
-{"prob_id": "prob_3634", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_890.png", "question": "If AB = 60 and DE = 48, find FE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [24.0, 30.0, 54.991, 56.604]}
-{"prob_id": "prob_3648", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1002.png", "question": "Find the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "116.000", "choices": [64.0, 81.0, 82.0, 116.0]}
-{"prob_id": "prob_3649", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_286.png", "question": "Find the circumference. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "47.752", "choices": [23.876, 47.752, 181.458, 1221.305]}
-{"prob_id": "prob_3654", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1812.png", "question": "For the pair of similar figures, the area of the blue figure is 30 m^{2} and the green figure is 40 m^{2}, find the scale factor from the blue to the green figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.866", "choices": [0.75, 0.8660254037844386, 1.1547005383792517, 1.3333333333333333]}
-{"prob_id": "prob_3658", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2862.png", "question": "Find the value of variable b. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "109.000", "choices": [11.0, 109.0, 150.0, 218.0]}
-{"prob_id": "prob_3665", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3296.png", "question": "m \\angle WXY = m \\angle TXY. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [2.0, 4.0, 5.0, 10.0]}
-{"prob_id": "prob_3670", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1828.png", "question": "Find the area of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "584.240", "choices": [73.0, 292.1, 584.2, 1168.5]}
-{"prob_id": "prob_3685", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_806.png", "question": "Determine the value of z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [2.364, 6.077, 7.0, 11.875]}
-{"prob_id": "prob_3689", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1116.png", "question": "What is the measure of \\angle 1? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "123.000", "choices": [3.0, 63.0, 123.0, 126.0]}
-{"prob_id": "prob_3692", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3746.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [1.8, 5.0, 46.0, 90.0]}
-{"prob_id": "prob_3700", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_401.png", "question": "In \\odot R, find m \\widehat TUV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "113.889", "choices": [54.071, 113.889, 125.929, 130.751]}
-{"prob_id": "prob_3706", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1528.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "31.416", "choices": [21.991, 25.133, 31.416, 87.965]}
-{"prob_id": "prob_3711", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3323.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.735", "choices": [13.735, 77.735, 100.531, 258.754]}
-{"prob_id": "prob_3716", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2053.png", "question": "Find the area of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 2.236, 3.0, 6.0]}
-{"prob_id": "prob_3719", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2675.png", "question": "Determine x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.000", "choices": [1.0, 4.0, 4.01, 57.342]}
-{"prob_id": "prob_3743", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1593.png", "question": "BD bisects \\angle EBC. If m \\angle EBD = 4x-8 and m \\angle EBC = 5x+20, find m \\angle EBC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [40.0, 80.0, 140.0, 300.0]}
-{"prob_id": "prob_3748", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3330.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "96.000", "choices": [28.0, 48.0, 96.0, 192.0]}
-{"prob_id": "prob_3755", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2384.png", "question": "Q is the incenter of \\triangle JKL. Find JN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [20.0, 27.061, 30.755, 34.218]}
-{"prob_id": "prob_3766", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1236.png", "question": "Solve for g. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.705", "choices": [2.898, 5.472, 6.437, 14.705]}
-{"prob_id": "prob_3770", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3861.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [19.292, 22.0, 24.0, 28.0]}
-{"prob_id": "prob_3773", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_878.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.206", "choices": [21.1, 29.2, 32.7, 42.4]}
-{"prob_id": "prob_3776", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_752.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [5.162, 6.0, 7.292, 14.649]}
-{"prob_id": "prob_3786", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1403.png", "question": "Use rhombus QRST. Find m \\angle TQS if m \\angle RST = 56. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [28.0, 56.0, 62.0, 124.0]}
-{"prob_id": "prob_3791", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1947.png", "question": "Find the measure of PQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.600", "choices": [3.924, 4.8, 9.6, 12.4]}
-{"prob_id": "prob_3819", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2238.png", "question": "What is the length of QN? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.450", "choices": [14.422, 14.697, 19.698, 32.45]}
-{"prob_id": "prob_3821", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3821.png", "question": "Find the measure of \\angle CFD on \\odot F with diameter AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "123.000", "choices": [115.0, 119.0, 120.0, 123.0]}
-{"prob_id": "prob_3830", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1084.png", "question": "Find the measure of \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "42.000", "choices": [28.0, 32.0, 38.0, 42.0]}
-{"prob_id": "prob_3831", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2208.png", "question": "Find ST. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 10.0, 12.0, 16.0]}
-{"prob_id": "prob_3846", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2271.png", "question": "Use \\triangle ABC, where L, M, and N are midpoints of the sides. If AC = 20, what is LN? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [10.0, 20.0, 40.0, 60.0]}
-{"prob_id": "prob_3848", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3975.png", "question": "Express the ratio of \\sin C. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.600", "choices": [0.6, 0.75, 0.8, 1.33]}
-{"prob_id": "prob_3852", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2986.png", "question": "Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [2.714, 6.0, 11.5, 14.538]}
-{"prob_id": "prob_3855", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2462.png", "question": "Find the area of quadrilateral XYZW if XZ = 39, HW = 20, and YG = 21. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "799.500", "choices": [390.0, 409.5, 799.5, 1599.0]}
-{"prob_id": "prob_3883", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3954.png", "question": "In \\odot B, m \\angle LBM = 3x and m \\angle LBQ = 4x+61. What is the measure of \\widehat LK? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "39.000", "choices": [39.0, 51.0, 77.571, 129.0]}
-{"prob_id": "prob_3888", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3365.png", "question": "What is the value of \\tan Y? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.667", "choices": [0.555, 0.667, 0.832, 1.5]}
-{"prob_id": "prob_3890", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2949.png", "question": "Find the measure of \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "45.000", "choices": [40.0, 45.0, 50.0, 95.0]}
-{"prob_id": "prob_3906", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1262.png", "question": "m \\angle 13 = 2x+94, m \\angle 14 = 7x+49, find the measurement of \\angle 14. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "112.000", "choices": [77.778, 102.222, 112.0, 224.0]}
-{"prob_id": "prob_3915", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3832.png", "question": "In \\triangle STR, H is the centroid, EH = 6, DH = 4, and SM = 24. What is HR? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [8.0, 12.0, 16.0, 18.0]}
-{"prob_id": "prob_3924", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_379.png", "question": "Determine the length of XY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.689", "choices": [11.0, 12.689, 24.62, 26.589]}
-{"prob_id": "prob_3931", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2383.png", "question": "Given line a \\parallel line b, find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "79.000", "choices": [47.0, 54.0, 79.0, 101.0]}
-{"prob_id": "prob_3940", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_479.png", "question": "Find the area of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "46.765", "choices": [15.588, 46.765, 72.0, 144.0]}
-{"prob_id": "prob_3945", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_877.png", "question": "Find the perimeter of triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.324", "choices": [48.0, 51.324, 52.0, 55.324]}
-{"prob_id": "prob_3952", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2039.png", "question": "In \\odot J, GH = 9 and KL = 4x+1. Find GR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.500", "choices": [4.5, 6.727, 9.0, 13.454]}
-{"prob_id": "prob_3964", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3139.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_3967", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1844.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.214", "choices": [8.7, 14.6, 22.2, 37.2]}
-{"prob_id": "prob_3975", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_345.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.798", "choices": [2.449489742783178, 2.449489742783178, 4.0, 9.797958971132712]}
-{"prob_id": "prob_3992", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3740.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.191", "choices": [19.5, 30.2, 60.4, 120.8]}
-{"prob_id": "prob_4007", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3241.png", "question": "What is the perimeter of the kite? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.530", "choices": [23.324, 30.53, 35.956, 37.736]}
-{"prob_id": "prob_4021", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1285.png", "question": "Assume the segments that appear to be tangent are tangent. Find JM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [11.0, 22.0, 31.113, 44.0]}
-{"prob_id": "prob_4022", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_349.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [10.0, 15.0, 26.25, 27.857]}
-{"prob_id": "prob_4025", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2052.png", "question": "If FG = 59, what is EF? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "102.000", "choices": [25.0, 34.0, 37.5, 102.0]}
-{"prob_id": "prob_4029", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2064.png", "question": "Find the value of variable x in the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [9.375, 15.0, 18.562, 30.0]}
-{"prob_id": "prob_4040", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_626.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.667", "choices": [1.3333333333333333, 4.333333333333333, 6.0, 8.666666666666666]}
-{"prob_id": "prob_4044", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_9.png", "question": "In rhombus ABCD, m \\angle DAB = 2 m \\angle ADC and CB = 6. Find m \\angle ADB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_4046", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3682.png", "question": "m \\angle 2 = 2x, m \\angle 3 = x. Find m \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 45.0, 60.0, 90.0]}
-{"prob_id": "prob_4052", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1399.png", "question": "Determine m \\angle U. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "101.000", "choices": [32.0, 47.0, 79.0, 101.0]}
-{"prob_id": "prob_4062", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1733.png", "question": "Find the measure of \\angle ADB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "42.379", "choices": [23.991, 26.0, 42.379, 79.901]}
-{"prob_id": "prob_4068", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_198.png", "question": "VWXY is a rhombus. Find m \\angle ZWX if m \\angle WVY = 4b+10 and m \\angle XZW = 10b-5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "66.000", "choices": [24.0, 45.0, 66.0, 90.0]}
-{"prob_id": "prob_4084", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1665.png", "question": "EFGH is a parallelogram. Find HF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [9.0, 12.0, 18.0, 24.0]}
-{"prob_id": "prob_4088", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1103.png", "question": "Solve for m \\angle RST. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_4097", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2946.png", "question": "Find f. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.400", "choices": [4.286, 8.4, 29.4, 52.5]}
-{"prob_id": "prob_4100", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2418.png", "question": "\\parallelogram ABCD \\sim \\parallelogram EFGH. Find the perimeter of \\parallelogram EFGH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [10.0, 12.0, 14.0, 18.0]}
-{"prob_id": "prob_4108", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1890.png", "question": "Find the value of the variable x for the quadrilateral. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_4133", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2817.png", "question": "JH is a midsegment of \\triangle KLM. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [5.0, 10.0, 11.0, 22.0]}
-{"prob_id": "prob_4138", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1091.png", "question": "BD bisects \\angle ABC. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [6.5, 10.0, 11.5, 15.125]}
-{"prob_id": "prob_4146", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3784.png", "question": "XY and XZ are midsegments of \\triangle RST. Find SZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [3.5, 6.5, 7.0, 13.0]}
-{"prob_id": "prob_4151", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2071.png", "question": "What is m \\widehat EF? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "130.000", "choices": [125.0, 130.0, 235.0, 245.0]}
-{"prob_id": "prob_4153", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3051.png", "question": "Find m \\angle Z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "143.000", "choices": [34.0, 68.0, 136.0, 143.0]}
-{"prob_id": "prob_4166", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3752.png", "question": "JH is tangent to \\odot G at J. Find the length of GH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.000", "choices": [8.0, 8.667, 12.0, 13.0]}
-{"prob_id": "prob_4167", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2282.png", "question": "What is GH? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.299", "choices": [10.299, 11.583, 15.858, 19.304]}
-{"prob_id": "prob_4192", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1990.png", "question": "What is the value of k? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.364", "choices": [6.364, 9.0, 9.363, 12.728]}
-{"prob_id": "prob_4199", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_726.png", "question": "Given \\triangle EFG \\cong \\triangle GHE. Find m \\angle FEG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [34.0, 36.0, 108.0, 110.0]}
-{"prob_id": "prob_4208", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2046.png", "question": "Find the exact circumference of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "53.407", "choices": [53.407, 66.643, 106.814, 226.98]}
-{"prob_id": "prob_4226", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1142.png", "question": "AB \\parallel CD \\parallel EF. Find AE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.600", "choices": [10.0, 10.3, 20.0, 20.6]}
-{"prob_id": "prob_4264", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2999.png", "question": "If ED = x+4 and DB = 3x-8, find ED. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [8.0, 10.0, 20.0, 40.0]}
-{"prob_id": "prob_4265", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2355.png", "question": "JKMN is a rectangle. If NQ = 5x-3 and QM = 4x+6, find NK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "84.000", "choices": [21.0, 42.0, 59.397, 84.0]}
-{"prob_id": "prob_4272", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2512.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [6.103, 7.0, 7.433, 14.0]}
-{"prob_id": "prob_4278", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3234.png", "question": "In rhombus RSTV, m \\angle TZV = 8n+18, and m \\angle SRV = 9n+1. Find the measure of \\angle TVS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "49.000", "choices": [41.0, 49.0, 82.0, 90.0]}
-{"prob_id": "prob_4293", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3972.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [15.0, 27.5, 41.0, 80.0]}
-{"prob_id": "prob_4299", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_533.png", "question": "What is the area of the shaded region? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.708", "choices": [5.498, 9.425, 15.708, 25.133]}
-{"prob_id": "prob_4300", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2985.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.000", "choices": [17.0, 36.0, 74.0, 112.0]}
-{"prob_id": "prob_4302", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1366.png", "question": "GD and FH are diameters of circle C. Solve for m \\widehat DH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [65.0, 80.0, 100.0, 145.0]}
-{"prob_id": "prob_4314", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1867.png", "question": "The radius of \\odot P is 5 and PR = 3. Find the measure of \\widehat SQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "106.260", "choices": [53.13, 61.928, 73.74, 106.26]}
-{"prob_id": "prob_4333", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_257.png", "question": "Trapezoid MNPQ has an area of 360 square feet. Find the length of MN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [14.0, 16.0, 18.0, 20.0]}
-{"prob_id": "prob_4335", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_963.png", "question": "Find m \\widehat QS if m \\widehat QTS = 238. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "122.000", "choices": [61.0, 122.0, 238.0, 506.774]}
-{"prob_id": "prob_4360", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2153.png", "question": "For trapezoid LMNO, P and Q are midpoints of the legs. Determine m \\angle PQN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "84.000", "choices": [36.0, 84.0, 96.0, 144.0]}
-{"prob_id": "prob_4366", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_329.png", "question": "Find m \\angle A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 90.0, 180.0, 360.0]}
-{"prob_id": "prob_4372", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_98.png", "question": "m \\angle 11 = x-4, m \\angle 12 = 2x-5, find the measure of \\angle 11. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "59.000", "choices": [43.5, 59.0, 61.0, 121.0]}
-{"prob_id": "prob_4385", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2465.png", "question": "What is AB? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [11.0, 15.0, 18.601, 23.558]}
-{"prob_id": "prob_4391", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1758.png", "question": "AB = DE = 8, and CD = 5. Find CF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 2.5, 3.0, 4.0]}
-{"prob_id": "prob_4395", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2809.png", "question": "AE \\parallel BF \\parallel CG \\parallel DH, AB = BC = CD = 2, and EF = 2.25. What is EH? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.750", "choices": [2.25, 4.5, 6.0, 6.75]}
-{"prob_id": "prob_4397", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_962.png", "question": "Find the area of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [7.0, 9.093, 14.0, 28.0]}
-{"prob_id": "prob_4400", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2943.png", "question": "Use rhombus JKLM to find m \\angle L. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "124.000", "choices": [28.0, 62.0, 76.0, 124.0]}
-{"prob_id": "prob_4414", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1350.png", "question": "If XY = WX, YZ = WX, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [1.929, 3.0, 9.136, 10.941]}
-{"prob_id": "prob_4416", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3886.png", "question": "Find BC if DF = 6 and FB = 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.211, 5.0, 6.325, 7.746]}
-{"prob_id": "prob_4421", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_973.png", "question": "In \\odot D, DE = EC, m \\widehat CF = 60, and DE \\perp EC. Find m \\widehat AF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_4432", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_541.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1200.000", "choices": [600.0, 900.0, 1200.0, 2400.0]}
-{"prob_id": "prob_4433", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2325.png", "question": "Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "39.000", "choices": [39.0, 42.0, 48.0, 51.0]}
-{"prob_id": "prob_4434", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_129.png", "question": "What is BC? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.100", "choices": [16.2, 32.4, 35.1, 64.8]}
-{"prob_id": "prob_4442", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_442.png", "question": "Solve for a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "108.000", "choices": [103.5, 107.429, 108.0, 108.571]}
-{"prob_id": "prob_4453", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1630.png", "question": "Find the exact value of DE, given AD = 12 and BD = 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.464", "choices": [3.4641016151377544, 4.898979485566356, 6.928203230275509, 9.797958971132712]}
-{"prob_id": "prob_4455", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1930.png", "question": "If WXYZ is a kite, find WX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [10.0, 22.627, 24.739, 25.298]}
-{"prob_id": "prob_4457", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2256.png", "question": "AD, BD, and CD are angle bisectors of \\triangle ABC. Suppose CD = 10 and EC = 8. Find the measure of \\angle BCA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "73.740", "choices": [36.87, 53.13, 73.74, 106.26]}
-{"prob_id": "prob_4458", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2365.png", "question": "What is x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [2.217, 3.385, 6.0, 6.708]}
-{"prob_id": "prob_4463", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1748.png", "question": "What is m \\widehat KJ? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "110.300", "choices": [110.3, 120.0, 129.246, 135.951]}
-{"prob_id": "prob_4487", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2210.png", "question": "If ZY = 42, what is the length of ZX? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "54.000", "choices": [30.0, 42.0, 54.0, 96.0]}
-{"prob_id": "prob_4492", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3052.png", "question": "Find the area of the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "286.000", "choices": [48.0, 143.0, 286.0, 572.0]}
-{"prob_id": "prob_4495", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1504.png", "question": "If FK = 3x-1, KG = 4y+3, JK = 6y-2, and KH = 2x+3, find x so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 5.0, 10.0, 12.0]}
-{"prob_id": "prob_4504", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_378.png", "question": "Find m \\angle WYZ. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "67.380", "choices": [22.62, 24.624, 65.376, 67.38]}
-{"prob_id": "prob_4508", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1306.png", "question": "Solve for the measure of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "73.000", "choices": [31.0, 73.0, 107.0, 109.0]}
-{"prob_id": "prob_4518", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3773.png", "question": "m \\widehat QR = 40, and m \\widehat TS = 110. What is m \\angle 6? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [20.0, 55.0, 75.0, 105.0]}
-{"prob_id": "prob_4527", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3001.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "82.867", "choices": [57.7, 82.9, 101.7, 108.0]}
-{"prob_id": "prob_4528", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1346.png", "question": "What is m \\angle X? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "41.410", "choices": [36.87, 41.41, 48.59, 53.13]}
-{"prob_id": "prob_4566", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2725.png", "question": "Determine the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "36.000", "choices": [36.0, 38.0, 52.0, 54.0]}
-{"prob_id": "prob_4573", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3433.png", "question": "Find the length of \\widehat BDA shown in red. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "103.673", "choices": [18.85, 103.673, 131.947, 207.345]}
-{"prob_id": "prob_4574", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2056.png", "question": "Polygon ABCD \\sim polygon AEFG, m \\angle AGF = 108, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26. Find DC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.400", "choices": [12.0, 14.0, 22.4, 26.0]}
-{"prob_id": "prob_4582", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_396.png", "question": "CA is tangent to the circle at A. If BF = 9 and CB = 3, find CA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [3.0, 6.0, 9.0, 10.392]}
-{"prob_id": "prob_4616", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1877.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [25.0, 32.5, 33.75, 47.5]}
-{"prob_id": "prob_4618", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_37.png", "question": "PQ = RQ, m \\widehat PS = 45, and m \\widehat SR = 75. Find the measure of \\angle 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [22.5, 37.5, 52.5, 60.0]}
-{"prob_id": "prob_4619", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1940.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.745", "choices": [5.385164807134504, 5.5677643628300215, 5.744562646538029, 5.916079783099616]}
-{"prob_id": "prob_4639", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2475.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [1.75, 2.571, 3.111, 22.0]}
-{"prob_id": "prob_4651", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2219.png", "question": "Determine x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.765", "choices": [7.0, 10.954, 13.0, 14.765]}
-{"prob_id": "prob_4661", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2666.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.558", "choices": [17.643, 19.635, 34.558, 78.54]}
-{"prob_id": "prob_4663", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3102.png", "question": "For what value of variable y must ABCD be a parallelogram? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [2.0, 5.0, 5.5, 6.0]}
-{"prob_id": "prob_4670", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3951.png", "question": "PACE is a parallelogram and m \\angle PAC = 124. What is the measurement of \\angle CEP? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "124.000", "choices": [41.462, 48.538, 56.0, 124.0]}
-{"prob_id": "prob_4677", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_622.png", "question": "PX, PY, and PZ are the perpendicular bisectors of \\triangle RST. Find RS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "164.600", "choices": [46.7, 77.5, 82.3, 164.6]}
-{"prob_id": "prob_4684", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2818.png", "question": "Find the length of MR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [4.0, 12.0, 16.0, 22.0]}
-{"prob_id": "prob_4700", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3769.png", "question": "In \\odot O, m \\widehat AB = 40, m \\widehat BC = 100, and m \\widehat AD = m \\widehat DC. Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [20.0, 50.0, 55.0, 90.0]}
-{"prob_id": "prob_4714", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3272.png", "question": "Find m \\widehat KM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "81.000", "choices": [51.0, 81.0, 99.0, 129.0]}
-{"prob_id": "prob_4715", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1290.png", "question": "If FG = GJ = J H, and m \\angle F = 40, find m \\angle GJH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [20.0, 35.0, 70.0, 105.0]}
-{"prob_id": "prob_4716", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2283.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 4.0, 5.0, 6.0]}
-{"prob_id": "prob_4737", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_382.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.971", "choices": [6.0, 9.0, 12.0, 16.970562748477143]}
-{"prob_id": "prob_4745", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1744.png", "question": "\\triangle WLJ \\sim \\triangle QBV. Find the scale factor of \\triangle WLJ to \\triangle QBV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [0.5, 0.625, 1.6, 2.0]}
-{"prob_id": "prob_4752", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3247.png", "question": "Find the length of BA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.054", "choices": [6.428, 8.391, 11.918, 13.054]}
-{"prob_id": "prob_4769", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3368.png", "question": "Determine the length of HE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 6.0, 10.0, 12.728]}
-{"prob_id": "prob_4774", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3318.png", "question": "In rhombus LMPQ, m \\angle QLM = 2x^{2}-10, m \\angle QPM = 8x, and MP = 10. Find the perimeter of LMPQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [10.0, 40.0, 70.0, 140.0]}
-{"prob_id": "prob_4779", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3325.png", "question": "If RU = 8, US = 14, TV = x-1, and VS = 17.5, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [3.0, 7.4, 11.0, 31.625]}
-{"prob_id": "prob_4783", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_263.png", "question": "Find m \\widehat DPA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "264.000", "choices": [168.0, 192.0, 264.0, 276.0]}
-{"prob_id": "prob_4789", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1941.png", "question": "Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [12.0, 16.0, 24.0, 44.0]}
-{"prob_id": "prob_4793", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2068.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [6.667, 10.0, 12.667, 12.857]}
-{"prob_id": "prob_4818", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1746.png", "question": "What is the measure of \\angle K? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "165.000", "choices": [30.0, 139.149, 165.0, 201.818]}
-{"prob_id": "prob_4826", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3309.png", "question": "Find m \\angle B. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [20.0, 30.0, 60.0, 80.0]}
-{"prob_id": "prob_4833", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_466.png", "question": "AB = DF. Find the length of FE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [9.0, 18.0, 20.125, 36.0]}
-{"prob_id": "prob_4847", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3775.png", "question": "What is m \\widehat GE? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [120.0, 130.0, 150.0, 190.0]}
-{"prob_id": "prob_4850", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3489.png", "question": "Find the measure of \\angle 6. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_4859", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1921.png", "question": "The polygon circumscribes a circle. What is the perimeter of polygon? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.200", "choices": [14.2, 17.8, 21.8, 25.2]}
-{"prob_id": "prob_4862", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2543.png", "question": "Determine the measurement of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "132.000", "choices": [46.0, 48.0, 94.0, 132.0]}
-{"prob_id": "prob_4900", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2199.png", "question": "P is the centroid of \\triangle ABC. If SC = 6, find CP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [2.0, 4.0, 9.0, 18.0]}
-{"prob_id": "prob_4905", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_812.png", "question": "If JM = KL = JK, find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [1.0, 2.0, 3.0, 6.0]}
-{"prob_id": "prob_4909", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1118.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [51.962, 60.0, 84.853, 120.0]}
-{"prob_id": "prob_4911", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_698.png", "question": "Find RS if PQ = 12, QR = 2, and TS = 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [2.0, 3.0, 4.0, 12.0]}
-{"prob_id": "prob_4929", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2357.png", "question": "Find m \\angle N. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.000", "choices": [17.0, 54.0, 86.727, 108.0]}
-{"prob_id": "prob_4937", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2376.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [40.0, 50.0, 60.0, 80.0]}
-{"prob_id": "prob_4939", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1134.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "139.626", "choices": [15.359, 61.436, 139.626, 262.498]}
-{"prob_id": "prob_4951", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1151.png", "question": "UV = 8. Find XY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.856", "choices": [4.0, 6.928, 13.856, 16.0]}
-{"prob_id": "prob_4954", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1658.png", "question": "The circle is inscribed in polygon. Find the perimeter of polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "76.000", "choices": [70.0, 74.0, 76.0, 84.0]}
-{"prob_id": "prob_4968", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_734.png", "question": "Find x if AB = 6, AF = 8, BC = x, CD = y, DE = 2y-3, and FE = x+\\frac{10}{3}. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [5.459, 6.0, 10.0, 13.333]}
-{"prob_id": "prob_4969", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_482.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "142.000", "choices": [132.0, 138.0, 142.0, 148.0]}
-{"prob_id": "prob_4987", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2397.png", "question": "Use parallelogram JKLM to find JK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [4.5, 6.0, 10.0, 12.0]}
-{"prob_id": "prob_4990", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1225.png", "question": "Find the area of sector KLM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "26.180", "choices": [10.472, 15.355, 26.18, 52.36]}
-{"prob_id": "prob_4993", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1124.png", "question": "Find the perimeter of \\triangle CPD if the perimeter of \\triangle BPA is 12, AP = \\sqrt{13}, and DP = 3\\sqrt{13}. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "36.000", "choices": [3.25, 4.0, 10.817, 36.0]}
-{"prob_id": "prob_4994", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3849.png", "question": "Find ST. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.966", "choices": [8.485, 10.966, 12.5, 13.865]}
-{"prob_id": "prob_5003", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3535.png", "question": "If AP = 1, find PD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.500", "choices": [0.333, 0.5, 0.667, 1.5]}
-{"prob_id": "prob_5014", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_762.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "727.461", "choices": [420.0, 594.0, 727.5, 840.0]}
-{"prob_id": "prob_5017", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3694.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [10.0, 20.0, 30.0, 40.0]}
-{"prob_id": "prob_5030", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_693.png", "question": "Use parallelogram to find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 10.0, 15.0, 20.0]}
-{"prob_id": "prob_5033", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1145.png", "question": "Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [40.0, 70.0, 90.0, 110.0]}
-{"prob_id": "prob_5034", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3900.png", "question": "BD bisects \\angle ABF. If m \\angle ABF = 3x-8 and m \\angle ABD = x+14, find m \\angle ABD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [14.0, 36.0, 50.0, 54.0]}
-{"prob_id": "prob_5035", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_439.png", "question": "What is area of sector RST? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.524", "choices": [0.091, 0.524, 1.047, 2.618]}
-{"prob_id": "prob_5037", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3906.png", "question": "Find DC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "53.443", "choices": [43.557, 48.247, 53.443, 107.446]}
-{"prob_id": "prob_5053", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3869.png", "question": "Refer to rectangle QRTS. If QS = 3x+40 and RT = 16-3x, find QS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [14.0, 28.0, 32.666, 56.0]}
-{"prob_id": "prob_5055", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2894.png", "question": "Quadrilateral ABCD is a rectangle. Find m \\angle DCA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [25.0, 34.158, 50.0, 65.0]}
-{"prob_id": "prob_5068", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_97.png", "question": "M is the midpoint of PQ. The diameter of \\odot O is 13 in, and RM = 4 in. Find PQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [4.0, 6.0, 9.0, 12.0]}
-{"prob_id": "prob_5077", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1162.png", "question": "Find the perimeter of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.700", "choices": [12.7, 13.7, 16.7, 17.7]}
-{"prob_id": "prob_5084", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2012.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.000", "choices": [13.5, 19.0, 23.5, 47.0]}
-{"prob_id": "prob_5103", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_737.png", "question": "PQ is the perpendicular bisector of ST. Find the value of n. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.500", "choices": [2.5, 7.0, 7.833, 8.5]}
-{"prob_id": "prob_5113", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_379.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.899", "choices": [24.62, 29.899, 65.0, 130.76]}
-{"prob_id": "prob_5121", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2635.png", "question": "Use rhombus XYZW with m \\angle WYZ = 53, VW = 3, XV = 2a-2, and ZV = \\frac{5a+1}{4}. Find XW. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 10.0, 15.0, 20.0]}
-{"prob_id": "prob_5140", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_500.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [24.0, 56.0, 65.0, 115.0]}
-{"prob_id": "prob_5147", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_42.png", "question": "What is the measure of \\angle 10? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.000", "choices": [44.0, 46.0, 56.0, 90.0]}
-{"prob_id": "prob_5150", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2938.png", "question": "Find the measure of \\angle TVU in rectangle STUV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.417", "choices": [35.417, 45.0, 45.325, 54.583]}
-{"prob_id": "prob_5152", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1295.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [6.0, 9.0, 10.4, 12.7]}
-{"prob_id": "prob_5157", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3687.png", "question": "For isosceles trapezoid ABCD, X and Y are midpoints of the legs. Find m \\angle XBC if m \\angle ADY = 78. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "102.000", "choices": [39.0, 51.0, 78.0, 102.0]}
-{"prob_id": "prob_5176", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3731.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.600", "choices": [10.9, 13.6, 15.2, 26.6]}
-{"prob_id": "prob_5177", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2014.png", "question": "Find the area of the shaded sector. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.036", "choices": [10.0, 27.4, 65.5, 78.5]}
-{"prob_id": "prob_5183", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2498.png", "question": "Find PM in \\triangle JMP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "106.000", "choices": [45.0, 53.0, 90.0, 106.0]}
-{"prob_id": "prob_5211", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2346.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.063", "choices": [7.1, 14.1, 22.1, 30.0]}
-{"prob_id": "prob_5247", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1986.png", "question": "Find the value of variable c. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [30.0, 42.0, 50.0, 80.0]}
-{"prob_id": "prob_5257", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_927.png", "question": "Find PN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [9.0, 10.0, 11.0, 12.0]}
-{"prob_id": "prob_5289", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1322.png", "question": "Find the length of XZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [18.0, 20.0, 24.0, 50.0]}
-{"prob_id": "prob_5291", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2155.png", "question": "In \\odot A, m \\angle EAD = 42. Find m \\widehat BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "42.000", "choices": [42.0, 48.0, 52.0, 108.0]}
-{"prob_id": "prob_5303", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_284.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [5.0, 6.0, 7.0, 8.0]}
-{"prob_id": "prob_5314", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3126.png", "question": "Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [10.0, 15.0, 20.0, 40.0]}
-{"prob_id": "prob_5317", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2076.png", "question": "What is w? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "68.251", "choices": [68.251, 75.801, 91.841, 152.437]}
-{"prob_id": "prob_5319", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1401.png", "question": "In \\odot K, MN = 16 and m \\widehat MN = 98. Find the measure of PK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [4.0, 6.0, 8.0, 15.199]}
-{"prob_id": "prob_5330", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1545.png", "question": "Find m \\angle PQS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "42.000", "choices": [36.0, 42.0, 48.0, 63.0]}
-{"prob_id": "prob_5334", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1733.png", "question": "Find CB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.190", "choices": [1.403, 2.876, 3.507, 7.19]}
-{"prob_id": "prob_5339", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2930.png", "question": "What is the length of \\widehat QSR? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.944", "choices": [5.236, 10.472, 20.944, 26.18]}
-{"prob_id": "prob_5347", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2444.png", "question": "Find m \\angle 9. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [60.0, 120.0, 240.0, 300.0]}
-{"prob_id": "prob_5367", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3439.png", "question": "In the trapezoid, NP = 15. What is the length of KL? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [10.0, 20.0, 40.0, 65.0]}
-{"prob_id": "prob_5374", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_743.png", "question": "Chords AC and DF are equidistant from the center. If the radius of \\odot G is 26, find AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.000", "choices": [5.0, 10.0, 13.0, 48.0]}
-{"prob_id": "prob_5380", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3603.png", "question": "Find b in the given parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [2.0, 8.0, 9.0, 10.0]}
-{"prob_id": "prob_5384", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_214.png", "question": "Find the area of the square. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [1.732, 3.142, 4.0, 16.0]}
-{"prob_id": "prob_5391", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1915.png", "question": "Solve for a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "105.000", "choices": [41.0, 66.0, 91.0, 105.0]}
-{"prob_id": "prob_5397", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2111.png", "question": "What is the perimeter of the figure? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [30.0, 35.292, 40.0, 44.0]}
-{"prob_id": "prob_5422", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2641.png", "question": "Find the value of x for given rectangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.600", "choices": [6.6, 18.6, 24.6, 90.0]}
-{"prob_id": "prob_5424", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2054.png", "question": "AD = 6 and DE = 7.5. What is the length of AC? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [6.0, 7.5, 12.0, 15.0]}
-{"prob_id": "prob_5427", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_170.png", "question": "BT / RT = ES / LS, find TR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.667", "choices": [1.714, 2.4, 4.286, 6.667]}
-{"prob_id": "prob_5437", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_362.png", "question": "KLMN is a rectangle. Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [5.0, 20.0, 50.0, 90.0]}
-{"prob_id": "prob_5438", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_977.png", "question": "Find the measure of \\angle 5 if PQ \\perp QR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "68.000", "choices": [12.0, 22.0, 34.0, 68.0]}
-{"prob_id": "prob_5445", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3617.png", "question": "Find m \\angle AGE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [60.0, 120.0, 210.0, 330.0]}
-{"prob_id": "prob_5447", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2917.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 8.0, 16.0, 32.0]}
-{"prob_id": "prob_5470", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3732.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.785", "choices": [10.392304845413264, 20.784609690826528, 25.455844122715714, 36.0]}
-{"prob_id": "prob_5475", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1625.png", "question": "What is the length of diameter? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [3.0, 6.0, 12.0, 18.85]}
-{"prob_id": "prob_5482", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_101.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.392", "choices": [3.4641016151377544, 5.196152422706632, 8.660254037844386, 10.392304845413264]}
-{"prob_id": "prob_5484", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_219.png", "question": "Find AC, if \\triangle ABC \\sim \\triangle CBD, AD = 5, CD = 12, and BC = 31.2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.000", "choices": [10.909, 13.0, 28.8, 33.428]}
-{"prob_id": "prob_5489", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1801.png", "question": "Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [10.0, 35.0, 55.0, 70.0]}
-{"prob_id": "prob_5494", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2827.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 10.0, 15.0, 20.0]}
-{"prob_id": "prob_5500", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_622.png", "question": "PX, PY, and PZ are the perpendicular bisectors of \\triangle RST. Find PY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.307", "choices": [16.307, 46.7, 82.3, 83.9]}
-{"prob_id": "prob_5502", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_804.png", "question": "Find x in the given parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [38.0, 75.0, 76.0, 109.0]}
-{"prob_id": "prob_5538", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1918.png", "question": "Find m \\angle Q. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "121.000", "choices": [50.0, 58.0, 60.0, 121.0]}
-{"prob_id": "prob_5548", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_523.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 3.0, 4.0, 6.0]}
-{"prob_id": "prob_5560", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1646.png", "question": "Find VW. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [6.0, 8.0, 10.0, 12.0]}
-{"prob_id": "prob_5563", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1485.png", "question": "Find the value of variable q in the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [7.167, 8.0, 9.0, 11.124]}
-{"prob_id": "prob_5591", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3679.png", "question": "Find m \\angle 5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [32.5, 65.0, 115.0, 230.0]}
-{"prob_id": "prob_5605", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2298.png", "question": "Find x so that line r \\parallel line s. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [30.0, 31.667, 40.0, 115.0]}
-{"prob_id": "prob_5640", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3176.png", "question": "Find MN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "61.794", "choices": [31.872, 45.705, 53.364, 61.794]}
-{"prob_id": "prob_5642", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3550.png", "question": "Find the area of the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.426", "choices": [16.0, 18.475, 27.713, 55.426]}
-{"prob_id": "prob_5644", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2534.png", "question": "DB \\perp AC and BA = BC. Find CD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [12.0, 13.0, 20.0, 26.0]}
-{"prob_id": "prob_5658", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1195.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.165", "choices": [6.0, 9.16515138991168, 10.0, 10.770329614269007]}
-{"prob_id": "prob_5662", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2676.png", "question": "The diameters of \\odot L and \\odot M are 20 and 13 units, respectively, and QR = 4. Determine the length of RM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.500", "choices": [2.5, 6.0, 6.5, 20.0]}
-{"prob_id": "prob_5665", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_862.png", "question": "For rhombus ABCD, find AB, given that m \\angle DEC = 30y, m \\angle EDC = 8y+15, AB = 2x+8, and BC = 4x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [16.0, 22.627, 32.0, 82.0]}
-{"prob_id": "prob_5678", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3845.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "216.000", "choices": [156.0, 216.0, 234.0, 324.0]}
-{"prob_id": "prob_5682", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2395.png", "question": "Find m \\angle EDB if m \\widehat FE = 118, m \\widehat AB = 108, m \\angle EGB = 52, and m \\angle EFB = 30. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [15.0, 52.0, 108.0, 118.0]}
-{"prob_id": "prob_5685", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3034.png", "question": "Use parallelogram WXYZ to find WX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [11.665, 24.0, 28.0, 203.0]}
-{"prob_id": "prob_5712", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3655.png", "question": "What is x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [4.364, 11.25, 15.04, 16.0]}
-{"prob_id": "prob_5720", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_751.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [60.0, 80.0, 100.0, 120.0]}
-{"prob_id": "prob_5764", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1276.png", "question": "Find WT, if ZX = 20 and TY = 15. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 15.0, 20.0, 35.0]}
-{"prob_id": "prob_5773", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1786.png", "question": "WXYZ is a parallelogram. Solve for YZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.500", "choices": [9.5, 19.0, 36.333, 143.667]}
-{"prob_id": "prob_5776", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1292.png", "question": "For the pair of similar figures, the area of the blue figure is 500 in^{2}, find the scale factor of the blue to the green figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.818", "choices": [0.55, 1.0, 1.818, 5.698]}
-{"prob_id": "prob_5789", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_94.png", "question": "Find the value of variable a in the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "79.000", "choices": [50.5, 79.0, 90.0, 101.0]}
-{"prob_id": "prob_5795", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_256.png", "question": "m \\angle 3 = 43. Find the measure of \\angle 10. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "137.000", "choices": [117.0, 127.0, 137.0, 147.0]}
-{"prob_id": "prob_5813", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1907.png", "question": "Find the measure of \\widehat YXZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "166.000", "choices": [145.0, 166.0, 194.0, 215.0]}
-{"prob_id": "prob_5819", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2935.png", "question": "If JK = 48, find the length of HJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [23.0, 25.0, 48.0, 75.0]}
-{"prob_id": "prob_5827", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_625.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.928", "choices": [3.4641016151377544, 4.0, 6.928203230275509, 8.0]}
-{"prob_id": "prob_5840", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_482.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [15.0, 34.0, 39.5, 142.0]}
-{"prob_id": "prob_5848", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_890.png", "question": "If AB = 32 and FC = 11, find DE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.238", "choices": [5.5, 11.619, 16.0, 23.238]}
-{"prob_id": "prob_5855", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1642.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [0.8, 1.0, 2.0, 4.0]}
-{"prob_id": "prob_5881", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3627.png", "question": "Find the measure of \\angle 2 in the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "27.000", "choices": [27.0, 63.0, 76.5, 126.0]}
-{"prob_id": "prob_5883", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3487.png", "question": "m \\angle BZD = 107, m \\angle FZE = 2x+5, m \\angle CZD = x, what is the measure of \\angle FZE? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "73.000", "choices": [22.667, 34.0, 73.0, 107.0]}
-{"prob_id": "prob_5885", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2784.png", "question": "Use parallelogram ABCD to find CD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 9.0, 12.0, 18.0]}
-{"prob_id": "prob_5890", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3698.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "61.500", "choices": [13.0, 51.5, 61.5, 123.0]}
-{"prob_id": "prob_5895", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_371.png", "question": "Find m \\angle 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "56.000", "choices": [28.5, 56.0, 57.0, 123.0]}
-{"prob_id": "prob_5898", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_433.png", "question": "If m \\angle 1 = 3y-6, find the value of variable x for the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.333, 5.0, 10.0, 90.0]}
-{"prob_id": "prob_5900", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2802.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "97.529", "choices": [97.53, 103.0, 108.0, 113.0]}
-{"prob_id": "prob_5909", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1597.png", "question": "Find the measure of the altitude drawn to the hypotenuse. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.099", "choices": [1.4142135623730951, 2.5495097567963922, 3.605551275463989, 5.0990195135927845]}
-{"prob_id": "prob_5912", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_279.png", "question": "m \\angle DBE = 50. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 6.714, 9.571, 13.143]}
-{"prob_id": "prob_5922", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_219.png", "question": "Find the perimeter of the \\triangle ABC, if \\triangle ABC \\sim \\triangle CBD, AD = 5, CD = 12, and BC = 31.2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "78.000", "choices": [32.5, 72.0, 78.0, 187.2]}
-{"prob_id": "prob_5932", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1324.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 6.0, 9.0, 12.0]}
-{"prob_id": "prob_5936", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3946.png", "question": "In \\odot R, m \\widehat MN = 120. Solve for m \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 120.0, 150.0]}
-{"prob_id": "prob_5943", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1527.png", "question": "Find the measure of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "112.000", "choices": [46.0, 67.0, 90.0, 112.0]}
-{"prob_id": "prob_5950", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3036.png", "question": "What is the measure of \\angle 1? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 33.0, 84.0, 150.0]}
-{"prob_id": "prob_5991", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_256.png", "question": "m \\angle 3 = 43. Find the measure of \\angle 11. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.000", "choices": [43.0, 53.0, 63.0, 137.0]}
-{"prob_id": "prob_5992", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1482.png", "question": "What is the circumference of \\odot P? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.133", "choices": [12.566, 25.133, 50.265, 7200.0]}
-{"prob_id": "prob_6001", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3463.png", "question": "Find the area of the shaded sector. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.460", "choices": [1.5, 2.2, 3.8, 5.3]}
-{"prob_id": "prob_6007", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_695.png", "question": "Find BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.000", "choices": [5.0, 9.0, 12.0, 13.0]}
-{"prob_id": "prob_6010", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1797.png", "question": "If m \\angle FGE = 5x+10, find the value of x so that FC \\perp AE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [4.0, 10.0, 16.0, 90.0]}
-{"prob_id": "prob_6012", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2609.png", "question": "Polygon BGHF \\sim polygon ADEC. Determine the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [4.5, 5.25, 9.0, 18.0]}
-{"prob_id": "prob_6024", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3053.png", "question": "What is the perimeter of the right triangle? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "33.498", "choices": [33.5, 39.1, 49.9, 55.5]}
-{"prob_id": "prob_6031", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2035.png", "question": "QR \\parallel TS, QT \\parallel RS, and m \\angle 1 = 131. Find the measure of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "49.000", "choices": [49.0, 59.0, 69.0, 131.0]}
-{"prob_id": "prob_6051", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1960.png", "question": "What is m \\angle 3? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [40.0, 50.0, 70.0, 90.0]}
-{"prob_id": "prob_6055", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2903.png", "question": "What is the value of y for which line a \\parallel line b? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [32.5, 65.0, 115.0, 130.0]}
-{"prob_id": "prob_6073", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3481.png", "question": "Find the diameter. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [5.0, 10.0, 20.0, 31.416]}
-{"prob_id": "prob_6086", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2196.png", "question": "Determine the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [5.143, 6.75, 11.25, 12.0]}
-{"prob_id": "prob_6107", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1009.png", "question": "If x = 14, find b. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.333", "choices": [8.083, 9.333, 12.124, 16.166]}
-{"prob_id": "prob_6112", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_130.png", "question": "AC and EB are diameters of \\odot R. What is m \\widehat DEB? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "210.000", "choices": [180.0, 210.0, 280.0, 330.0]}
-{"prob_id": "prob_6113", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3286.png", "question": "Use the Law of Sines to find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.598", "choices": [2.142, 2.976, 3.598, 6.949]}
-{"prob_id": "prob_6117", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1325.png", "question": "The perpendicular bisectors of \\triangle MNP meet at point Q. Find QP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [7.0, 25.0, 47.487, 48.0]}
-{"prob_id": "prob_6149", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2408.png", "question": "Find the value of a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [0.95, 16.9, 19.45, 22.0]}
-{"prob_id": "prob_6173", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_89.png", "question": "Find m \\angle A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "51.318", "choices": [32.005, 38.682, 51.318, 57.995]}
-{"prob_id": "prob_6178", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1867.png", "question": "The radius of \\odot P is 5 and PR = 3. Find QR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [3.0, 4.0, 5.0, 6.0]}
-{"prob_id": "prob_6183", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2063.png", "question": "Find KL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [3.0, 6.0, 12.0, 18.0]}
-{"prob_id": "prob_6194", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3523.png", "question": "Find the perimeter of the quadrilateral. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "98.354", "choices": [54.0, 56.785, 72.0, 98.354]}
-{"prob_id": "prob_6196", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3847.png", "question": "Find the area of the shaded sector. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.212", "choices": [40.2, 80.4, 160.8, 201.1]}
-{"prob_id": "prob_6206", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_666.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.588", "choices": [5.196152422706632, 9.0, 12.727922061357857, 15.588457268119894]}
-{"prob_id": "prob_6215", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_802.png", "question": "What is z? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [9.0, 15.0, 18.0, 30.0]}
-{"prob_id": "prob_6218", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1974.png", "question": "Find the perimeter of the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "124.964", "choices": [80.0, 88.0, 96.0, 124.964]}
-{"prob_id": "prob_6231", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_467.png", "question": "In the diagram, JL = 120. What is KL? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "78.000", "choices": [42.0, 66.0, 78.0, 120.0]}
-{"prob_id": "prob_6248", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3175.png", "question": "If AC = 12 and BC = 9, what is the radius? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.937", "choices": [3.5, 7.937, 8.485, 12.5]}
-{"prob_id": "prob_6251", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2056.png", "question": "Polygon ABCD \\sim polygon AEFG, m \\angle AGF = 108, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26. Find AG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.500", "choices": [4.5, 7.5, 12.0, 20.0]}
-{"prob_id": "prob_6254", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3826.png", "question": "Find the measure of \\widehat WTV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "235.000", "choices": [205.0, 235.0, 280.0, 335.0]}
-{"prob_id": "prob_6260", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2645.png", "question": "Find the area of the rectangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.890", "choices": [1.251, 2.89, 5.78, 9.079]}
-{"prob_id": "prob_6272", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3438.png", "question": "QS is the angle bisector of \\angle PQR, find the measure of \\angle PQR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "104.000", "choices": [26.0, 52.0, 104.0, 128.0]}
-{"prob_id": "prob_6281", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_25.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.500", "choices": [37.5, 47.0, 52.5, 133.0]}
-{"prob_id": "prob_6283", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2533.png", "question": "Find the area of the circle. Assume that all polygons that appear to be regular are regular. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "314.159", "choices": [62.832, 125.664, 314.159, 1256.637]}
-{"prob_id": "prob_6284", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3397.png", "question": "The diameter of \\odot C is 32 units long. Find the length of \\widehat HDF if m \\angle HCF = 125. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.624", "choices": [15.359, 34.907, 65.624, 69.813]}
-{"prob_id": "prob_6286", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2960.png", "question": "In parallelogram ABCD, BD and AC intersect at E. If AE = 9, BE = 3x-7, and DE = x+5, find DE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [9.0, 9.8, 10.333, 11.0]}
-{"prob_id": "prob_6293", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1066.png", "question": "Tangent MP is drawn to \\odot O. Find x if MO = 20. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [5.0, 8.94427190999916, 12.0, 16.0]}
-{"prob_id": "prob_6299", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_187.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [24.249, 28.0, 39.598, 56.0]}
-{"prob_id": "prob_6300", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3541.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "471.239", "choices": [392.7, 471.2, 589.0, 785.4]}
-{"prob_id": "prob_6308", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_172.png", "question": "Equilateral pentagon PQRST is inscribed in \\odot U. Find m \\angle PQR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "108.000", "choices": [60.0, 72.0, 90.0, 108.0]}
-{"prob_id": "prob_6310", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1936.png", "question": "In \\triangle ABC, CP = 30, EP = 18, and BF = 39. Find PD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [12.0, 13.0, 15.0, 26.0]}
-{"prob_id": "prob_6316", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2389.png", "question": "Find the exact radius of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.500", "choices": [4.5, 9.0, 18.0, 28.274]}
-{"prob_id": "prob_6318", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1414.png", "question": "Find m \\angle A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "49.000", "choices": [41.0, 49.0, 90.0, 188.0]}
-{"prob_id": "prob_6321", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3627.png", "question": "Find the measure of \\angle 3 in the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "27.000", "choices": [27.0, 63.0, 76.5, 126.0]}
-{"prob_id": "prob_6333", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2843.png", "question": "Find the measure of \\angle 2 in the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [20.0, 40.0, 55.0, 70.0]}
-{"prob_id": "prob_6351", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3322.png", "question": "Quadrilateral ABDC is a rectangle. m \\angle 2 = 40. Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [40.0, 50.0, 90.0, 130.0]}
-{"prob_id": "prob_6354", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1841.png", "question": "Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [7.0, 9.105, 12.357, 20.75]}
-{"prob_id": "prob_6366", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3787.png", "question": "If m \\angle RQT = 155, what is m \\angle RQS? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "72.000", "choices": [72.0, 83.0, 155.0, 581.0]}
-{"prob_id": "prob_6380", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2092.png", "question": "Find the length of \\widehat KL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.123", "choices": [5.061, 9.076, 10.123, 15.01]}
-{"prob_id": "prob_6382", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1185.png", "question": "Find the measure of DB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.699", "choices": [8.764, 16.43, 17.309, 23.699]}
-{"prob_id": "prob_6388", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3706.png", "question": "Find m \\widehat SU. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [22.0, 23.0, 34.0, 68.0]}
-{"prob_id": "prob_6405", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1965.png", "question": "Find m \\angle M. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "96.000", "choices": [62.0, 71.0, 96.0, 106.0]}
-{"prob_id": "prob_6407", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2091.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [25.0, 40.249, 42.827, 56.25]}
-{"prob_id": "prob_6417", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2153.png", "question": "For trapezoid LMNO, P and Q are midpoints of the legs. Find PQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.000", "choices": [13.0, 17.0, 19.0, 25.0]}
-{"prob_id": "prob_6418", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_524.png", "question": "If PB = 6, what is SB? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [2.0, 4.0, 9.0, 18.0]}
-{"prob_id": "prob_6426", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2804.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [10.0, 25.0, 40.0, 90.0]}
-{"prob_id": "prob_6430", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2840.png", "question": "What is the value of y? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "100.000", "choices": [80.0, 90.0, 100.0, 140.0]}
-{"prob_id": "prob_6432", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1800.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.400", "choices": [0.8, 1.0, 1.4, 1.6]}
-{"prob_id": "prob_6434", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_347.png", "question": "Find the measure of \\angle 2 if AB \\perp BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "68.000", "choices": [64.0, 68.0, 72.0, 76.0]}
-{"prob_id": "prob_6442", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_943.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [30.0, 35.0, 45.0, 85.0]}
-{"prob_id": "prob_6449", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2231.png", "question": "Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "145.000", "choices": [17.5, 72.5, 90.0, 145.0]}
-{"prob_id": "prob_6467", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_130.png", "question": "AC and EB are diameters of \\odot R. What is m \\widehat CB? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [30.0, 50.0, 100.0, 130.0]}
-{"prob_id": "prob_6470", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2564.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.745", "choices": [5.657, 5.745, 8.062, 9.899]}
-{"prob_id": "prob_6472", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1693.png", "question": "Find m \\widehat RQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [14.0, 28.0, 37.0, 51.0]}
-{"prob_id": "prob_6497", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1949.png", "question": "Find m \\angle D. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_6512", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_391.png", "question": "Find the perimeter of \\triangle DEF if \\triangle DEF \\sim \\triangle ABC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [15.0, 16.0, 24.0, 30.0]}
-{"prob_id": "prob_6518", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_256.png", "question": "m \\angle 3 = 43. Find the measure of \\angle 16. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "137.000", "choices": [117.0, 127.0, 137.0, 147.0]}
-{"prob_id": "prob_6522", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1305.png", "question": "Quadrilateral WXYZ is a rectangle. If PY = 3x-5 and WP = 2x+11, find ZP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.000", "choices": [8.0, 16.0, 32.0, 43.0]}
-{"prob_id": "prob_6527", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1336.png", "question": "\\triangle WXY and \\triangle XYZ are isosceles and m \\angle XYZ = 128. Find the measure of \\angle YZX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "26.000", "choices": [22.0, 24.0, 26.0, 28.0]}
-{"prob_id": "prob_6537", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1056.png", "question": "PQRS \\sim TVWX. Find the scale factor of PQRS to TVWX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.500", "choices": [0.667, 1.5, 1.667, 2.5]}
-{"prob_id": "prob_6566", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3857.png", "question": "Triangles FGH and FHJ are inscribed in \\odot K with m \\widehat FG = m \\widehat FJ. Find m \\angle FHG if m \\angle 1 = 6x-5, and m \\angle 2 = 7x+4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "53.000", "choices": [37.0, 53.0, 90.0, 106.0]}
-{"prob_id": "prob_6582", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_165.png", "question": "Find the circumference of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "26.389", "choices": [13.195, 26.389, 55.418, 360.0]}
-{"prob_id": "prob_6602", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2721.png", "question": "\\triangle ABD \\cong \\triangle CDB, m \\angle A = 2x+14, m \\angle C = 3x-15, and m \\angle DBA = 49. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.000", "choices": [17.5, 21.333, 26.4, 29.0]}
-{"prob_id": "prob_6618", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1284.png", "question": "In \\odot X, AB = CD = 30, and m \\widehat CZ = 40. Find m \\widehat AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [30.0, 40.0, 60.0, 80.0]}
-{"prob_id": "prob_6685", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_826.png", "question": "Find the measure of \\angle B. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "81.000", "choices": [46.0, 53.0, 81.0, 134.0]}
-{"prob_id": "prob_6691", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_546.png", "question": "Find b in the given parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [3.0, 4.0, 5.0, 13.0]}
-{"prob_id": "prob_6699", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2532.png", "question": "Determine the measure of \\widehat JK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "108.000", "choices": [27.0, 54.0, 108.0, 126.0]}
-{"prob_id": "prob_6701", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2110.png", "question": "Find m \\angle LMN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.694", "choices": [19.132, 21.453, 38.694, 46.547]}
-{"prob_id": "prob_6733", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_706.png", "question": "Circle A has diameters DF and PG. If DF = 10, find DA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 10.0, 20.0, 25.0]}
-{"prob_id": "prob_6743", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2152.png", "question": "Find the measure of \\widehat TCD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "180.000", "choices": [180.0, 218.0, 270.0, 308.0]}
-{"prob_id": "prob_6749", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2168.png", "question": "Quadrilateral DKLM is a rhombus. If DK = 8, find ML. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [4.0, 8.0, 11.314, 16.0]}
-{"prob_id": "prob_6760", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2187.png", "question": "Solve for m \\angle AKG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "157.000", "choices": [23.0, 67.0, 113.0, 157.0]}
-{"prob_id": "prob_6770", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1221.png", "question": "In \\triangle JKL, ZW = 7, and LX = 8.1. Determine the length of LZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.400", "choices": [2.7, 5.4, 21.0, 24.3]}
-{"prob_id": "prob_6776", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_852.png", "question": "In rectangle ABCD, CD = 18, and CE = 19.8. Find the length of BE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.800", "choices": [9.9, 18.0, 19.8, 39.6]}
-{"prob_id": "prob_6787", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2023.png", "question": "In \\odot X, WS, VR, and QT are diameters, m \\angle WXV = 25 and m \\angle VXU = 45. Find the measure of \\angle UXR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "135.000", "choices": [45.0, 65.0, 135.0, 155.0]}
-{"prob_id": "prob_6825", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2894.png", "question": "Quadrilateral ABCD is a rectangle. Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 10.0, 15.0, 20.0]}
-{"prob_id": "prob_6831", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2779.png", "question": "H is the incenter of \\triangle ABC. Find HC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.910", "choices": [7.0, 12.124, 13.165, 14.91]}
-{"prob_id": "prob_6832", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_785.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.750", "choices": [6.0, 6.25, 6.5, 6.75]}
-{"prob_id": "prob_6833", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1231.png", "question": "Find the measure of \\angle G. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "84.000", "choices": [36.0, 60.0, 84.0, 132.0]}
-{"prob_id": "prob_6834", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2456.png", "question": "Triangle LMN is equilateral, and MP bisects LN. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 4.0, 5.0, 6.0]}
-{"prob_id": "prob_6837", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_598.png", "question": "PA = 2.9, and HC = 10.8. Solve for the length of PC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.600", "choices": [3.6, 7.2, 8.7, 32.4]}
-{"prob_id": "prob_6868", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2119.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "92.000", "choices": [46.0, 92.0, 184.0, 420.0]}
-{"prob_id": "prob_6869", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3092.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.657", "choices": [10.0, 13.7, 14.9, 16.0]}
-{"prob_id": "prob_6874", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1497.png", "question": "What is the perimeter of \\parallelogram ABCD? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "36.000", "choices": [28.0, 32.0, 36.0, 43.324]}
-{"prob_id": "prob_6882", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1408.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [28.0, 38.0, 52.0, 62.0]}
-{"prob_id": "prob_6899", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_196.png", "question": "Find m \\widehat AE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [5.0, 90.0, 120.0, 270.0]}
-{"prob_id": "prob_6905", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3545.png", "question": "Determine m \\widehat AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "123.000", "choices": [57.0, 114.0, 123.0, 132.0]}
-{"prob_id": "prob_6926", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1997.png", "question": "m \\angle BDK = 3x+4, m \\angle JDR = 5x-10, find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [7.0, 12.0, 23.25, 90.0]}
-{"prob_id": "prob_6941", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1657.png", "question": "Find the area of the polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [24.0, 30.0, 48.0, 60.0]}
-{"prob_id": "prob_6943", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1616.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.155", "choices": [13.74772708486752, 16.15549442140351, 17.0, 21.0]}
-{"prob_id": "prob_6944", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1462.png", "question": "ABCD \\sim EFGD. What is the value of y? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.333", "choices": [3.333, 6.0, 7.5, 13.5]}
-{"prob_id": "prob_6951", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1869.png", "question": "GHJK is a rhombus. Find m \\angle GHJ if m \\angle JLH = 4b-6 and m \\angle JKH = 2b+11. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "118.000", "choices": [31.0, 59.0, 90.0, 118.0]}
-{"prob_id": "prob_6952", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1104.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.077", "choices": [32.077, 33.866, 38.0, 45.509]}
-{"prob_id": "prob_6970", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2168.png", "question": "Quadrilateral DKLM is a rhombus. If m \\angle DML = 82 find m \\angle MDK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "98.000", "choices": [41.0, 49.0, 90.0, 98.0]}
-{"prob_id": "prob_6985", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3761.png", "question": "Solve for the measure of \\widehat NQL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "274.000", "choices": [86.0, 102.0, 180.0, 274.0]}
-{"prob_id": "prob_6986", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1745.png", "question": "In \\odot O, EC and AB are diameters, and m \\angle BOD = m \\angle DOE = m \\angle EOF = m \\angle FOA. Find m \\widehat AE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 90.0, 180.0, 360.0]}
-{"prob_id": "prob_6988", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3214.png", "question": "Find the height of the parallelogram given its area with 2000 square units. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [30.0, 40.0, 50.0, 60.0]}
-{"prob_id": "prob_6991", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2860.png", "question": "Use \\triangle MAN with right angle N to express ratio of \\cos A if m = 21, a = 28, n = 35. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.600", "choices": [0.6, 0.8, 1.0, 1.333]}
-{"prob_id": "prob_6998", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3284.png", "question": "P is the centroid of \\triangle DEF, EH \\perp DF, DH = 9, DG = 7.5, EP = 8, and DE = FE. Find the length of FH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [4.0, 7.5, 9.0, 12.0]}
-{"prob_id": "prob_6999", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3359.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "72.000", "choices": [30.0, 60.0, 72.0, 120.0]}
-{"prob_id": "prob_7001", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3682.png", "question": "m \\angle 2 = 2x, m \\angle 3 = x. Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 39.0, 78.0, 114.0]}
-{"prob_id": "prob_7005", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2735.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.274", "choices": [28.274, 32.538, 61.726, 90.0]}
-{"prob_id": "prob_7040", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1042.png", "question": "In \\odot S, m \\angle TSR = 42. Find m \\widehat KE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "42.000", "choices": [42.0, 84.0, 90.0, 138.0]}
-{"prob_id": "prob_7043", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3261.png", "question": "Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "113.000", "choices": [67.0, 90.0, 113.0, 182.0]}
-{"prob_id": "prob_7046", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_720.png", "question": "WXYZ is a kite. If m \\angle WXY = 13x+24, m \\angle WZY = 35, and m \\angle ZYX = 13x+14, find m \\angle ZWX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "105.000", "choices": [35.0, 52.5, 63.333, 105.0]}
-{"prob_id": "prob_7051", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3642.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [2.5, 5.0, 10.0, 60.0]}
-{"prob_id": "prob_7063", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2405.png", "question": "Determine m \\angle S. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "52.000", "choices": [14.0, 52.0, 128.0, 242.0]}
-{"prob_id": "prob_7065", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1430.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.328", "choices": [4.2, 8.3, 16.7, 69.4]}
-{"prob_id": "prob_7066", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2953.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "130.000", "choices": [50.0, 80.0, 100.0, 130.0]}
-{"prob_id": "prob_7069", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1959.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.000", "choices": [26.0, 37.0, 80.0, 89.0]}
-{"prob_id": "prob_7076", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2451.png", "question": "Find m \\angle FEA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 45.0, 60.0, 150.0]}
-{"prob_id": "prob_7085", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3024.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "100.006", "choices": [80.0, 93.438, 100.006, 104.452]}
-{"prob_id": "prob_7092", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_673.png", "question": "Find a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.165", "choices": [4.6, 5.9, 7.2, 9.2]}
-{"prob_id": "prob_7103", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_935.png", "question": "In quadrilateral PQRS, PQ = 721, QR = 547, RS = 593, PS = 756, and m \\angle P = 58. Find m \\angle PQS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "63.448", "choices": [43.1, 56.4, 63.45, 87.4]}
-{"prob_id": "prob_7122", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_592.png", "question": "\\triangle ADB \\cong \\triangle CDB, find the length of AD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [2.0, 3.0, 4.0, 5.0]}
-{"prob_id": "prob_7124", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_100.png", "question": "GHJK is a square with diagonals intersecting at L. Given that GH = 2 and GL = \\sqrt{2}, determine the length of HJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [1.414, 2.0, 2.828, 4.0]}
-{"prob_id": "prob_7131", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1997.png", "question": "m \\angle BDK = 3x+4, m \\angle JDR = 5x-10, find the measurement of \\angle KDR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [25.0, 40.0, 50.0, 65.0]}
-{"prob_id": "prob_7134", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3064.png", "question": "Find m \\angle C. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "62.000", "choices": [35.0, 53.0, 62.0, 83.0]}
-{"prob_id": "prob_7135", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3776.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.167", "choices": [10.285714285714286, 14.0, 15.833333333333334, 16.166666666666668]}
-{"prob_id": "prob_7146", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2840.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [80.0, 90.0, 100.0, 140.0]}
-{"prob_id": "prob_7172", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1966.png", "question": "Find \\tan R. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.333", "choices": [0.6, 0.75, 0.8, 1.3333333333333333]}
-{"prob_id": "prob_7177", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_697.png", "question": "Find m \\widehat BCA of \\odot Q. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "313.000", "choices": [47.0, 227.0, 266.0, 313.0]}
-{"prob_id": "prob_7185", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3882.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.500", "choices": [1.714, 2.0, 4.5, 6.0]}
-{"prob_id": "prob_7187", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3657.png", "question": "In kite PQRS, m \\angle SRT = 24, and m \\angle TSP = 53. Find m \\angle QPS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "74.000", "choices": [37.0, 66.0, 74.0, 90.0]}
-{"prob_id": "prob_7194", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1313.png", "question": "Find the area of the shaded region. Assume that the triangle is equilateral. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.481", "choices": [20.8, 29.5, 50.3, 71.1]}
-{"prob_id": "prob_7203", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1740.png", "question": "Quadrilateral DEFG is a rectangle. If m \\angle EDF = 5x-3 and m \\angle DFG = 3x+7, find m \\angle GDF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "68.000", "choices": [22.0, 39.25, 50.75, 68.0]}
-{"prob_id": "prob_7207", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3063.png", "question": "PRYZ is a rhombus. If RK = 5, RY = 13 and m \\angle YRZ = 67, what is m \\angle YKZ? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [23.0, 46.0, 90.0, 134.0]}
-{"prob_id": "prob_7215", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_984.png", "question": "Points P, Q, and R are the midpoints of JK, KL, and JL, respectively. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.500", "choices": [0.83, 1.1, 2.0, 5.5]}
-{"prob_id": "prob_7229", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_920.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.500", "choices": [13.5, 14.0, 14.5, 15.0]}
-{"prob_id": "prob_7231", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2643.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "33.941", "choices": [24.0, 33.941125496954285, 36.0, 41.569219381653056]}
-{"prob_id": "prob_7236", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1785.png", "question": "For what value of x must ABCD be a parallelogram? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [2.0, 5.0, 13.571, 15.0]}
-{"prob_id": "prob_7253", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1685.png", "question": "Find m \\angle T. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "68.000", "choices": [44.0, 56.0, 62.0, 68.0]}
-{"prob_id": "prob_7257", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2036.png", "question": "Find the length of BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [7.5, 12.0, 15.0, 21.333]}
-{"prob_id": "prob_7262", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1003.png", "question": "Find the measure of \\angle E. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "45.000", "choices": [9.899, 45.0, 90.0, 360.0]}
-{"prob_id": "prob_7274", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_662.png", "question": "For trapezoid ABDC, E and F are midpoints of the legs. Find CD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [3.0, 8.0, 10.5, 18.0]}
-{"prob_id": "prob_7280", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1343.png", "question": "Find the value of d. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.750", "choices": [3.75, 10.293, 12.25, 18.286]}
-{"prob_id": "prob_7305", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3118.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [5.3, 6.0, 8.0, 10.0]}
-{"prob_id": "prob_7309", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_198.png", "question": "VWXY is a rhombus. Find YX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "31.500", "choices": [15.75, 25.2, 31.5, 63.0]}
-{"prob_id": "prob_7320", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_39.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [57.5, 81.3, 99.6, 115.0]}
-{"prob_id": "prob_7337", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1578.png", "question": "JL = 5z+3, and KM = 9z-12. Find the value of z so that JKLM is isosceles trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.750", "choices": [2.077, 3.75, 11.333, 21.75]}
-{"prob_id": "prob_7361", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1450.png", "question": "Find the value of the variable z for the quadrilateral. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [40.0, 45.0, 80.0, 160.0]}
-{"prob_id": "prob_7365", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3997.png", "question": "\\angle 6 and \\angle 8 are complementary, m \\angle 8 = 47. Find the measure of \\angle 7. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [43.0, 47.0, 86.0, 90.0]}
-{"prob_id": "prob_7379", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_201.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [25.0, 40.0, 65.0, 115.0]}
-{"prob_id": "prob_7392", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2694.png", "question": "In \\odot A, AE = 13.1 and AC \\perp BD. If BC = 6.8, what is AC? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.197", "choices": [1.827, 4.973, 11.197, 22.394]}
-{"prob_id": "prob_7396", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3607.png", "question": "Find the area of the inscribed regular polygon shown. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "187.061", "choices": [46.765, 72.0, 187.061, 288.0]}
-{"prob_id": "prob_7399", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3068.png", "question": "Point S is the incenter of \\triangle JPL. Find m \\angle MPQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "56.000", "choices": [24.5, 28.0, 49.0, 56.0]}
-{"prob_id": "prob_7402", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1690.png", "question": "Find the area of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "54.000", "choices": [27.0, 36.0, 54.0, 108.0]}
-{"prob_id": "prob_7403", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2226.png", "question": "Find DA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [2.5, 5.0, 8.0, 9.165]}
-{"prob_id": "prob_7418", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2924.png", "question": "Find the area of the shaded region. Assume that the triangle is equilateral. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.481", "choices": [1.449, 18.265, 29.481, 48.816]}
-{"prob_id": "prob_7421", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3482.png", "question": "\\triangle MNL \\sim \\triangle SPT. Find PT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.209", "choices": [12.0, 14.422, 15.0, 19.209]}
-{"prob_id": "prob_7429", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1393.png", "question": "Quadrilateral JKLM is a rectangle. If m \\angle KJL = 2x+4 and m \\angle JLK = 7x+5, find m \\angle KML. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [22.0, 44.0, 68.0, 136.0]}
-{"prob_id": "prob_7439", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3444.png", "question": "The figures in the pair are similar. Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "63.000", "choices": [4.0, 27.0, 32.0, 63.0]}
-{"prob_id": "prob_7440", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2272.png", "question": "What is x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.824", "choices": [13.824, 20.179, 43.0, 79.911]}
-{"prob_id": "prob_7466", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2839.png", "question": "G is the incenter of \\triangle DEF, m \\angle EDF = 50. What is m \\angle EGF? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [25.0, 50.0, 115.0, 155.0]}
-{"prob_id": "prob_7478", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_246.png", "question": "Find the area of the shaded sector. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "175.808", "choices": [37.4, 101.8, 175.8, 277.6]}
-{"prob_id": "prob_7489", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3060.png", "question": "Find m \\angle DIG if m \\angle DGI = 24 and IG = 6. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "132.000", "choices": [24.0, 48.0, 78.0, 132.0]}
-{"prob_id": "prob_7498", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3372.png", "question": "QS is the angle bisector of \\angle PQR, find the measure of \\angle RQS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.000", "choices": [32.0, 64.0, 116.0, 128.0]}
-{"prob_id": "prob_7500", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3501.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.889", "choices": [11.313708498984761, 13.856406460551018, 17.88854381999832, 21.166010488516726]}
-{"prob_id": "prob_7503", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3062.png", "question": "Find the measure of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [10.392, 12.0, 18.0, 41.569]}
-{"prob_id": "prob_7517", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1645.png", "question": "JL / NJ = MK / PK, find JN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.857", "choices": [3.857, 4.32, 6.857, 9.143]}
-{"prob_id": "prob_7527", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3658.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [21.7, 28.0, 38.5, 49.0]}
-{"prob_id": "prob_7530", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2152.png", "question": "Find the measure of \\widehat BCD in \\odot P. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "270.000", "choices": [180.0, 218.0, 270.0, 308.0]}
-{"prob_id": "prob_7538", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_272.png", "question": "What is m \\widehat DF? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "129.000", "choices": [39.0, 90.0, 129.0, 141.0]}
-{"prob_id": "prob_7539", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1007.png", "question": "The perpendicular bisectors of \\triangle RST meet at point D. Find DT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [4.68, 7.687, 9.0, 16.0]}
-{"prob_id": "prob_7544", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1144.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [9.0, 11.0, 37.0, 47.0]}
-{"prob_id": "prob_7554", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3610.png", "question": "Find \\sin N. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.923", "choices": [0.38, 0.42, 0.92, 2.4]}
-{"prob_id": "prob_7555", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3474.png", "question": "Find m \\angle B. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "112.000", "choices": [112.0, 116.0, 122.0, 127.0]}
-{"prob_id": "prob_7557", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2740.png", "question": "Express the ratio of \\tan L. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.417", "choices": [0.38, 0.42, 0.92, 2.4]}
-{"prob_id": "prob_7562", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3615.png", "question": "Find the length of ST. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.060", "choices": [6.357, 7.06, 8.554, 12.784]}
-{"prob_id": "prob_7593", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_623.png", "question": "Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [7.429, 18.0, 21.2, 22.0]}
-{"prob_id": "prob_7594", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1794.png", "question": "Find YZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.053", "choices": [4.592, 7.0, 8.053, 9.275]}
-{"prob_id": "prob_7602", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2976.png", "question": "What is m \\widehat XZV? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "260.000", "choices": [80.0, 180.0, 260.0, 280.0]}
-{"prob_id": "prob_7609", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1651.png", "question": "Use rhombus WXYZ with m \\angle XYZ = 5 m \\angle WZY and YZ = 12. Find WX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [6.0, 12.0, 24.0, 84.0]}
-{"prob_id": "prob_7614", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_59.png", "question": "Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "73.000", "choices": [73.0, 82.0, 107.0, 146.0]}
-{"prob_id": "prob_7622", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1720.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.381", "choices": [4.898979485566356, 6.6332495807108, 9.38083151964686, 9.433981132056603]}
-{"prob_id": "prob_7646", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3388.png", "question": "Find the area of the shaded figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "27.000", "choices": [1.25, 6.0, 15.0, 27.0]}
-{"prob_id": "prob_7649", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1934.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "56.000", "choices": [28.0, 56.0, 112.0, 164.0]}
-{"prob_id": "prob_7656", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1239.png", "question": "Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [27.713, 36.661, 40.0, 42.332]}
-{"prob_id": "prob_7681", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1368.png", "question": "EFGH is a parallelogram. Find w. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.500", "choices": [4.5, 6.3, 6.5, 6.7]}
-{"prob_id": "prob_7691", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3890.png", "question": "Find the value of n. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 45.0, 60.0, 90.0]}
-{"prob_id": "prob_7695", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1024.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [25.0, 50.0, 100.0, 144.0]}
-{"prob_id": "prob_7716", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1613.png", "question": "Find the area of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "280.592", "choices": [256.785, 280.592, 305.47, 374.123]}
-{"prob_id": "prob_7719", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2289.png", "question": "Find the measure of \\angle A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "78.463", "choices": [11.3, 11.5, 78.5, 78.7]}
-{"prob_id": "prob_7720", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_142.png", "question": "m \\widehat UY = m \\widehat XZ = m \\widehat UV = m \\widehat XW = 56. Solve for m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "56.000", "choices": [28.0, 56.0, 96.0, 124.0]}
-{"prob_id": "prob_7728", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1590.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [5.6, 5.667, 6.0, 13.273]}
-{"prob_id": "prob_7740", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2967.png", "question": "Find WZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [18.0, 24.0, 30.0, 32.0]}
-{"prob_id": "prob_7748", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3236.png", "question": "The two triangles in the diagram are similar. Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.429", "choices": [2.182, 3.429, 10.5, 16.5]}
-{"prob_id": "prob_7749", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1806.png", "question": "Find the measure of RT for equilateral triangle SRT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [9.0, 12.0, 15.0, 18.0]}
-{"prob_id": "prob_7770", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2698.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.485", "choices": [8.485281374238571, 10.392304845413264, 12.0, 14.696938456699067]}
-{"prob_id": "prob_7778", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2994.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "45.000", "choices": [30.0, 45.0, 60.0, 90.0]}
-{"prob_id": "prob_7781", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2967.png", "question": "Find WU. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [8.727, 18.0, 24.0, 30.0]}
-{"prob_id": "prob_7784", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2469.png", "question": "Find m \\angle S. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.363", "choices": [22.363, 23.0, 29.088, 128.549]}
-{"prob_id": "prob_7787", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2558.png", "question": "PR and QT are diameters of \\odot A. Solve for the measure of \\widehat PQS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "230.000", "choices": [140.0, 180.0, 230.0, 320.0]}
-{"prob_id": "prob_7795", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3562.png", "question": "EG and FG are angle bisectors of \\triangle DEF. Find the distance from G to EF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.700", "choices": [3.7, 7.4, 25.0, 42.0]}
-{"prob_id": "prob_7799", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1096.png", "question": "Use rectangle LMNP, parallelogram LKMJ. If MK = 6x, KL = 3x+2y, and JN = 14-x, find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 3.0, 6.0, 12.0]}
-{"prob_id": "prob_7803", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_652.png", "question": "Find the perimeter of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [8.0, 12.0, 20.785, 25.133]}
-{"prob_id": "prob_7836", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3650.png", "question": "Lines that appear to be tangent are tangent. O is the center of the circle. What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [30.0, 60.0, 120.0, 210.0]}
-{"prob_id": "prob_7840", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1042.png", "question": "In \\odot S, m \\angle TSR = 42. Find m \\widehat KT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "138.000", "choices": [21.0, 42.0, 63.0, 138.0]}
-{"prob_id": "prob_7860", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1444.png", "question": "QRST is a rectangle. If m \\angle QTR = 2x^{2}-7 and m \\angle SRT = x^{2}+18, find m \\angle PSR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.000", "choices": [43.0, 44.333, 45.667, 86.0]}
-{"prob_id": "prob_7866", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_157.png", "question": "What is the length of QP? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [11.18, 12.166, 14.0, 22.0]}
-{"prob_id": "prob_7869", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3308.png", "question": "What is c? Lines that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "47.500", "choices": [47.5, 62.5, 70.0, 132.5]}
-{"prob_id": "prob_7907", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_451.png", "question": "WXYZ is a square. If WT = 3, find m \\angle WTZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [15.0, 30.0, 45.0, 90.0]}
-{"prob_id": "prob_7913", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2655.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "106.066", "choices": [75.0, 106.1, 150.0, 212.1]}
-{"prob_id": "prob_7914", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3702.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [26.0, 52.0, 64.0, 90.0]}
-{"prob_id": "prob_7923", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2101.png", "question": "Find the value of q. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "27.500", "choices": [11.136, 14.583, 27.5, 39.6]}
-{"prob_id": "prob_7925", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2464.png", "question": "BD = x-1, CE = x+2. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.800", "choices": [1.0, 2.8, 4.623, 9.0]}
-{"prob_id": "prob_7934", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_47.png", "question": "Find the area of the shaded region of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "53.014", "choices": [13.894, 50.364, 53.014, 201.455]}
-{"prob_id": "prob_7940", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1594.png", "question": "If DB = 6, AD = 2, and CB = 20, find EB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 6.667, 15.0, 60.0]}
-{"prob_id": "prob_7941", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_813.png", "question": "In kite EFGH, m \\angle FEJ = 25, and m \\angle FGJ = 57. Find the measure of \\angle GFJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "33.000", "choices": [25.0, 33.0, 65.0, 90.0]}
-{"prob_id": "prob_7946", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2293.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.385", "choices": [1.0, 2.217, 2.25, 3.385]}
-{"prob_id": "prob_7967", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1132.png", "question": "If QRST is a parallelogram, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.400", "choices": [5.4, 9.0, 11.0, 13.0]}
-{"prob_id": "prob_7969", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3902.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [30.0, 45.0, 60.0, 90.0]}
-{"prob_id": "prob_7977", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2354.png", "question": "Find the area of \\odot K. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "283.487", "choices": [27.387, 59.686, 283.487, 2136.283]}
-{"prob_id": "prob_7990", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_793.png", "question": "Find y if m \\angle 5 = 68 and m \\angle 3 = 3y-2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [22.0, 23.3, 38.0, 82.0]}
-{"prob_id": "prob_7996", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_184.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.000", "choices": [3.0, 20.333, 29.0, 81.0]}
-{"prob_id": "prob_8003", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_42.png", "question": "What is the measure of \\angle 8? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.000", "choices": [34.0, 44.0, 46.0, 90.0]}
-{"prob_id": "prob_8015", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1156.png", "question": "Use parallelogram ABCD to find m \\angle BAD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "103.000", "choices": [49.0, 54.0, 77.0, 103.0]}
-{"prob_id": "prob_8018", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3026.png", "question": "Find m \\angle 1 in the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "57.000", "choices": [57.0, 61.5, 66.0, 114.0]}
-{"prob_id": "prob_8022", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3288.png", "question": "For the pair of similar figures, the area of the blue figure is 400 mm^{2} and the green figure is 64 mm^{2}, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [6.4, 16.0, 100.0, 250.0]}
-{"prob_id": "prob_8035", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3162.png", "question": "Find RV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [1.667, 2.333, 5.0, 7.0]}
-{"prob_id": "prob_8045", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3356.png", "question": "In \\odot A, m \\widehat PQ = m \\widehat RS. Find y if m \\angle 1 = 6x+11, m \\angle 2 = 9x+19, m \\angle 3 = 4y-25, and m \\angle 4 = 3y-9. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [16.0, 17.714, 30.571, 33.0]}
-{"prob_id": "prob_8069", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1705.png", "question": "Use \\odot P to find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [30.0, 40.0, 70.0, 130.0]}
-{"prob_id": "prob_8078", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3082.png", "question": "Find m \\widehat ABE for \\odot O. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "230.000", "choices": [50.0, 160.0, 230.0, 260.0]}
-{"prob_id": "prob_8116", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3015.png", "question": "m \\angle 17 = 2x+7, m \\angle 18 = x+30, find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.000", "choices": [23.0, 47.667, 53.0, 60.0]}
-{"prob_id": "prob_8120", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1221.png", "question": "In \\triangle JKL, ZW = 7, and LX = 8.1. Determine the length of XZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.700", "choices": [2.7, 5.4, 21.0, 24.3]}
-{"prob_id": "prob_8125", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_538.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "93.923", "choices": [91.9, 93.9, 95.9, 97.9]}
-{"prob_id": "prob_8162", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1297.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.738", "choices": [17.7, 36.6, 57.7, 66.0]}
-{"prob_id": "prob_8163", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3589.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.091", "choices": [22.045407685048602, 44.090815370097204, 54.0, 62.35382907247958]}
-{"prob_id": "prob_8166", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1997.png", "question": "m \\angle BDJ = 7y+2, m \\angle JDR = 2y+7, find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [1.0, 9.0, 19.0, 41.5]}
-{"prob_id": "prob_8168", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1127.png", "question": "What is the circumference of \\odot T? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.841", "choices": [37.2, 39.6, 40.8, 42.4]}
-{"prob_id": "prob_8186", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3724.png", "question": "Given m \\angle GFI = 128, what is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [4.154, 10.0, 14.444, 26.0]}
-{"prob_id": "prob_8187", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_889.png", "question": "For the pair of similar figures, the area of the blue figure is 72 m^{2} and the green figure is 50 m^{2}, find the scale factor of the blue to the green figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.200", "choices": [0.6944444444444444, 0.8333333333333334, 1.2, 1.44]}
-{"prob_id": "prob_8199", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_892.png", "question": "Solve for t. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.250", "choices": [0.5, 0.714, 0.833, 1.25]}
-{"prob_id": "prob_8211", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1973.png", "question": "If m \\angle BNC = 20, find m \\widehat BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [20.0, 30.0, 40.0, 50.0]}
-{"prob_id": "prob_8222", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3073.png", "question": "Find RQ if AU = 15, QU = 25, AD = 3x+6, DR = 8x-2, and UD = 15. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [6.75, 18.0, 30.0, 40.0]}
-{"prob_id": "prob_8228", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1180.png", "question": "Find the measure of \\angle 1 for the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "95.000", "choices": [37.0, 48.0, 85.0, 95.0]}
-{"prob_id": "prob_8232", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1381.png", "question": "CG, EH, and FJ are midsegments of \\triangle ABD, \\triangle GCD, and \\triangle GHE, respectively. What is m \\angle GHE? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "57.000", "choices": [28.5, 57.0, 66.0, 123.0]}
-{"prob_id": "prob_8240", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2371.png", "question": "The perpendicular bisectors of \\triangle ABC meet at point G. Find BF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.708", "choices": [2.0, 4.899, 6.708, 7.0]}
-{"prob_id": "prob_8258", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1975.png", "question": "Find the value of variable x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.800", "choices": [2.333, 10.714, 25.8, 53.0]}
-{"prob_id": "prob_8270", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3034.png", "question": "Use parallelogram WXYZ to find m \\angle XYZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "105.000", "choices": [30.0, 75.0, 105.0, 180.0]}
-{"prob_id": "prob_8273", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1675.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.028", "choices": [6.0, 15.905973720586866, 17.0, 18.027756377319946]}
-{"prob_id": "prob_8274", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2470.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [1.647, 7.765, 10.0, 16.118]}
-{"prob_id": "prob_8275", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1130.png", "question": "CE bisects \\angle DCF, and CG bisects \\angle FCB. If m \\angle DCE = 4x+15 and m \\angle ECF = 6x-5, find m \\angle GCB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [35.0, 55.0, 70.0, 125.0]}
-{"prob_id": "prob_8276", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1879.png", "question": "Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [9.798, 10.0, 10.667, 12.649]}
-{"prob_id": "prob_8282", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2024.png", "question": "Find the area of the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [22.0, 30.0, 60.0, 120.0]}
-{"prob_id": "prob_8292", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2779.png", "question": "H is the incenter of \\triangle ABC. Find m \\angle DHG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [60.0, 100.0, 120.0, 150.0]}
-{"prob_id": "prob_8303", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3831.png", "question": "\\triangle DFG and \\triangle FGH are isosceles. Find the measure of \\angle FGH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "56.000", "choices": [56.0, 58.0, 64.0, 68.0]}
-{"prob_id": "prob_8313", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2565.png", "question": "Find m \\angle K. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "49.000", "choices": [16.0, 49.0, 82.0, 98.0]}
-{"prob_id": "prob_8320", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2284.png", "question": "What is the measure of \\widehat PQR in \\odot T? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "180.000", "choices": [120.0, 180.0, 220.0, 240.0]}
-{"prob_id": "prob_8325", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1712.png", "question": "Find the area of the segment. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.540", "choices": [3.915, 28.54, 114.159, 310.245]}
-{"prob_id": "prob_8333", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2345.png", "question": "m \\angle UOW = 50, and OV bisects \\angle UOW. What is m \\angle VOY? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "155.000", "choices": [25.0, 65.0, 90.0, 155.0]}
-{"prob_id": "prob_8337", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2867.png", "question": "Solve for m \\angle FGH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [12.5, 25.0, 90.0, 155.0]}
-{"prob_id": "prob_8342", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_508.png", "question": "m \\angle 5 = 72 and m \\angle 9 = 102. Find the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "102.000", "choices": [72.0, 78.0, 102.0, 108.0]}
-{"prob_id": "prob_8346", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_591.png", "question": "Find the perimeter of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "27.713", "choices": [23.511, 24.0, 27.713, 29.062]}
-{"prob_id": "prob_8348", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3693.png", "question": "\\triangle RST \\cong \\triangle XYZ. Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [5.0, 14.0, 15.0, 35.0]}
-{"prob_id": "prob_8376", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2815.png", "question": "Find the measure of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [34.0, 56.0, 68.0, 146.0]}
-{"prob_id": "prob_8379", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3506.png", "question": "Find the length of AD if AB = DC, AD = DC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [6.25, 25.0, 50.0, 64.375]}
-{"prob_id": "prob_8386", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1513.png", "question": "Find x if \\triangle JMN is an isosceles triangle with JM = MN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [2.0, 3.0, 4.0, 4.0]}
-{"prob_id": "prob_8398", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3795.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [7.0, 9.0, 12.0, 15.0]}
-{"prob_id": "prob_8399", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2961.png", "question": "Find m \\angle D of quadrilateral ABCD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "45.000", "choices": [45.0, 90.0, 135.0, 180.0]}
-{"prob_id": "prob_8414", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3699.png", "question": "Quadrilateral WXYZ is a rectangle. If XZ = 2c and ZY = 6, and XY = 8, find WY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [6.0, 8.0, 10.0, 20.0]}
-{"prob_id": "prob_8415", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3234.png", "question": "In rhombus RSTV, m \\angle TZV = 8n+18, and m \\angle SRV = 9n+1. Find the measure of \\angle RSV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "49.000", "choices": [41.0, 49.0, 82.0, 164.0]}
-{"prob_id": "prob_8427", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1751.png", "question": "Find the measure of \\angle 1 in special parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "58.000", "choices": [32.0, 58.0, 74.0, 90.0]}
-{"prob_id": "prob_8428", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1193.png", "question": "Find the measure of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [23.0, 24.0, 28.0, 33.0]}
-{"prob_id": "prob_8438", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3820.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "125.000", "choices": [55.0, 115.0, 125.0, 135.0]}
-{"prob_id": "prob_8450", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1216.png", "question": "What is m \\angle A? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "71.000", "choices": [71.0, 76.0, 80.0, 133.0]}
-{"prob_id": "prob_8468", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1493.png", "question": "Find the measure of XT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [3.5, 7.0, 14.0, 28.0]}
-{"prob_id": "prob_8489", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_862.png", "question": "For rhombus ABCD, find m \\angle BAD, given that m \\angle DEC = 30y, m \\angle EDC = 8y+15, AB = 2x+8, and BC = 4x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "102.000", "choices": [51.0, 78.0, 90.0, 102.0]}
-{"prob_id": "prob_8491", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_993.png", "question": "Find the value of b that would make the quadrilateral a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [19.286, 19.615, 20.0, 71.667]}
-{"prob_id": "prob_8494", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1253.png", "question": "m \\widehat AB = 176, and m \\widehat BC = 42. Solve for the measure of \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "88.000", "choices": [21.0, 71.0, 88.0, 109.0]}
-{"prob_id": "prob_8501", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3821.png", "question": "Find the measure of \\angle DFB on \\odot F with diameter AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "165.000", "choices": [163.0, 165.0, 167.0, 169.0]}
-{"prob_id": "prob_8502", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_103.png", "question": "The angle bisectors of \\triangle XYZ intersect at W. Find WB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 8.0, 10.0, 12.0]}
-{"prob_id": "prob_8503", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1524.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.806", "choices": [6.0, 8.0, 10.0, 12.806248474865697]}
-{"prob_id": "prob_8506", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3407.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.000", "choices": [26.472, 31.165, 32.0, 40.0]}
-{"prob_id": "prob_8511", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3992.png", "question": "Solve for the diameter of \\odot S. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [7.5, 30.0, 47.124, 133.5]}
-{"prob_id": "prob_8516", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_361.png", "question": "Find the area of the kite. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [15.0, 17.5, 18.0, 21.0]}
-{"prob_id": "prob_8517", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1172.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [18.0, 20.0, 22.0, 24.0]}
-{"prob_id": "prob_8519", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1733.png", "question": "Find the measure of \\angle C. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "26.000", "choices": [9.946, 26.0, 47.621, 66.009]}
-{"prob_id": "prob_8523", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1379.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.314", "choices": [8.0, 11.314, 12.649, 36.0]}
-{"prob_id": "prob_8534", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1905.png", "question": "In \\odot T, ZV = 1, and TW = 13. Find VT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [5.0, 10.0, 12.0, 13.0]}
-{"prob_id": "prob_8548", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2928.png", "question": "m \\angle 3 = x-12 and m \\angle 6 = 72. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "84.000", "choices": [6.0, 18.0, 72.0, 84.0]}
-{"prob_id": "prob_8562", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2421.png", "question": "If CD = 3 and AD = 12, what is BA? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.416", "choices": [6.0, 6.708, 12.369, 13.416]}
-{"prob_id": "prob_8567", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_748.png", "question": "\\angle 6 and \\angle 8 are complementary, m \\angle 8 = 47. Find the measure of \\angle 6. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.000", "choices": [43.0, 47.0, 86.0, 90.0]}
-{"prob_id": "prob_8582", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2146.png", "question": "What is the measure of \\angle E? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "135.000", "choices": [81.0, 108.0, 113.684, 135.0]}
-{"prob_id": "prob_8584", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2464.png", "question": "BD = x-1, CE = x+2. Find CF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.330", "choices": [1.8, 3.499, 4.8, 9.33]}
-{"prob_id": "prob_8594", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3305.png", "question": "Rhombus MNPQ has an area of 375 square inches. If MP is 25 inches, find PQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.526", "choices": [15.0, 19.526, 30.0, 375.0]}
-{"prob_id": "prob_8600", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1753.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [17.0, 24.041630560342618, 34.0, 41.641325627314025]}
-{"prob_id": "prob_8623", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3869.png", "question": "Refer to rectangle QRTS. If RU = 3x-6 and UT = x+9, find RS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "33.000", "choices": [8.25, 16.5, 19.25, 33.0]}
-{"prob_id": "prob_8628", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_505.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.071", "choices": [5.0, 7.0710678118654755, 10.0, 14.142135623730951]}
-{"prob_id": "prob_8634", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3254.png", "question": "Find m \\angle 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "64.000", "choices": [26.0, 32.0, 64.0, 78.0]}
-{"prob_id": "prob_8635", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3419.png", "question": "Find the height of the trapezoid, in which Area = 280 cm^{2}. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [20.0, 35.0, 50.0, 160.0]}
-{"prob_id": "prob_8644", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_173.png", "question": "For the pair of similar figures, the area of the blue figure is 32 cm^{2}, find the area of the green figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.500", "choices": [12.5, 20.0, 51.2, 81.9]}
-{"prob_id": "prob_8648", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_630.png", "question": "Find the area of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "84.000", "choices": [40.0, 84.0, 85.0, 105.0]}
-{"prob_id": "prob_8665", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1417.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.657", "choices": [5.656854249492381, 6.928203230275509, 8.0, 8.94427190999916]}
-{"prob_id": "prob_8676", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_860.png", "question": "In rectangle PLCM, LC = 19, and LM = 23. Find TC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.500", "choices": [9.5, 11.5, 12.961, 19.0]}
-{"prob_id": "prob_8677", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2185.png", "question": "Find the measure of \\angle 3 in the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 60.0, 75.0, 90.0]}
-{"prob_id": "prob_8679", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1720.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.745", "choices": [4.898979485566356, 5.744562646538029, 5.830951894845301, 6.6332495807108]}
-{"prob_id": "prob_8680", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1831.png", "question": "If MNPQ \\sim XYZW, find the perimeter of XYZW. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.000", "choices": [17.0, 18.0, 20.0, 34.0]}
-{"prob_id": "prob_8682", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3192.png", "question": "What is the measure of \\widehat FA? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "58.000", "choices": [58.0, 140.0, 158.0, 182.0]}
-{"prob_id": "prob_8685", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3679.png", "question": "Find m \\angle 7. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [32.5, 65.0, 115.0, 230.0]}
-{"prob_id": "prob_8699", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2198.png", "question": "In \\triangle PQR, NQ = 6, RK = 3, and PK = 4. Solve for the length of NK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 2.667, 6.0, 9.0]}
-{"prob_id": "prob_8701", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1617.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [3.5, 7.0, 14.0, 86.5]}
-{"prob_id": "prob_8702", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_404.png", "question": "AE, BF, and CG are medians. Find CG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [6.0, 12.0, 12.0, 18.0]}
-{"prob_id": "prob_8713", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_640.png", "question": "Find x. Perimeter = 41 yards. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [5.375, 6.0, 6.833, 7.0]}
-{"prob_id": "prob_8724", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2984.png", "question": "Find the length of \\widehat WN if \\triangle IWN is equilateral and WN = 5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.236", "choices": [1.8849555921538759, 5.235987755982989, 15.707963267948966, 31.41592653589793]}
-{"prob_id": "prob_8740", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2562.png", "question": "Determine the area of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "314.159", "choices": [62.832, 314.159, 1186.824, 1256.637]}
-{"prob_id": "prob_8742", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1042.png", "question": "In \\odot S, m \\angle TSR = 42. Find m \\widehat ERT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "180.000", "choices": [42.0, 84.0, 138.0, 180.0]}
-{"prob_id": "prob_8746", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2355.png", "question": "JKMN is a rectangle. If NQ = 2x+3 and QK = 5x-9, find QM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [5.5, 11.0, 15.556, 22.0]}
-{"prob_id": "prob_8749", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2588.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.168", "choices": [22.1, 23.4, 26.3, 28.2]}
-{"prob_id": "prob_8750", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2528.png", "question": "If MD = 7, find RI. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [7.0, 14.0, 21.0, 28.0]}
-{"prob_id": "prob_8759", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2015.png", "question": "isosceles trapezoid TWYZ with m \\angle Z = m \\angle Y, m \\angle Z = 30x, m \\angle T = m \\angle W, and m \\angle T = 20x, find m \\angle T. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "72.000", "choices": [62.0, 72.0, 108.0, 118.0]}
-{"prob_id": "prob_8778", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3951.png", "question": "PACE is a parallelogram and m \\angle PAC = 124. What is the measurement of \\angle ECA? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "56.000", "choices": [41.462, 48.538, 56.0, 124.0]}
-{"prob_id": "prob_8802", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2094.png", "question": "Find the perimeter of \\triangle STU. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "31.000", "choices": [31.0, 62.0, 76.0, 77.0]}
-{"prob_id": "prob_8805", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3764.png", "question": "Quadrilateral ABCD is a rhombus. If m \\angle BCD = 120, find m \\angle DAC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 90.0, 120.0]}
-{"prob_id": "prob_8809", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3951.png", "question": "PACE is a parallelogram and m \\angle PAC = 124. What is the length of RE? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.500", "choices": [3.5, 6.6, 7.47, 14.94]}
-{"prob_id": "prob_8812", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_79.png", "question": "Find the value of variable y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.962", "choices": [3.611, 4.792, 7.962, 9.97]}
-{"prob_id": "prob_8831", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2513.png", "question": "Find the value of b. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [55.0, 70.0, 110.0, 125.0]}
-{"prob_id": "prob_8832", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1415.png", "question": "PQ = QR = RS. Solve for the length of XW. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.500", "choices": [3.0, 4.5, 6.75, 9.0]}
-{"prob_id": "prob_8853", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1087.png", "question": "Find m \\angle N. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "102.000", "choices": [78.0, 86.4, 102.0, 108.857]}
-{"prob_id": "prob_8854", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3098.png", "question": "Find CA. Assume that segments that appear tangent to circles are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.000", "choices": [14.5, 29.0, 41.012, 58.0]}
-{"prob_id": "prob_8858", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3597.png", "question": "If RS = 15 and ST = 9, find RT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [6.0, 15.0, 21.0, 24.0]}
-{"prob_id": "prob_8887", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1555.png", "question": "RP = 3.5 and JP = 9. Find PL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [3.5, 4.5, 7.0, 9.0]}
-{"prob_id": "prob_8894", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_627.png", "question": "In \\odot E, EG = EF. Find FC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.500", "choices": [13.5, 27.0, 30.187, 54.0]}
-{"prob_id": "prob_8900", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2869.png", "question": "Find PN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [25.0, 30.0, 50.0, 60.0]}
-{"prob_id": "prob_8904", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_3900.png", "question": "BD bisects \\angle ABF. If m \\angle ABF = 3x-8 and m \\angle ABD = x+14, find m \\angle CBF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [50.0, 80.0, 100.0, 130.0]}
-{"prob_id": "prob_8926", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1795.png", "question": "In ABCD, m \\angle ABC = 79, BC = 62.4, and BD = 75. Find the measurement of \\angle CDA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "79.000", "choices": [11.0, 79.0, 101.0, 158.0]}
-{"prob_id": "prob_8928", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1131.png", "question": "Find TY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.500", "choices": [5.0, 7.5, 10.0, 12.5]}
-{"prob_id": "prob_8930", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2221.png", "question": "Find m \\angle MNP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "130.000", "choices": [40.0, 50.0, 130.0, 140.0]}
-{"prob_id": "prob_8946", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_176.png", "question": "Find the perimeter of the polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.534", "choices": [16.0, 17.534, 17.602, 19.602]}
-{"prob_id": "prob_8948", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1479.png", "question": "What is the length of \\widehat BD? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.064", "choices": [10.21, 15.551, 18.064, 22.934]}
-{"prob_id": "prob_8952", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2065.png", "question": "MN \\parallel BC. Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [6.0, 9.0, 12.0, 15.0]}
-{"prob_id": "prob_8963", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2860.png", "question": "Use \\triangle MAN with right angle N to express ratio of \\tan M if m = 21, a = 28, n = 35. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.750", "choices": [0.6, 0.75, 1.0, 1.333]}
-{"prob_id": "prob_8965", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1410.png", "question": "m \\angle 11 = x+40, m \\angle 12 = x+10, m \\angle 13 = 3x+30, what is the measure of \\angle 12? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [15.0, 30.0, 60.0, 90.0]}
-{"prob_id": "prob_8968", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_2558.png", "question": "PR and QT are diameters of \\odot A. Solve for the measure of \\widehat UPQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "130.000", "choices": [130.0, 140.0, 180.0, 320.0]}
-{"prob_id": "prob_8988", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_1204.png", "question": "Circle O has a radius of 13 inches. Radius OB is perpendicular to chord CD which is 24 inches long. Find XB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [5.0, 8.0, 10.0, 12.0]}
-{"prob_id": "prob_8994", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_889.png", "question": "For the pair of similar figures, the area of the blue figure is 72 m^{2} and the green figure is 50 m^{2}, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [8.3, 10.0, 14.4, 17.3]}
-{"prob_id": "prob_9003", "image_path": "/gpfs/work/int/xiaoqiangkang/datasets/PGPS9K/Diagram_Visual/img_552.png", "question": "Find the perimeter of the polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.409", "choices": [20.0, 24.0, 28.0, 34.409]}
+{"prob_id": "prob_13", "image_path": "images/img_3909.png", "question": "In \\triangle QRS, T, U, and B are midpoints. What is the length of UB? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [25.0, 30.0, 40.0, 80.0]}
+{"prob_id": "prob_27", "image_path": "images/img_423.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.000", "choices": [24.0, 33.941125496954285, 41.569219381653056, 48.0]}
+{"prob_id": "prob_31", "image_path": "images/img_2339.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [35.0, 70.0, 75.0, 82.0]}
+{"prob_id": "prob_46", "image_path": "images/img_2654.png", "question": "If ABCD is a kite. Find m \\angle C. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [60.0, 70.0, 85.0, 120.0]}
+{"prob_id": "prob_55", "image_path": "images/img_794.png", "question": "Solve for m \\angle 2 in the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "33.500", "choices": [33.5, 56.5, 67.0, 113.0]}
+{"prob_id": "prob_59", "image_path": "images/img_169.png", "question": "Find the value of x in the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "100.000", "choices": [20.0, 80.0, 100.0, 160.0]}
+{"prob_id": "prob_60", "image_path": "images/img_662.png", "question": "For trapezoid ABDC, E and F are midpoints of the legs. Let XY be the median of ABFE. Find XY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.500", "choices": [8.0, 9.25, 10.5, 18.0]}
+{"prob_id": "prob_72", "image_path": "images/img_1475.png", "question": "Find SP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.000", "choices": [5.0, 6.0, 7.0, 17.0]}
+{"prob_id": "prob_87", "image_path": "images/img_883.png", "question": "If AB \\parallel DC, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [32.5, 65.0, 105.0, 115.0]}
+{"prob_id": "prob_88", "image_path": "images/img_2023.png", "question": "In \\odot X, WS, VR, and QT are diameters, m \\angle WXV = 25 and m \\angle VXU = 45. Find the measure of \\widehat WRV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "335.000", "choices": [180.0, 245.0, 270.0, 335.0]}
+{"prob_id": "prob_92", "image_path": "images/img_1191.png", "question": "In \\triangle MIV, Z is the centroid, MZ = 6, YI = 18, and NZ = 12. What is the measure of ZV? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [12.0, 24.0, 36.0, 54.0]}
+{"prob_id": "prob_111", "image_path": "images/img_73.png", "question": "Use the diagram of \\parallelogram ABCD to find m \\angle A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "53.000", "choices": [26.5, 53.0, 90.0, 127.0]}
+{"prob_id": "prob_112", "image_path": "images/img_3063.png", "question": "PRYZ is a rhombus. If RK = 5, RY = 13 and m \\angle YRZ = 67, what is m \\angle RYK? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.000", "choices": [23.0, 46.0, 90.0, 134.0]}
+{"prob_id": "prob_120", "image_path": "images/img_884.png", "question": "What is m \\angle W? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [22.0, 52.0, 73.6, 90.0]}
+{"prob_id": "prob_129", "image_path": "images/img_1776.png", "question": "Find YZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [6.0, 7.0, 8.0, 9.0]}
+{"prob_id": "prob_132", "image_path": "images/img_3361.png", "question": "What is m \\angle C? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "110.000", "choices": [40.0, 70.0, 82.0, 110.0]}
+{"prob_id": "prob_143", "image_path": "images/img_3291.png", "question": "For \\parallelogram ABCD, what is perimeter of ABCD? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.800", "choices": [36.8, 44.0, 44.8, 52.0]}
+{"prob_id": "prob_152", "image_path": "images/img_3063.png", "question": "PRYZ is a rhombus. If RK = 5, RY = 13 and m \\angle YRZ = 67, what is m \\angle PKR? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [23.0, 46.0, 90.0, 134.0]}
+{"prob_id": "prob_159", "image_path": "images/img_1591.png", "question": "Find a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [12.0, 12.5, 15.0, 17.5]}
+{"prob_id": "prob_165", "image_path": "images/img_3687.png", "question": "For isosceles trapezoid ABCD, X and Y are midpoints of the legs. Find m \\angle C if m \\angle ADY = 78. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "102.000", "choices": [51.0, 78.0, 90.0, 102.0]}
+{"prob_id": "prob_172", "image_path": "images/img_3125.png", "question": "Find the measure of \\angle FJE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "62.000", "choices": [25.0, 62.0, 90.0, 118.0]}
+{"prob_id": "prob_173", "image_path": "images/img_535.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 4.0, 5.0, 6.0]}
+{"prob_id": "prob_175", "image_path": "images/img_1655.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.200", "choices": [16.8, 19.2, 21.6, 22.7]}
+{"prob_id": "prob_180", "image_path": "images/img_408.png", "question": "Find m \\angle ABD, given that m \\angle ABC = 112. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "56.000", "choices": [34.0, 56.0, 112.0, 124.0]}
+{"prob_id": "prob_182", "image_path": "images/img_947.png", "question": "Find the scale from B to B'. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.333", "choices": [0.75, 0.8333333333333334, 1.2, 1.3333333333333333]}
+{"prob_id": "prob_184", "image_path": "images/img_422.png", "question": "Find the value of y if line p \\parallel line q. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "105.000", "choices": [75.0, 85.0, 95.0, 105.0]}
+{"prob_id": "prob_186", "image_path": "images/img_3797.png", "question": "NPLM \\cong EFGH. Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [0.143, 9.0, 11.143, 14.429]}
+{"prob_id": "prob_187", "image_path": "images/img_1746.png", "question": "What is the measure of \\angle M? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 139.149, 165.0, 201.818]}
+{"prob_id": "prob_193", "image_path": "images/img_2502.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [20.0, 28.0, 36.0, 44.0]}
+{"prob_id": "prob_198", "image_path": "images/img_1783.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.600", "choices": [9.0, 9.6, 12.0, 14.4]}
+{"prob_id": "prob_200", "image_path": "images/img_2166.png", "question": "What is the measure of \\angle 3? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "52.000", "choices": [38.0, 52.0, 90.0, 128.0]}
+{"prob_id": "prob_218", "image_path": "images/img_597.png", "question": "Find the perimeter of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "41.569", "choices": [24.0, 41.569, 45.255, 64.0]}
+{"prob_id": "prob_247", "image_path": "images/img_1676.png", "question": "What is the measure of \\angle 3? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "129.000", "choices": [51.0, 90.0, 129.0, 258.0]}
+{"prob_id": "prob_276", "image_path": "images/img_1108.png", "question": "Find the value of variable w. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "104.000", "choices": [22.0, 44.0, 72.0, 104.0]}
+{"prob_id": "prob_300", "image_path": "images/img_763.png", "question": "Use parallelogram ABCD to find m \\angle FBC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "59.000", "choices": [20.0, 49.0, 59.0, 111.0]}
+{"prob_id": "prob_311", "image_path": "images/img_3147.png", "question": "Find m \\angle 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [45.0, 60.0, 75.0, 120.0]}
+{"prob_id": "prob_312", "image_path": "images/img_3068.png", "question": "Point S is the incenter of \\triangle JPL. Find QJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [4.0, 6.0, 8.0, 10.0]}
+{"prob_id": "prob_313", "image_path": "images/img_2332.png", "question": "Find the area of the trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "500.000", "choices": [125.0, 250.0, 500.0, 1000.0]}
+{"prob_id": "prob_335", "image_path": "images/img_1086.png", "question": "Find PX, if XZ = 18 and PY = 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 15.0, 18.0, 21.0]}
+{"prob_id": "prob_350", "image_path": "images/img_2369.png", "question": "What is m \\angle 3 in the isosceles trapezoid? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "111.000", "choices": [34.5, 42.0, 69.0, 111.0]}
+{"prob_id": "prob_367", "image_path": "images/img_1037.png", "question": "Find the value of n. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [-3.333, -1.818, -1.25, 5.0]}
+{"prob_id": "prob_371", "image_path": "images/img_3302.png", "question": "If AC = 12 and AB = 25, what is the measure of \\angle B? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.685", "choices": [25.6, 28.7, 61.3, 64.4]}
+{"prob_id": "prob_375", "image_path": "images/img_2576.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [52.0, 60.0, 105.0, 475.933]}
+{"prob_id": "prob_377", "image_path": "images/img_8.png", "question": "Find the area of the trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "132.000", "choices": [72.0, 132.0, 144.0, 192.0]}
+{"prob_id": "prob_387", "image_path": "images/img_2262.png", "question": "Solve for the length of CD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [0.0, 1.0, 6.0, 11.0]}
+{"prob_id": "prob_396", "image_path": "images/img_3185.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "42.000", "choices": [28.0, 32.286, 42.0, 53.0]}
+{"prob_id": "prob_413", "image_path": "images/img_1152.png", "question": "Find m \\angle DAB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "125.000", "choices": [55.0, 110.0, 125.0, 135.0]}
+{"prob_id": "prob_419", "image_path": "images/img_2010.png", "question": "Find the area of the shaded sector. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "167.133", "choices": [47.5, 167.1, 285.3, 452.4]}
+{"prob_id": "prob_425", "image_path": "images/img_1488.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [2.222, 2.812, 6.0, 7.2]}
+{"prob_id": "prob_439", "image_path": "images/img_3633.png", "question": "m \\angle RST = x+50, and m \\angle STU = 3x+20. Find m \\angle SRV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [65.0, 77.5, 102.5, 115.0]}
+{"prob_id": "prob_441", "image_path": "images/img_2011.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [-1.0, 0.548, 0.646, 2.0]}
+{"prob_id": "prob_443", "image_path": "images/img_850.png", "question": "J is the incenter of \\angle ABC. Find BE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.343", "choices": [9.0, 13.343, 14.403, 16.984]}
+{"prob_id": "prob_445", "image_path": "images/img_2224.png", "question": "A regular polygon is inscribed in a circle. What is the measure of \\angle SRL? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 36.0, 60.0, 90.0]}
+{"prob_id": "prob_448", "image_path": "images/img_2240.png", "question": "Find the measure of \\angle KLG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [57.0, 70.0, 103.5, 123.0]}
+{"prob_id": "prob_472", "image_path": "images/img_30.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [3.111, 4.0, 65.0, 80.0]}
+{"prob_id": "prob_494", "image_path": "images/img_2270.png", "question": "Find the variable of x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 7.0, 8.0, 9.0]}
+{"prob_id": "prob_495", "image_path": "images/img_695.png", "question": "Find BD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [5.0, 10.0, 13.0, 24.0]}
+{"prob_id": "prob_500", "image_path": "images/img_2815.png", "question": "Find the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [34.0, 56.0, 68.0, 146.0]}
+{"prob_id": "prob_508", "image_path": "images/img_890.png", "question": "If AB = 60 and DE = 48, find DC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [24.0, 30.0, 54.991, 56.604]}
+{"prob_id": "prob_517", "image_path": "images/img_801.png", "question": "Find the area of the shaded sector. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.815", "choices": [0.9, 1.8, 10.8, 12.6]}
+{"prob_id": "prob_533", "image_path": "images/img_3852.png", "question": "The diagonals of rectangle MNPQ intersect at S. If MN = 4.1 meters, MS = 2.35 meters, and MQ = 2.3 meters, what is the length of NQ? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.700", "choices": [2.35, 4.1, 4.7, 8.2]}
+{"prob_id": "prob_537", "image_path": "images/img_1184.png", "question": "If QT = 11, what is QU? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [7.0, 8.0, 11.0, 16.0]}
+{"prob_id": "prob_538", "image_path": "images/img_3448.png", "question": "Find the area of the polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [60.0, 92.0, 120.0, 172.5]}
+{"prob_id": "prob_547", "image_path": "images/img_1457.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [3.5, 7.0, 14.0, 56.0]}
+{"prob_id": "prob_572", "image_path": "images/img_2716.png", "question": "Find m \\angle JKL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 50.0, 60.0, 80.0]}
+{"prob_id": "prob_579", "image_path": "images/img_1994.png", "question": "Find x so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [11.0, 25.0, 26.0, 33.0]}
+{"prob_id": "prob_584", "image_path": "images/img_3350.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "280.000", "choices": [259.0, 280.0, 294.0, 336.0]}
+{"prob_id": "prob_587", "image_path": "images/img_532.png", "question": "E is between D and F. Find DF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [3.667, 9.333, 11.0, 24.0]}
+{"prob_id": "prob_617", "image_path": "images/img_3286.png", "question": "Use the Law of Sines to find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.142", "choices": [2.142, 2.976, 3.598, 6.949]}
+{"prob_id": "prob_640", "image_path": "images/img_850.png", "question": "J is the incenter of \\angle ABC. Find DB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.343", "choices": [9.0, 13.343, 14.403, 16.984]}
+{"prob_id": "prob_667", "image_path": "images/img_1490.png", "question": "What is x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "46.000", "choices": [2.0, 36.8, 46.0, 72.8]}
+{"prob_id": "prob_679", "image_path": "images/img_371.png", "question": "Find m \\angle 8. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.500", "choices": [28.0, 28.5, 56.0, 57.0]}
+{"prob_id": "prob_687", "image_path": "images/img_2481.png", "question": "Find the value of variable a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.828, 3.0, 5.657, 6.0]}
+{"prob_id": "prob_689", "image_path": "images/img_3738.png", "question": "RS and RT are tangent to \\odot Q. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.400", "choices": [5.457, 8.4, 12.6, 293.04]}
+{"prob_id": "prob_692", "image_path": "images/img_390.png", "question": "Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 4.0, 5.0, 6.0]}
+{"prob_id": "prob_694", "image_path": "images/img_2054.png", "question": "AD = 6 and DE = 7.5. What is the length of DC? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 7.5, 12.0, 15.0]}
+{"prob_id": "prob_697", "image_path": "images/img_664.png", "question": "JKLM is a rectangle. MLPR is a rhombus. m \\angle JMK = m \\angle RMP, m \\angle JMK = 55, and m \\angle MRP = 70. Find m \\angle KML. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [35.0, 70.0, 110.0, 140.0]}
+{"prob_id": "prob_701", "image_path": "images/img_2340.png", "question": "Find the value of variable x. Lines that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [50.0, 65.0, 115.0, 130.0]}
+{"prob_id": "prob_716", "image_path": "images/img_2447.png", "question": "What is \\tan A? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.417", "choices": [0.38, 0.42, 0.92, 2.4]}
+{"prob_id": "prob_731", "image_path": "images/img_3639.png", "question": "Find CB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 3.0, 4.0, 55.0]}
+{"prob_id": "prob_738", "image_path": "images/img_1662.png", "question": "Find FH if \\triangle ABC \\sim \\triangle DEF, BG is an altitude of \\triangle ABC, EH is an altitude of \\triangle DEF, BG = 3, BF = 4, FC = 2, and CE = 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.598", "choices": [1.5, 2.0, 2.5, 2.598]}
+{"prob_id": "prob_756", "image_path": "images/img_1148.png", "question": "UA and VA are angle bisectors of \\triangle UVW. Determine m \\angle WVA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.000", "choices": [20.0, 24.0, 37.0, 66.0]}
+{"prob_id": "prob_760", "image_path": "images/img_1750.png", "question": "The segment is tangent to the circle. Find TR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.000", "choices": [9.5, 19.0, 26.87, 38.0]}
+{"prob_id": "prob_761", "image_path": "images/img_2689.png", "question": "Given that line t is the perpendicular bisector of JK and GK = 8.25, find GJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.250", "choices": [4.125, 8.25, 16.5, 90.0]}
+{"prob_id": "prob_765", "image_path": "images/img_65.png", "question": "Find m \\widehat BCD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "206.000", "choices": [52.0, 206.0, 283.0, 308.0]}
+{"prob_id": "prob_774", "image_path": "images/img_2368.png", "question": "What is z? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [3.84, 15.0, 16.667, 37.5]}
+{"prob_id": "prob_782", "image_path": "images/img_293.png", "question": "Quadrilateral EFGH is a rectangle. If FK = 32 feet, find KG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.000", "choices": [16.0, 32.0, 45.255, 64.0]}
+{"prob_id": "prob_784", "image_path": "images/img_3994.png", "question": "Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [6.0, 10.0, 28.0, 29.333]}
+{"prob_id": "prob_785", "image_path": "images/img_3894.png", "question": "PM is a diameter of \\odot R. Find m \\widehat NMQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "155.000", "choices": [155.0, 205.0, 270.0, 295.0]}
+{"prob_id": "prob_799", "image_path": "images/img_2733.png", "question": "Find TQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [6.0, 7.0, 12.0, 18.0]}
+{"prob_id": "prob_802", "image_path": "images/img_2842.png", "question": "WXYZ is a rhombus. If m \\angle XYZ = 110, find m \\angle ZWY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [35.0, 55.0, 70.0, 110.0]}
+{"prob_id": "prob_812", "image_path": "images/img_2295.png", "question": "Find the value of variable y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.928", "choices": [4.571, 6.928, 10.583, 24.5]}
+{"prob_id": "prob_815", "image_path": "images/img_163.png", "question": "ABCD \\sim QSRP. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "63.000", "choices": [34.0, 63.0, 82.0, 83.0]}
+{"prob_id": "prob_816", "image_path": "images/img_40.png", "question": "In kite WXYZ, m \\angle VXY = 58, and m \\angle ZWX = 50. What is m \\angle WZY? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "123.000", "choices": [40.0, 65.0, 90.0, 123.0]}
+{"prob_id": "prob_817", "image_path": "images/img_3078.png", "question": "PQRS is a rhombus. Find the length of QR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [3.375, 6.75, 9.0, 18.0]}
+{"prob_id": "prob_818", "image_path": "images/img_1259.png", "question": "Solve for y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "45.000", "choices": [30.0, 45.0, 67.5, 90.0]}
+{"prob_id": "prob_829", "image_path": "images/img_2067.png", "question": "In \\odot P, m \\angle MPL = 65 and NP \\perp PL. Find m \\widehat JM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [25.0, 65.0, 90.0, 115.0]}
+{"prob_id": "prob_832", "image_path": "images/img_1757.png", "question": "The square is circumscribed to the circle. Find the exact circumference of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.982", "choices": [21.991148575128552, 43.982297150257104, 65.97344572538566, 87.96459430051421]}
+{"prob_id": "prob_835", "image_path": "images/img_2589.png", "question": "YZ is the midsegment of trapezoid TWRV. Determine the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.200", "choices": [1.2, 8.0, 14.8, 16.0]}
+{"prob_id": "prob_837", "image_path": "images/img_285.png", "question": "Find QP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 3.0, 5.0, 6.0]}
+{"prob_id": "prob_845", "image_path": "images/img_3307.png", "question": "If m \\angle AFE = 14x+8 and m \\angle BFC = 8x-15, find the value of x so that \\angle AFC is a right angle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.167", "choices": [4.409, 8.5, 11.167, 19.0]}
+{"prob_id": "prob_866", "image_path": "images/img_334.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.400", "choices": [2.7, 5.4, 6.0, 9.0]}
+{"prob_id": "prob_872", "image_path": "images/img_424.png", "question": "Find the circumference of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.850", "choices": [9.4, 18.85, 28.3, 37.7]}
+{"prob_id": "prob_878", "image_path": "images/img_2927.png", "question": "S is between R and T. Find RT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [14.0, 28.0, 42.0, 70.0]}
+{"prob_id": "prob_887", "image_path": "images/img_3050.png", "question": "m \\angle 9 = 141+x, m \\angle 10 = 25+x, find m \\angle 10. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.000", "choices": [32.0, 103.0, 148.0, 206.0]}
+{"prob_id": "prob_888", "image_path": "images/img_1509.png", "question": "ABCD is a square. Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [3.6, 9.0, 18.0, 90.0]}
+{"prob_id": "prob_889", "image_path": "images/img_2782.png", "question": "In \\triangle TUV, Y is the centroid. If UZ = 13.5, find UY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [4.5, 6.75, 9.0, 40.5]}
+{"prob_id": "prob_891", "image_path": "images/img_220.png", "question": "Given isosceles \\triangle JKL with base JL. If JL = 5, find ML. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.500", "choices": [2.5, 4.33, 5.0, 10.0]}
+{"prob_id": "prob_908", "image_path": "images/img_1871.png", "question": "Find the length of \\widehat AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.967", "choices": [19.967, 20.874, 39.933, 41.748]}
+{"prob_id": "prob_909", "image_path": "images/img_63.png", "question": "What is the measure of \\angle 4? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "75.000", "choices": [52.5, 75.0, 90.0, 105.0]}
+{"prob_id": "prob_919", "image_path": "images/img_3652.png", "question": "In the diagram of the collinear points, PT = 20, QS = 6, and PQ = QR = RS. Find ST. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [3.0, 6.0, 9.0, 11.0]}
+{"prob_id": "prob_925", "image_path": "images/img_1400.png", "question": "Find the area of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.018", "choices": [6.02, 7.54, 7.99, 9.42]}
+{"prob_id": "prob_927", "image_path": "images/img_3646.png", "question": "If ABCD is a kite, find BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [2.5, 4.0, 5.0, 8.0]}
+{"prob_id": "prob_942", "image_path": "images/img_2217.png", "question": "Use rhombus ABCD with AY = 6, DY = 3r+3, and BY = \\frac{10r-4}{2}. Find m \\angle CAB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.000", "choices": [29.745, 60.255, 90.0, 120.51]}
+{"prob_id": "prob_951", "image_path": "images/img_1140.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 4.0, 5.0, 6.0]}
+{"prob_id": "prob_964", "image_path": "images/img_2273.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [0.571, 2.25, 15.75, 28.0]}
+{"prob_id": "prob_969", "image_path": "images/img_3483.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [32.5, 40.0, 72.5, 85.0]}
+{"prob_id": "prob_971", "image_path": "images/img_3071.png", "question": "Find MK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.000", "choices": [2.0, 4.0, 9.0, 37.0]}
+{"prob_id": "prob_972", "image_path": "images/img_2536.png", "question": "What is the length of \\widehat JL? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.499", "choices": [11.1, 15.499, 22.201, 46.496]}
+{"prob_id": "prob_987", "image_path": "images/img_3870.png", "question": "Quadrilateral ABCD is inscribed in \\odot P. If m \\angle B = 80 and m \\angle C = 40, find m \\widehat DCB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "280.000", "choices": [180.0, 200.0, 240.0, 280.0]}
+{"prob_id": "prob_991", "image_path": "images/img_3154.png", "question": "What is the area of the shaded region? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "113.097", "choices": [28.274, 84.823, 113.097, 169.646]}
+{"prob_id": "prob_995", "image_path": "images/img_1008.png", "question": "Cut four congruent triangles off the corners of a rectangle to make an octagon. What is the area of the octagon? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "528.000", "choices": [456.0, 528.0, 552.0, 564.0]}
+{"prob_id": "prob_998", "image_path": "images/img_776.png", "question": "If \\triangle CAB \\sim \\triangle FDE, find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [12.0, 14.0, 16.0, 18.0]}
+{"prob_id": "prob_1010", "image_path": "images/img_2290.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 5.733, 7.5, 10.444]}
+{"prob_id": "prob_1037", "image_path": "images/img_3855.png", "question": "line a \\parallel line b, line c \\parallel line d, and m \\angle 4 = 57. Find the measure of \\angle 8. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "57.000", "choices": [57.0, 113.0, 123.0, 133.0]}
+{"prob_id": "prob_1040", "image_path": "images/img_1353.png", "question": "Use parallelogram JKLM to find m \\angle MJK if JK = 2b+3 and JM = 3a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "100.000", "choices": [30.0, 70.0, 80.0, 100.0]}
+{"prob_id": "prob_1043", "image_path": "images/img_3405.png", "question": "Find m \\angle B. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "79.000", "choices": [22.0, 39.5, 79.0, 101.0]}
+{"prob_id": "prob_1049", "image_path": "images/img_352.png", "question": "PQRS is a rhombus. Find m \\angle TQR, given that m \\angle QTR = 6y+6 and m \\angle SPR = 3y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.000", "choices": [42.0, 48.0, 84.0, 96.0]}
+{"prob_id": "prob_1053", "image_path": "images/img_2955.png", "question": "Find c. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [0.258, 0.586, 2.0, 4.449]}
+{"prob_id": "prob_1091", "image_path": "images/img_2834.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [15.0, 30.0, 60.0, 90.0]}
+{"prob_id": "prob_1097", "image_path": "images/img_2017.png", "question": "Find m \\angle A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "81.000", "choices": [81.0, 89.0, 91.0, 99.0]}
+{"prob_id": "prob_1138", "image_path": "images/img_1178.png", "question": "Find m \\angle B. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "76.000", "choices": [52.0, 76.0, 104.0, 128.0]}
+{"prob_id": "prob_1140", "image_path": "images/img_410.png", "question": "If PQ = UQ and m \\angle P = 32, find m \\angle PUQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.000", "choices": [32.0, 74.0, 79.0, 116.0]}
+{"prob_id": "prob_1142", "image_path": "images/img_2580.png", "question": "If AB = DA = ED = CF, find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.400", "choices": [0.425, 2.4, 3.0, 8.0]}
+{"prob_id": "prob_1158", "image_path": "images/img_3797.png", "question": "NPLM \\cong EFGH. Find m \\angle G. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "110.000", "choices": [21.0, 72.0, 87.0, 110.0]}
+{"prob_id": "prob_1166", "image_path": "images/img_3894.png", "question": "PM is a diameter of \\odot R. Find m \\widehat NPQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "205.000", "choices": [180.0, 205.0, 270.0, 295.0]}
+{"prob_id": "prob_1169", "image_path": "images/img_277.png", "question": "\\triangle JKL \\sim \\triangle MNP. Find PM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [3.75, 6.0, 10.0, 16.0]}
+{"prob_id": "prob_1175", "image_path": "images/img_3285.png", "question": "m \\angle 1 = 123. Find the measure of \\angle 14. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "57.000", "choices": [47.0, 57.0, 67.0, 123.0]}
+{"prob_id": "prob_1177", "image_path": "images/img_470.png", "question": "What is the value of b? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [18.0, 72.0, 108.0, 162.0]}
+{"prob_id": "prob_1187", "image_path": "images/img_3830.png", "question": "Use parallelogram JKLM to find m \\angle KJL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 40.0, 50.0, 60.0]}
+{"prob_id": "prob_1190", "image_path": "images/img_2708.png", "question": "Find m \\widehat MN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 67.5, 90.0, 180.0]}
+{"prob_id": "prob_1193", "image_path": "images/img_1605.png", "question": "The angle bisectors of \\triangle XYZ meet at point W. Find AX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "72.284", "choices": [20.0, 72.284, 75.0, 144.568]}
+{"prob_id": "prob_1202", "image_path": "images/img_2558.png", "question": "PR and QT are diameters of \\odot A. Solve for the measure of \\widehat PQR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "180.000", "choices": [140.0, 180.0, 230.0, 320.0]}
+{"prob_id": "prob_1224", "image_path": "images/img_3192.png", "question": "What is the measure of \\angle DCE? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "79.000", "choices": [70.0, 79.0, 101.0, 110.0]}
+{"prob_id": "prob_1234", "image_path": "images/img_2642.png", "question": "Find the value of variable x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.500", "choices": [2.571, 3.5, 14.0, 27.333]}
+{"prob_id": "prob_1238", "image_path": "images/img_3664.png", "question": "If WXYZ is a kite, find XY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [4.0, 4.472, 6.0, 8.944]}
+{"prob_id": "prob_1242", "image_path": "images/img_1372.png", "question": "For what value of y must ABCD be a parallelogram? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "39.000", "choices": [22.385, 25.5, 30.0, 39.0]}
+{"prob_id": "prob_1255", "image_path": "images/img_1925.png", "question": "Find the area of the trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "84.000", "choices": [28.0, 42.0, 84.0, 168.0]}
+{"prob_id": "prob_1256", "image_path": "images/img_2879.png", "question": "Find the value of variable a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [3.464, 4.899, 6.0, 8.0]}
+{"prob_id": "prob_1260", "image_path": "images/img_3548.png", "question": "PR and PS are tangent to \\odot Q. What is m \\angle Q? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "138.000", "choices": [42.0, 48.0, 90.0, 138.0]}
+{"prob_id": "prob_1266", "image_path": "images/img_2461.png", "question": "Square WXYZ is inscribed in \\odot R. Determine the measure of \\widehat ZY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 60.0, 72.0, 90.0]}
+{"prob_id": "prob_1324", "image_path": "images/img_3176.png", "question": "Find m \\angle N. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.912", "choices": [35.889, 40.111, 48.912, 61.794]}
+{"prob_id": "prob_1333", "image_path": "images/img_3536.png", "question": "What is the measure of \\angle 1? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [55.0, 62.5, 117.5, 235.0]}
+{"prob_id": "prob_1338", "image_path": "images/img_3111.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [1.7320508075688772, 3.0, 5.196152422706632, 6.0]}
+{"prob_id": "prob_1350", "image_path": "images/img_3255.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.785", "choices": [4.2, 4.8, 7.9, 16.9]}
+{"prob_id": "prob_1353", "image_path": "images/img_1874.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 3.0, 4.0, 5.0]}
+{"prob_id": "prob_1355", "image_path": "images/img_1370.png", "question": "CB is a tangent segment. Find the measure of \\angle BAC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 90.0, 720.0]}
+{"prob_id": "prob_1356", "image_path": "images/img_1192.png", "question": "\\triangle LMN \\cong \\triangle PQR. What is LM? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 10.0, 12.0, 24.0]}
+{"prob_id": "prob_1358", "image_path": "images/img_1792.png", "question": "Find b. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.622", "choices": [1.869, 1.947, 2.88, 4.622]}
+{"prob_id": "prob_1363", "image_path": "images/img_1083.png", "question": "The HIJK is circumscribed about the circle. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.000", "choices": [1.923, 5.0, 13.0, 21.0]}
+{"prob_id": "prob_1364", "image_path": "images/img_1819.png", "question": "The diameters of \\odot A, \\odot B, and \\odot C are 10, 30 and 10 units, respectively. Find ZX if AZ = CW and CW = 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 4.0, 5.0, 6.0]}
+{"prob_id": "prob_1366", "image_path": "images/img_3565.png", "question": "AM bisects \\angle LAR, and AS bisects \\angle MAR. If m \\angle RAL = x+32 and m \\angle MAR = x-31, find m \\angle LAM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "63.000", "choices": [54.0, 63.0, 117.0, 126.0]}
+{"prob_id": "prob_1375", "image_path": "images/img_2876.png", "question": "QRST is an isosceles trapezoid with median XY. Find TS if QR = 22 and XY = 15. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [2.0, 4.0, 8.0, 16.0]}
+{"prob_id": "prob_1380", "image_path": "images/img_969.png", "question": "Quadrilateral RSTU is a rectangle. If RZ = 3x+8 and ZS = 6x-28, find UZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.000", "choices": [14.667, 29.333, 44.0, 88.0]}
+{"prob_id": "prob_1394", "image_path": "images/img_2461.png", "question": "Square WXYZ is inscribed in \\odot R. Solve for m \\angle YRS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "45.000", "choices": [30.0, 36.0, 45.0, 90.0]}
+{"prob_id": "prob_1399", "image_path": "images/img_603.png", "question": "Find the area of triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.004", "choices": [2.928, 16.004, 32.009, 142.684]}
+{"prob_id": "prob_1400", "image_path": "images/img_198.png", "question": "VWXY is a rhombus. Find m \\angle VWX if m \\angle WVY = 4b+10 and m \\angle XZW = 10b-5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "132.000", "choices": [24.0, 45.0, 90.0, 132.0]}
+{"prob_id": "prob_1401", "image_path": "images/img_3122.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.142", "choices": [1.4, 7.1, 14.1, 15.6]}
+{"prob_id": "prob_1425", "image_path": "images/img_3690.png", "question": "Find the area of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "127.306", "choices": [84.303, 116.504, 127.306, 169.741]}
+{"prob_id": "prob_1460", "image_path": "images/img_3999.png", "question": "For isosceles trapezoid XYZW, find m \\angle W. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "110.000", "choices": [15.0, 70.0, 110.0, 250.0]}
+{"prob_id": "prob_1463", "image_path": "images/img_2579.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 3.0, 6.0, 9.0]}
+{"prob_id": "prob_1469", "image_path": "images/img_3249.png", "question": "Find the area of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1122.369", "choices": [770.356, 841.777, 916.41, 1122.369]}
+{"prob_id": "prob_1479", "image_path": "images/img_1390.png", "question": "Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "39.000", "choices": [33.0, 39.0, 51.0, 108.0]}
+{"prob_id": "prob_1488", "image_path": "images/img_338.png", "question": "Find the length of CB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [2.857, 5.0, 6.0, 13.62]}
+{"prob_id": "prob_1494", "image_path": "images/img_714.png", "question": "Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.100", "choices": [3.5, 4.1, 4.5, 5.1]}
+{"prob_id": "prob_1496", "image_path": "images/img_2485.png", "question": "ED is tangent to \\odot F at point E. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 4.0, 5.0, 6.0]}
+{"prob_id": "prob_1498", "image_path": "images/img_1525.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "144.000", "choices": [36.0, 72.0, 136.0, 144.0]}
+{"prob_id": "prob_1501", "image_path": "images/img_532.png", "question": "E is between D and F. Find ED. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [3.667, 9.333, 11.0, 24.0]}
+{"prob_id": "prob_1508", "image_path": "images/img_1261.png", "question": "Find the area of the figure. Perimeter = 90 centimeters. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "584.567", "choices": [387.107, 540.0, 584.567, 21044.419]}
+{"prob_id": "prob_1511", "image_path": "images/img_759.png", "question": "Assume the segments that appear to be tangent are tangent. Find the length of AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "41.000", "choices": [18.0, 23.0, 41.0, 46.0]}
+{"prob_id": "prob_1517", "image_path": "images/img_3835.png", "question": "Find m \\angle 2 in the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "58.000", "choices": [32.0, 58.0, 74.0, 90.0]}
+{"prob_id": "prob_1543", "image_path": "images/img_2170.png", "question": "If GK = 30, what is HJ? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 15.0, 21.0, 30.0]}
+{"prob_id": "prob_1551", "image_path": "images/img_1031.png", "question": "Express the ratio of \\cos Q. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.882", "choices": [0.47, 0.53, 0.88, 1.88]}
+{"prob_id": "prob_1554", "image_path": "images/img_3432.png", "question": "Find m \\angle KLM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "100.000", "choices": [80.0, 88.125, 91.875, 100.0]}
+{"prob_id": "prob_1572", "image_path": "images/img_2306.png", "question": "Find the perimeter of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [12.0, 18.0, 31.177, 37.699]}
+{"prob_id": "prob_1573", "image_path": "images/img_3721.png", "question": "Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "113.000", "choices": [46.0, 67.0, 90.0, 113.0]}
+{"prob_id": "prob_1589", "image_path": "images/img_2491.png", "question": "a = 8, b = 15, and c = 17, find \\tan B. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.875", "choices": [1.23, 1.67, 1.88, 2.43]}
+{"prob_id": "prob_1594", "image_path": "images/img_3783.png", "question": "TV is tangent to the circle, and R and S are points on the circle. What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.658", "choices": [4.8, 5.7, 6.4, 7.6]}
+{"prob_id": "prob_1613", "image_path": "images/img_3523.png", "question": "Find the area of the quadrilateral. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "561.185", "choices": [162.0, 187.061, 280.592, 561.185]}
+{"prob_id": "prob_1618", "image_path": "images/img_2152.png", "question": "Find the measure of \\widehat TBD in \\odot P. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "180.000", "choices": [180.0, 218.0, 270.0, 308.0]}
+{"prob_id": "prob_1628", "image_path": "images/img_1065.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "46.000", "choices": [26.857, 38.889, 46.0, 54.0]}
+{"prob_id": "prob_1632", "image_path": "images/img_2047.png", "question": "If m \\angle DEG is 6\\frac{1}{2} times m \\angle FEG, what is m \\angle DEG? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "156.000", "choices": [24.0, 78.0, 156.0, 173.5]}
+{"prob_id": "prob_1644", "image_path": "images/img_3511.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 37.667, 54.0, 68.2]}
+{"prob_id": "prob_1657", "image_path": "images/img_1538.png", "question": "Circle W has a radius of 4 units, \\odot Z has a radius of 7 units, and XY = 2. Find IC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [5.0, 10.0, 15.0, 20.0]}
+{"prob_id": "prob_1693", "image_path": "images/img_3894.png", "question": "PM is a diameter of \\odot R. Find m \\widehat NMP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "270.000", "choices": [180.0, 205.0, 270.0, 295.0]}
+{"prob_id": "prob_1695", "image_path": "images/img_3470.png", "question": "Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [40.0, 80.0, 110.0, 150.0]}
+{"prob_id": "prob_1706", "image_path": "images/img_96.png", "question": "Use \\odot D to find the length of \\widehat KL if JD = 7 centimeters. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.330", "choices": [6.109, 7.33, 9.774, 12.217]}
+{"prob_id": "prob_1729", "image_path": "images/img_3402.png", "question": "Use parallelogram to find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "79.000", "choices": [39.0, 79.0, 101.0, 180.0]}
+{"prob_id": "prob_1730", "image_path": "images/img_3863.png", "question": "Find the length of UR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [10.0, 14.0, 17.0, 27.0]}
+{"prob_id": "prob_1742", "image_path": "images/img_100.png", "question": "GHJK is a square with diagonals intersecting at L. Given that GH = 2 and GL = \\sqrt{2}, find the perimeter of \\triangle HJK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.828", "choices": [2.0, 2.828, 6.828, 8.828]}
+{"prob_id": "prob_1747", "image_path": "images/img_1147.png", "question": "Find the perimeter of the trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.325", "choices": [44.325, 50.53, 56.601, 57.235]}
+{"prob_id": "prob_1750", "image_path": "images/img_947.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 4.0, 6.0, 8.0]}
+{"prob_id": "prob_1766", "image_path": "images/img_3993.png", "question": "Find the measure of \\angle 1 in the isosceles trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "77.000", "choices": [26.0, 60.0, 77.0, 103.0]}
+{"prob_id": "prob_1769", "image_path": "images/img_559.png", "question": "Quadrilateral ABCD is a rhombus. If m \\angle BCD = 120, find m \\angle CDP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_1770", "image_path": "images/img_2267.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 6.928203230275509, 8.0, 10.392304845413264]}
+{"prob_id": "prob_1790", "image_path": "images/img_2750.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "42.000", "choices": [42.0, 69.0, 96.0, 138.0]}
+{"prob_id": "prob_1791", "image_path": "images/img_2045.png", "question": "WX = YZ. What is the length of YX? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "59.000", "choices": [25.0, 50.0, 59.0, 84.0]}
+{"prob_id": "prob_1794", "image_path": "images/img_3288.png", "question": "For the pair of similar figures, the area of the blue figure is 400 mm^{2} and the green figure is 64 mm^{2}, find the scale factor of the blue to the green figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.500", "choices": [0.16, 0.4, 2.5, 6.25]}
+{"prob_id": "prob_1822", "image_path": "images/img_3745.png", "question": "What is the measure of \\angle 1? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "127.000", "choices": [26.5, 53.0, 74.0, 127.0]}
+{"prob_id": "prob_1835", "image_path": "images/img_62.png", "question": "For what value of y must EFGH be a parallelogram? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.000", "choices": [6.0, 30.667, 43.0, 50.4]}
+{"prob_id": "prob_1842", "image_path": "images/img_3740.png", "question": "Find the radius of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.100", "choices": [1.55, 3.1, 6.2, 12.4]}
+{"prob_id": "prob_1850", "image_path": "images/img_758.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "21.000", "choices": [13.5, 21.0, 28.5, 43.5]}
+{"prob_id": "prob_1857", "image_path": "images/img_52.png", "question": "Polygon BCDE \\cong polygon RSTU. Find TS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [11.0, 12.0, 33.0, 49.0]}
+{"prob_id": "prob_1860", "image_path": "images/img_29.png", "question": "Q is the midpoint of RP. What is PQ? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "41.000", "choices": [6.833, 41.0, 82.0, 123.0]}
+{"prob_id": "prob_1871", "image_path": "images/img_3112.png", "question": "Find x of isosceles \\triangle XYZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [0.75, 1.167, 2.0, 5.333]}
+{"prob_id": "prob_1876", "image_path": "images/img_3954.png", "question": "In \\odot B, m \\angle LBM = 3x and m \\angle LBQ = 4x+61. What is the measure of \\angle PBQ? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "51.000", "choices": [17.0, 34.0, 51.0, 61.0]}
+{"prob_id": "prob_1877", "image_path": "images/img_3919.png", "question": "Quadrilateral DEFG is a kite. Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [38.0, 52.0, 64.0, 90.0]}
+{"prob_id": "prob_1890", "image_path": "images/img_220.png", "question": "Given isosceles \\triangle JKL with base JL. If m \\angle L = 58, what is m \\angle LKJ? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "64.000", "choices": [29.0, 32.0, 64.0, 90.0]}
+{"prob_id": "prob_1933", "image_path": "images/img_912.png", "question": "What is f? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.619", "choices": [4.0, 4.619, 6.928, 9.238]}
+{"prob_id": "prob_1934", "image_path": "images/img_3991.png", "question": "Quadrilateral ABCD is a rectangle. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [5.0, 12.0, 24.0, 25.0]}
+{"prob_id": "prob_1947", "image_path": "images/img_1129.png", "question": "Find the measure of \\widehat AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [53.13, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_1970", "image_path": "images/img_3515.png", "question": "Triangle RST is circumscribed about the circle. What is x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 6.0, 9.0, 11.0]}
+{"prob_id": "prob_1973", "image_path": "images/img_2671.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [5.0, 80.0, 85.0, 100.0]}
+{"prob_id": "prob_1980", "image_path": "images/img_2393.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [1.5, 1.854, 3.0, 6.0]}
+{"prob_id": "prob_1996", "image_path": "images/img_2149.png", "question": "WX = ZY, and m \\widehat ZW = 120. Find the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_2015", "image_path": "images/img_1926.png", "question": "Given that UT = TV and m \\angle PQS = 42, find m \\angle VTS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "132.000", "choices": [42.0, 48.0, 96.0, 132.0]}
+{"prob_id": "prob_2031", "image_path": "images/img_3169.png", "question": "What is the area of \\odot K? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "201.062", "choices": [50.265, 110.851, 201.062, 804.248]}
+{"prob_id": "prob_2043", "image_path": "images/img_3513.png", "question": "What is the measure of \\angle 1 in rhombus PQRS? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [38.0, 52.0, 76.0, 104.0]}
+{"prob_id": "prob_2053", "image_path": "images/img_3729.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.854", "choices": [3.9, 5.2, 7.9, 20.4]}
+{"prob_id": "prob_2057", "image_path": "images/img_2664.png", "question": "AB, BC, CD, and AD are tangent to a circle. If AB = 19, DC = 14, and AD = 27, find BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 22.0, 27.0, 32.0]}
+{"prob_id": "prob_2070", "image_path": "images/img_527.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.748", "choices": [11.0, 15.556349186104047, 17.74823934929885, 25.553864678361276]}
+{"prob_id": "prob_2071", "image_path": "images/img_925.png", "question": "Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [4.0, 6.0, 10.0, 11.0]}
+{"prob_id": "prob_2091", "image_path": "images/img_3690.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "26.632", "choices": [26.632, 37.434, 55.938, 127.306]}
+{"prob_id": "prob_2095", "image_path": "images/img_2404.png", "question": "Find the area of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "665.108", "choices": [456.507, 498.831, 665.108, 697.481]}
+{"prob_id": "prob_2099", "image_path": "images/img_3464.png", "question": "If TR = 12 what is CP? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [4.0, 8.0, 24.0, 36.0]}
+{"prob_id": "prob_2117", "image_path": "images/img_503.png", "question": "In \\triangle JKL, points Q, R, and S are midpoints of the sides. If QR = 6, determine the length of JL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [1.5, 3.0, 6.0, 12.0]}
+{"prob_id": "prob_2130", "image_path": "images/img_1900.png", "question": "Quadrilateral ABCD is a rectangle. If m \\angle ADB = 4x+8 and m \\angle DBA = 6x+12, find \\angle DBC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "36.000", "choices": [36.0, 54.0, 72.0, 108.0]}
+{"prob_id": "prob_2137", "image_path": "images/img_643.png", "question": "Find m \\angle UWT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "139.000", "choices": [20.5, 41.0, 98.0, 139.0]}
+{"prob_id": "prob_2141", "image_path": "images/img_566.png", "question": "Use parallelogram MNPR to find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [8.0, 20.0, 24.0, 32.0]}
+{"prob_id": "prob_2142", "image_path": "images/img_414.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 3.0, 4.0, 8.0]}
+{"prob_id": "prob_2146", "image_path": "images/img_2541.png", "question": "Find the value of variable y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "150.000", "choices": [30.0, 75.0, 105.0, 150.0]}
+{"prob_id": "prob_2173", "image_path": "images/img_1775.png", "question": "Polygon ABCD \\cong polygon PQRS. Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.000", "choices": [4.0, 8.0, 38.0, 48.0]}
+{"prob_id": "prob_2197", "image_path": "images/img_688.png", "question": "Find the value of variable z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_2200", "image_path": "images/img_1869.png", "question": "GHJK is a rhombus. Find m \\angle GKJ if m \\angle JLH = 4b-6 and m \\angle JKH = 2b+11. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "118.000", "choices": [31.0, 59.0, 90.0, 118.0]}
+{"prob_id": "prob_2202", "image_path": "images/img_425.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 7.5, 10.0, 12.5]}
+{"prob_id": "prob_2206", "image_path": "images/img_2129.png", "question": "In \\odot S, HJ = 22, LG = 18, m \\widehat IJ = 35, and m \\widehat LM = 30. Solve for the measure of HR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [9.0, 11.0, 22.0, 44.0]}
+{"prob_id": "prob_2209", "image_path": "images/img_48.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.402", "choices": [5.657, 6.364, 11.402, 12.728]}
+{"prob_id": "prob_2239", "image_path": "images/img_2307.png", "question": "In the triangle, what is the measure of \\angle X? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "72.000", "choices": [18.0, 72.0, 90.0, 120.0]}
+{"prob_id": "prob_2253", "image_path": "images/img_1772.png", "question": "Find AD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [5.4, 11.619, 16.0, 25.0]}
+{"prob_id": "prob_2254", "image_path": "images/img_2635.png", "question": "Use rhombus XYZW with m \\angle WYZ = 53, VW = 3, XV = 2a-2, and ZV = \\frac{5a+1}{4}. Find XZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.000", "choices": [2.0, 4.0, 8.0, 16.0]}
+{"prob_id": "prob_2259", "image_path": "images/img_2489.png", "question": "If a = 10\\sqrt{3}, find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.981", "choices": [10.0, 15.0, 17.32050807568877, 25.980762113533157]}
+{"prob_id": "prob_2264", "image_path": "images/img_1487.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.726", "choices": [7.1, 7.7, 21.9, 28.9]}
+{"prob_id": "prob_2273", "image_path": "images/img_499.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [20.0, 30.0, 40.0, 50.0]}
+{"prob_id": "prob_2281", "image_path": "images/img_973.png", "question": "In \\odot D, DE = EC, m \\widehat CF = 60, and DE \\perp EC. Find m \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [30.0, 45.0, 60.0, 90.0]}
+{"prob_id": "prob_2287", "image_path": "images/img_3110.png", "question": "Find AB if \\triangle ABC is an isosceles triangle with AB = BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [3.0, 4.0, 7.0, 11.0]}
+{"prob_id": "prob_2297", "image_path": "images/img_259.png", "question": "Find the diameter of \\odot P. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [5.0, 10.0, 20.0, 40.0]}
+{"prob_id": "prob_2325", "image_path": "images/img_3218.png", "question": "What is the value of e? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [32.0, 35.0, 58.0, 90.0]}
+{"prob_id": "prob_2330", "image_path": "images/img_907.png", "question": "Find RT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [6.667, 9.6, 14.667, 15.0]}
+{"prob_id": "prob_2331", "image_path": "images/img_1829.png", "question": "Use parallelogram NQRM to find QR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [13.0, 14.0, 15.0, 16.0]}
+{"prob_id": "prob_2349", "image_path": "images/img_3938.png", "question": "Find the value of variable d. Lines that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "124.000", "choices": [28.0, 60.0, 124.0, 184.0]}
+{"prob_id": "prob_2351", "image_path": "images/img_1749.png", "question": "Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "105.000", "choices": [75.0, 90.0, 105.0, 210.0]}
+{"prob_id": "prob_2363", "image_path": "images/img_1789.png", "question": "Find the length of RU if \\triangle RUW \\sim \\triangle STV, ST = 24, VS = 12, VT = 18 and UW = 21. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [20.571, 28.0, 36.0, 42.0]}
+{"prob_id": "prob_2366", "image_path": "images/img_1268.png", "question": "PT = 4x-6 and QT = 3x+4, find the length of TP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [6.8, 13.6, 34.0, 68.0]}
+{"prob_id": "prob_2385", "image_path": "images/img_810.png", "question": "For the pair of similar figures, the area of the blue figure is 36 yd^{2}, find the area of the green figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [9.0, 18.0, 72.0, 144.0]}
+{"prob_id": "prob_2386", "image_path": "images/img_1778.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [17.083, 17.899, 21.083, 22.0]}
+{"prob_id": "prob_2403", "image_path": "images/img_559.png", "question": "Quadrilateral ABCD is a rhombus. If m \\angle ABC = 2x-7 and m \\angle BCD = 2x+3, find m \\angle DAB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "95.000", "choices": [33.0, 50.0, 95.0, 120.0]}
+{"prob_id": "prob_2405", "image_path": "images/img_1136.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.000", "choices": [42.0, 48.0, 69.0, 90.0]}
+{"prob_id": "prob_2420", "image_path": "images/img_1723.png", "question": "What is the length of RS? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.773", "choices": [9.773, 18.0, 25.357, 35.097]}
+{"prob_id": "prob_2423", "image_path": "images/img_265.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "36.000", "choices": [30.0, 36.0, 45.0, 72.0]}
+{"prob_id": "prob_2427", "image_path": "images/img_1949.png", "question": "Find m \\angle C. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_2449", "image_path": "images/img_1795.png", "question": "In ABCD, m \\angle ABC = 79, BC = 62.4, and BD = 75. Find the measurement of \\angle DAB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "101.000", "choices": [11.0, 79.0, 101.0, 158.0]}
+{"prob_id": "prob_2450", "image_path": "images/img_1456.png", "question": "In \\odot R, SU = YW = 20, and m \\widehat YX = 45. Find m \\widehat SU. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [20.0, 30.0, 45.0, 90.0]}
+{"prob_id": "prob_2455", "image_path": "images/img_3223.png", "question": "Find the measure of \\angle Q. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "64.500", "choices": [2.5, 59.831, 64.5, 123.5]}
+{"prob_id": "prob_2457", "image_path": "images/img_3024.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "471.934", "choices": [332.3, 396.0, 471.9, 616.1]}
+{"prob_id": "prob_2460", "image_path": "images/img_1402.png", "question": "Quadrilateral WXZY is a rectangle. Find the measure of \\angle 7 if m \\angle 1 = 30. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 75.0, 120.0]}
+{"prob_id": "prob_2482", "image_path": "images/img_3526.png", "question": "\\triangle MHJ \\cong \\triangle PQJ. Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 4.0, 5.0, 6.0]}
+{"prob_id": "prob_2487", "image_path": "images/img_3561.png", "question": "What is the value of y? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.392", "choices": [2.133, 8.485, 10.392, 12.5]}
+{"prob_id": "prob_2495", "image_path": "images/img_3946.png", "question": "In \\odot R, m \\widehat MN = 120. Solve for m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 60.0, 120.0, 150.0]}
+{"prob_id": "prob_2504", "image_path": "images/img_3909.png", "question": "In \\triangle QRS, T, U, and B are midpoints. Find the perimeter of \\triangle UTB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "75.000", "choices": [75.0, 190.0, 200.0, 240.0]}
+{"prob_id": "prob_2505", "image_path": "images/img_3977.png", "question": "The polygons are similar. Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 4.8, 13.333, 16.0]}
+{"prob_id": "prob_2507", "image_path": "images/img_584.png", "question": "\\triangle JKL \\sim \\triangle WYZ. Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [44.0, 56.0, 65.0, 71.0]}
+{"prob_id": "prob_2550", "image_path": "images/img_3051.png", "question": "Find m \\angle W. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "76.000", "choices": [38.0, 38.0, 76.0, 152.0]}
+{"prob_id": "prob_2553", "image_path": "images/img_1105.png", "question": "\\triangle DFG \\sim \\triangle HKM. Determine the length of GD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [9.818, 13.75, 16.364, 25.0]}
+{"prob_id": "prob_2573", "image_path": "images/img_3860.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [0.75, 1.5, 3.0, 4.5]}
+{"prob_id": "prob_2580", "image_path": "images/img_1498.png", "question": "HJ is the perpendicular bisector of KL. HJ bisects \\angle KHL. Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [4.8, 12.0, 16.5, 48.0]}
+{"prob_id": "prob_2585", "image_path": "images/img_1969.png", "question": "What is the measure of \\angle 1 in the kite? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [22.5, 45.0, 67.5, 90.0]}
+{"prob_id": "prob_2602", "image_path": "images/img_953.png", "question": "\\triangle KLM is the midsegment triangle of \\triangle GHJ. What is the perimeter of \\triangle KLM? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.000", "choices": [17.0, 34.0, 39.0, 46.0]}
+{"prob_id": "prob_2627", "image_path": "images/img_3878.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [12.0, 14.0, 16.0, 18.0]}
+{"prob_id": "prob_2636", "image_path": "images/img_2084.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "39.961", "choices": [30.0, 35.0, 40.0, 45.0]}
+{"prob_id": "prob_2639", "image_path": "images/img_2131.png", "question": "ZA = 9. What is the length of ZC? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.500", "choices": [3.0, 4.5, 6.0, 13.5]}
+{"prob_id": "prob_2649", "image_path": "images/img_2152.png", "question": "Find the measure of \\widehat TC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "128.000", "choices": [52.0, 90.0, 128.0, 142.0]}
+{"prob_id": "prob_2656", "image_path": "images/img_1019.png", "question": "If CW = WF and ED = 30, what is AB? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [15.0, 30.0, 42.426, 60.0]}
+{"prob_id": "prob_2663", "image_path": "images/img_1253.png", "question": "m \\widehat AB = 176, and m \\widehat BC = 42. Solve for the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "21.000", "choices": [21.0, 71.0, 88.0, 109.0]}
+{"prob_id": "prob_2670", "image_path": "images/img_3928.png", "question": "Find the measure of \\angle S. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "135.000", "choices": [45.0, 49.091, 67.5, 135.0]}
+{"prob_id": "prob_2672", "image_path": "images/img_1238.png", "question": "Find y if P is between Q and R. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [1.0, 4.0, 5.25, 20.0]}
+{"prob_id": "prob_2673", "image_path": "images/img_2979.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "83.235", "choices": [48.0, 58.0, 68.0, 83.235]}
+{"prob_id": "prob_2675", "image_path": "images/img_3377.png", "question": "In \\triangle CDF, K is the centroid and DK = 16. Find GK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 8.0, 18.0, 24.0]}
+{"prob_id": "prob_2686", "image_path": "images/img_2217.png", "question": "Use rhombus ABCD with AY = 6, DY = 3r+3, and BY = \\frac{10r-4}{2}. Find m \\angle ADY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.745", "choices": [29.745, 60.255, 90.0, 120.51]}
+{"prob_id": "prob_2695", "image_path": "images/img_397.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [5.0, 36.0, 74.0, 115.0]}
+{"prob_id": "prob_2699", "image_path": "images/img_720.png", "question": "WXYZ is a kite. If m \\angle WXY = 13x+24, m \\angle WZY = 35, and m \\angle ZWX = 13x+14, find m \\angle ZYX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "105.000", "choices": [13.0, 24.0, 105.0, 210.0]}
+{"prob_id": "prob_2706", "image_path": "images/img_2491.png", "question": "a = 8, b = 15, and c = 17, find \\cos A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.882", "choices": [0.12, 0.22, 0.44, 0.88]}
+{"prob_id": "prob_2708", "image_path": "images/img_1480.png", "question": "Find WB if \\triangle RST \\sim \\triangle UVW, TA and WB are medians, TA = 8, RA = 3, WB = 3x-6, and UB = x+2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "96.000", "choices": [4.571, 36.0, 72.0, 96.0]}
+{"prob_id": "prob_2718", "image_path": "images/img_3613.png", "question": "What is x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 14.142, 17.321, 40.0]}
+{"prob_id": "prob_2726", "image_path": "images/img_2342.png", "question": "Find m \\angle PQM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "92.000", "choices": [44.0, 46.0, 88.0, 92.0]}
+{"prob_id": "prob_2736", "image_path": "images/img_256.png", "question": "m \\angle 3 = 43. Find the measure of \\angle 13. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.000", "choices": [33.0, 43.0, 53.0, 63.0]}
+{"prob_id": "prob_2747", "image_path": "images/img_3877.png", "question": "Find the area of the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "73.901", "choices": [64.0, 73.901, 110.851, 221.702]}
+{"prob_id": "prob_2782", "image_path": "images/img_1117.png", "question": "Find the value of variable y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.697", "choices": [8.485, 10.392, 13.416, 14.697]}
+{"prob_id": "prob_2802", "image_path": "images/img_3738.png", "question": "RS and RT are tangent to \\odot Q. Find RS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.100", "choices": [1.05, 2.1, 4.2, 286.74]}
+{"prob_id": "prob_2805", "image_path": "images/img_3407.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [36.0, 60.0, 80.0, 100.0]}
+{"prob_id": "prob_2808", "image_path": "images/img_1375.png", "question": "What is the measure of \\angle TSR? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "56.000", "choices": [34.0, 42.0, 56.0, 82.0]}
+{"prob_id": "prob_2811", "image_path": "images/img_3980.png", "question": "Find m \\widehat AD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [35.0, 65.0, 80.0, 145.0]}
+{"prob_id": "prob_2845", "image_path": "images/img_3402.png", "question": "Use parallelogram to find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "101.000", "choices": [79.0, 101.0, 180.0, 360.0]}
+{"prob_id": "prob_2871", "image_path": "images/img_1663.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "91.924", "choices": [65.0, 91.9, 112.6, 130.0]}
+{"prob_id": "prob_2875", "image_path": "images/img_826.png", "question": "Find the measure of \\angle A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "53.000", "choices": [46.0, 53.0, 81.0, 127.0]}
+{"prob_id": "prob_2878", "image_path": "images/img_978.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "74.000", "choices": [74.0, 81.456, 97.196, 112.0]}
+{"prob_id": "prob_2880", "image_path": "images/img_3687.png", "question": "For isosceles trapezoid ABCD, X and Y are midpoints of the legs. Find m \\angle CYX if m \\angle ADY = 78. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "78.000", "choices": [39.0, 51.0, 78.0, 102.0]}
+{"prob_id": "prob_2881", "image_path": "images/img_2311.png", "question": "\\triangle BTW \\sim \\triangle ETC. Find m \\angle TEC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "79.000", "choices": [34.0, 79.0, 101.0, 146.0]}
+{"prob_id": "prob_2887", "image_path": "images/img_1898.png", "question": "What is m \\angle APD? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 90.0, 120.0, 150.0]}
+{"prob_id": "prob_2898", "image_path": "images/img_1928.png", "question": "Find DF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.500", "choices": [1.15, 1.25, 2.3, 2.5]}
+{"prob_id": "prob_2899", "image_path": "images/img_2490.png", "question": "Find the measure of QR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.400", "choices": [3.8, 4.0, 4.1, 4.4]}
+{"prob_id": "prob_2908", "image_path": "images/img_2994.png", "question": "Find m \\angle DBC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "135.000", "choices": [45.0, 90.0, 135.0, 180.0]}
+{"prob_id": "prob_2920", "image_path": "images/img_167.png", "question": "Use parallelogram to find a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [7.0, 21.0, 27.0, 28.0]}
+{"prob_id": "prob_2927", "image_path": "images/img_56.png", "question": "What is the value of variable w? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "250.000", "choices": [110.0, 140.0, 210.0, 250.0]}
+{"prob_id": "prob_2934", "image_path": "images/img_456.png", "question": "Find h. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.849", "choices": [10.5, 14.849242404917499, 18.186533479473212, 21.0]}
+{"prob_id": "prob_2938", "image_path": "images/img_135.png", "question": "Find the area of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.383", "choices": [3.9, 11.7, 23.4, 46.8]}
+{"prob_id": "prob_2945", "image_path": "images/img_2709.png", "question": "Find the measure of \\angle 2 for the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.000", "choices": [32.0, 38.0, 70.0, 110.0]}
+{"prob_id": "prob_2951", "image_path": "images/img_3451.png", "question": "Find the area of sector LKJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.425", "choices": [5.188, 10.053, 80.425, 723.823]}
+{"prob_id": "prob_2953", "image_path": "images/img_3161.png", "question": "Parallelogram MNPQ is shown. Solve for m \\angle M. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "102.000", "choices": [78.0, 90.0, 102.0, 246.0]}
+{"prob_id": "prob_2963", "image_path": "images/img_696.png", "question": "Quadrilateral KLMN is a rectangle. If PL = x^{2}-1 and PM = 4x+11, find KP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [17.5, 35.0, 51.98, 70.0]}
+{"prob_id": "prob_2964", "image_path": "images/img_732.png", "question": "Find x so that line m \\parallel line n. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [9.0, 10.0, 11.0, 12.0]}
+{"prob_id": "prob_2970", "image_path": "images/img_2211.png", "question": "JH, JP, and PH are midsegments of \\triangle KLM. Find m \\angle JPM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "123.000", "choices": [28.5, 57.0, 66.0, 123.0]}
+{"prob_id": "prob_2976", "image_path": "images/img_1313.png", "question": "Find the area of the regular polygon. Assume that the triangle is equilateral. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.785", "choices": [20.785, 32.0, 50.265, 83.138]}
+{"prob_id": "prob_2989", "image_path": "images/img_2723.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [7.5, 13.125, 18.75, 30.0]}
+{"prob_id": "prob_2996", "image_path": "images/img_1183.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "452.389", "choices": [113.097, 226.195, 437.31, 452.389]}
+{"prob_id": "prob_2997", "image_path": "images/img_685.png", "question": "The segment is tangent to the circle. Find m \\angle J. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "53.130", "choices": [36.87, 38.66, 51.34, 53.13]}
+{"prob_id": "prob_3008", "image_path": "images/img_3215.png", "question": "Find the measure of \\angle DAC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [28.0, 62.0, 118.0, 152.0]}
+{"prob_id": "prob_3012", "image_path": "images/img_3802.png", "question": "Use \\odot P to find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "36.000", "choices": [18.0, 22.5, 30.0, 36.0]}
+{"prob_id": "prob_3016", "image_path": "images/img_2453.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "259.808", "choices": [86.6, 129.9, 150.0, 259.8]}
+{"prob_id": "prob_3024", "image_path": "images/img_415.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [20.0, 40.0, 80.0, 140.0]}
+{"prob_id": "prob_3028", "image_path": "images/img_398.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "58.000", "choices": [25.0, 37.0, 39.0, 58.0]}
+{"prob_id": "prob_3032", "image_path": "images/img_2740.png", "question": "Express the ratio of \\sin J. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.923", "choices": [0.385, 0.923, 1.083, 2.4]}
+{"prob_id": "prob_3036", "image_path": "images/img_912.png", "question": "What is h? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.238", "choices": [4.0, 4.619, 6.928, 9.238]}
+{"prob_id": "prob_3037", "image_path": "images/img_2445.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.809", "choices": [18.8, 23.2, 25.9, 44.0]}
+{"prob_id": "prob_3048", "image_path": "images/img_2275.png", "question": "Find m \\widehat CD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [40.0, 50.0, 80.0, 140.0]}
+{"prob_id": "prob_3050", "image_path": "images/img_2580.png", "question": "If AB = DA = ED = CF, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.625", "choices": [0.5, 0.559, 0.571, 0.625]}
+{"prob_id": "prob_3074", "image_path": "images/img_2531.png", "question": "If PR \\parallel KL, KN = 9, LN = 16, and PM = 2 KP, find ML. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [15.0, 16.0, 20.0, 24.0]}
+{"prob_id": "prob_3092", "image_path": "images/img_1756.png", "question": "m \\angle 19 = 100+20x, m \\angle 20 = 20x. Find the measure of \\angle 20. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [20.0, 40.0, 60.0, 80.0]}
+{"prob_id": "prob_3093", "image_path": "images/img_104.png", "question": "Each pair of polygons is similar. Find AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.600", "choices": [7.0, 7.6, 12.0, 19.0]}
+{"prob_id": "prob_3107", "image_path": "images/img_2841.png", "question": "Find the perimeter of \\triangle DEF, if \\triangle DEF \\sim \\triangle CBF, perimeter of \\triangle CBF = 27, DF = 6, and FC = 8. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.250", "choices": [16.0, 17.25, 20.25, 27.0]}
+{"prob_id": "prob_3144", "image_path": "images/img_2803.png", "question": "Find ML. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "39.000", "choices": [24.0, 32.726, 36.0, 39.0]}
+{"prob_id": "prob_3152", "image_path": "images/img_308.png", "question": "JKLM is a rhombus. If CK = 8, JK = 10 and \\angle JKM = 37. What is m \\angle MKL? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.000", "choices": [37.0, 53.0, 74.0, 106.0]}
+{"prob_id": "prob_3182", "image_path": "images/img_3879.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "45.000", "choices": [30.0, 45.0, 60.0, 90.0]}
+{"prob_id": "prob_3187", "image_path": "images/img_1811.png", "question": "\\triangle ABC \\sim \\triangle XYZ. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.500", "choices": [1.5, 2.667, 3.0, 6.0]}
+{"prob_id": "prob_3237", "image_path": "images/img_2639.png", "question": "In \\triangle ABC, AF = 9, and GE = 2.4. Find the length of AG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [3.6, 6.0, 7.2, 27.0]}
+{"prob_id": "prob_3247", "image_path": "images/img_2451.png", "question": "What is the length of GC? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "21.213", "choices": [15.0, 17.321, 21.213, 30.0]}
+{"prob_id": "prob_3255", "image_path": "images/img_3278.png", "question": "Find the exact area of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "157.080", "choices": [20.0, 44.429, 157.08, 628.319]}
+{"prob_id": "prob_3269", "image_path": "images/img_2474.png", "question": "In \\odot Y the radius is 34, AB = 60, and m \\widehat AC = 71. Find the length of YD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [16.0, 18.0, 30.0, 57.541]}
+{"prob_id": "prob_3272", "image_path": "images/img_3759.png", "question": "Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.946", "choices": [8.319, 9.239, 17.96, 19.946]}
+{"prob_id": "prob_3290", "image_path": "images/img_874.png", "question": "\\odot A and \\odot B are congruent. CD is a chord of both circles. If a radius = 13 ft and CD = 10 ft, how long is AB? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [10.0, 12.0, 15.199, 24.0]}
+{"prob_id": "prob_3371", "image_path": "images/img_1989.png", "question": "Find the measure of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [25.0, 30.0, 35.0, 40.0]}
+{"prob_id": "prob_3384", "image_path": "images/img_3967.png", "question": "If QR = 2, XW = 12, QW = 15, and ST = 5, find QS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [4.167, 7.5, 8.0, 10.0]}
+{"prob_id": "prob_3399", "image_path": "images/img_1653.png", "question": "What must the value of x if \\triangle EFG \\cong \\triangle EHG? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.500", "choices": [4.25, 4.667, 5.5, 24.0]}
+{"prob_id": "prob_3400", "image_path": "images/img_215.png", "question": "Given that \\angle PQR \\cong \\angle XYZ. Determine m \\angle Z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [35.0, 55.0, 70.0, 90.0]}
+{"prob_id": "prob_3421", "image_path": "images/img_1242.png", "question": "AD and BE are diameters. Find m \\angle AQE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "145.000", "choices": [35.0, 55.0, 125.0, 145.0]}
+{"prob_id": "prob_3424", "image_path": "images/img_845.png", "question": "TUWY is a rhombus. What is the length of UW? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.4, 3.0, 4.243, 6.0]}
+{"prob_id": "prob_3427", "image_path": "images/img_853.png", "question": "Assume that the segment is tangent, find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.644", "choices": [3.7416573867739413, 4.123105625617661, 9.643650760992955, 22.02271554554524]}
+{"prob_id": "prob_3428", "image_path": "images/img_3770.png", "question": "What is PQ? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [1.333, 12.0, 19.238, 21.238]}
+{"prob_id": "prob_3450", "image_path": "images/img_2677.png", "question": "What is the length of \\widehat AB? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.883", "choices": [10.973, 20.883, 21.945, 41.766]}
+{"prob_id": "prob_3455", "image_path": "images/img_3355.png", "question": "The area of \\parallelogram ABCD is 150 square meters. The area of \\parallelogram FGHJ is 54 square meters. If \\parallelogram ABCD \\sim \\parallelogram FGHJ, find the scale factor of \\parallelogram FGHJ to \\parallelogram ABCD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.600", "choices": [0.36, 0.6, 1.6666666666666667, 2.7777777777777777]}
+{"prob_id": "prob_3459", "image_path": "images/img_3382.png", "question": "Find the exact radius of circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.349", "choices": [9.192, 12.349, 24.698, 77.592]}
+{"prob_id": "prob_3462", "image_path": "images/img_2951.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "135.000", "choices": [45.0, 90.0, 135.0, 180.0]}
+{"prob_id": "prob_3464", "image_path": "images/img_2355.png", "question": "JKMN is a rectangle. If m \\angle NKM = x^{2}+4 and m \\angle KNM = x+30, find m \\angle QJK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.000", "choices": [37.0, 53.0, 74.0, 106.0]}
+{"prob_id": "prob_3468", "image_path": "images/img_3311.png", "question": "\\triangle KLN and \\triangle LMN are isosceles and m \\angle JKN = 130. Find the measure of \\angle J. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "106.000", "choices": [105.0, 106.0, 108.0, 111.0]}
+{"prob_id": "prob_3470", "image_path": "images/img_2925.png", "question": "m \\angle 1 = 94. Find the measure of \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "94.000", "choices": [76.0, 86.0, 94.0, 96.0]}
+{"prob_id": "prob_3475", "image_path": "images/img_1575.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.500", "choices": [5.5, 7.778174593052023, 11.0, 15.556349186104047]}
+{"prob_id": "prob_3481", "image_path": "images/img_3042.png", "question": "Find x so that line l \\parallel line m. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.000", "choices": [14.4, 19.0, 41.5, 67.0]}
+{"prob_id": "prob_3485", "image_path": "images/img_3209.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.000", "choices": [-2.0, 0.0, 3.0, 6.0]}
+{"prob_id": "prob_3497", "image_path": "images/img_935.png", "question": "In quadrilateral PQRS, PQ = 721, QR = 547, RS = 593, PS = 756, and m \\angle P = 58. Find m \\angle PSQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "58.552", "choices": [40.333, 58.552, 77.793, 122.0]}
+{"prob_id": "prob_3509", "image_path": "images/img_3049.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "61.726", "choices": [61.7, 71.2, 90.0, 118.3]}
+{"prob_id": "prob_3515", "image_path": "images/img_3618.png", "question": "Find the measure of \\angle 6. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "86.000", "choices": [24.0, 74.0, 86.0, 104.0]}
+{"prob_id": "prob_3516", "image_path": "images/img_2596.png", "question": "Solve for BA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "41.994", "choices": [11.885, 36.595, 41.994, 44.981]}
+{"prob_id": "prob_3517", "image_path": "images/img_848.png", "question": "Use parallelogram ABCD to find m \\angle BCD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [15.0, 65.0, 80.0, 115.0]}
+{"prob_id": "prob_3529", "image_path": "images/img_343.png", "question": "What is the measure of \\angle DEF? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "67.500", "choices": [67.5, 112.5, 202.5, 292.5]}
+{"prob_id": "prob_3569", "image_path": "images/img_3805.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_3584", "image_path": "images/img_3493.png", "question": "Find the measure of \\angle P. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "81.512", "choices": [33.762, 56.847, 64.725, 81.512]}
+{"prob_id": "prob_3589", "image_path": "images/img_355.png", "question": "The square is circumscribed to the circle. Find the exact circumference of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "78.540", "choices": [39.269908169872416, 78.53981633974483, 94.24777960769379, 157.07963267948966]}
+{"prob_id": "prob_3593", "image_path": "images/img_3051.png", "question": "Find m \\angle Y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "68.000", "choices": [34.0, 68.0, 70.0, 136.0]}
+{"prob_id": "prob_3594", "image_path": "images/img_2384.png", "question": "Q is the incenter of \\triangle JKL. Find LP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.755", "choices": [15.0, 27.061, 30.755, 34.218]}
+{"prob_id": "prob_3604", "image_path": "images/img_369.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "21.000", "choices": [7.0, 15.0, 21.0, 75.0]}
+{"prob_id": "prob_3616", "image_path": "images/img_2386.png", "question": "Find the area of sector JHG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.686", "choices": [15.708, 40.841, 70.686, 183.783]}
+{"prob_id": "prob_3617", "image_path": "images/img_3050.png", "question": "m \\angle 9 = 141+x, m \\angle 10 = 25+x, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [7.0, 65.0, 97.0, 148.0]}
+{"prob_id": "prob_3624", "image_path": "images/img_3672.png", "question": "WXYZ is a parallelogram. What is the measure of \\angle W? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "99.000", "choices": [81.0, 90.0, 99.0, 126.0]}
+{"prob_id": "prob_3625", "image_path": "images/img_3495.png", "question": "Find the length of YW. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.250", "choices": [2.25, 6.806, 7.2, 11.25]}
+{"prob_id": "prob_3634", "image_path": "images/img_890.png", "question": "If AB = 60 and DE = 48, find FE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [24.0, 30.0, 54.991, 56.604]}
+{"prob_id": "prob_3648", "image_path": "images/img_1002.png", "question": "Find the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "116.000", "choices": [64.0, 81.0, 82.0, 116.0]}
+{"prob_id": "prob_3649", "image_path": "images/img_286.png", "question": "Find the circumference. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "47.752", "choices": [23.876, 47.752, 181.458, 1221.305]}
+{"prob_id": "prob_3654", "image_path": "images/img_1812.png", "question": "For the pair of similar figures, the area of the blue figure is 30 m^{2} and the green figure is 40 m^{2}, find the scale factor from the blue to the green figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.866", "choices": [0.75, 0.8660254037844386, 1.1547005383792517, 1.3333333333333333]}
+{"prob_id": "prob_3658", "image_path": "images/img_2862.png", "question": "Find the value of variable b. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "109.000", "choices": [11.0, 109.0, 150.0, 218.0]}
+{"prob_id": "prob_3665", "image_path": "images/img_3296.png", "question": "m \\angle WXY = m \\angle TXY. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [2.0, 4.0, 5.0, 10.0]}
+{"prob_id": "prob_3670", "image_path": "images/img_1828.png", "question": "Find the area of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "584.240", "choices": [73.0, 292.1, 584.2, 1168.5]}
+{"prob_id": "prob_3685", "image_path": "images/img_806.png", "question": "Determine the value of z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [2.364, 6.077, 7.0, 11.875]}
+{"prob_id": "prob_3689", "image_path": "images/img_1116.png", "question": "What is the measure of \\angle 1? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "123.000", "choices": [3.0, 63.0, 123.0, 126.0]}
+{"prob_id": "prob_3692", "image_path": "images/img_3746.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [1.8, 5.0, 46.0, 90.0]}
+{"prob_id": "prob_3700", "image_path": "images/img_401.png", "question": "In \\odot R, find m \\widehat TUV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "113.889", "choices": [54.071, 113.889, 125.929, 130.751]}
+{"prob_id": "prob_3706", "image_path": "images/img_1528.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "31.416", "choices": [21.991, 25.133, 31.416, 87.965]}
+{"prob_id": "prob_3711", "image_path": "images/img_3323.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.735", "choices": [13.735, 77.735, 100.531, 258.754]}
+{"prob_id": "prob_3716", "image_path": "images/img_2053.png", "question": "Find the area of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 2.236, 3.0, 6.0]}
+{"prob_id": "prob_3719", "image_path": "images/img_2675.png", "question": "Determine x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.000", "choices": [1.0, 4.0, 4.01, 57.342]}
+{"prob_id": "prob_3743", "image_path": "images/img_1593.png", "question": "BD bisects \\angle EBC. If m \\angle EBD = 4x-8 and m \\angle EBC = 5x+20, find m \\angle EBC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [40.0, 80.0, 140.0, 300.0]}
+{"prob_id": "prob_3748", "image_path": "images/img_3330.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "96.000", "choices": [28.0, 48.0, 96.0, 192.0]}
+{"prob_id": "prob_3755", "image_path": "images/img_2384.png", "question": "Q is the incenter of \\triangle JKL. Find JN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [20.0, 27.061, 30.755, 34.218]}
+{"prob_id": "prob_3766", "image_path": "images/img_1236.png", "question": "Solve for g. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.705", "choices": [2.898, 5.472, 6.437, 14.705]}
+{"prob_id": "prob_3770", "image_path": "images/img_3861.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [19.292, 22.0, 24.0, 28.0]}
+{"prob_id": "prob_3773", "image_path": "images/img_878.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.206", "choices": [21.1, 29.2, 32.7, 42.4]}
+{"prob_id": "prob_3776", "image_path": "images/img_752.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [5.162, 6.0, 7.292, 14.649]}
+{"prob_id": "prob_3786", "image_path": "images/img_1403.png", "question": "Use rhombus QRST. Find m \\angle TQS if m \\angle RST = 56. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [28.0, 56.0, 62.0, 124.0]}
+{"prob_id": "prob_3791", "image_path": "images/img_1947.png", "question": "Find the measure of PQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.600", "choices": [3.924, 4.8, 9.6, 12.4]}
+{"prob_id": "prob_3819", "image_path": "images/img_2238.png", "question": "What is the length of QN? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.450", "choices": [14.422, 14.697, 19.698, 32.45]}
+{"prob_id": "prob_3821", "image_path": "images/img_3821.png", "question": "Find the measure of \\angle CFD on \\odot F with diameter AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "123.000", "choices": [115.0, 119.0, 120.0, 123.0]}
+{"prob_id": "prob_3830", "image_path": "images/img_1084.png", "question": "Find the measure of \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "42.000", "choices": [28.0, 32.0, 38.0, 42.0]}
+{"prob_id": "prob_3831", "image_path": "images/img_2208.png", "question": "Find ST. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 10.0, 12.0, 16.0]}
+{"prob_id": "prob_3846", "image_path": "images/img_2271.png", "question": "Use \\triangle ABC, where L, M, and N are midpoints of the sides. If AC = 20, what is LN? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [10.0, 20.0, 40.0, 60.0]}
+{"prob_id": "prob_3848", "image_path": "images/img_3975.png", "question": "Express the ratio of \\sin C. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.600", "choices": [0.6, 0.75, 0.8, 1.33]}
+{"prob_id": "prob_3852", "image_path": "images/img_2986.png", "question": "Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [2.714, 6.0, 11.5, 14.538]}
+{"prob_id": "prob_3855", "image_path": "images/img_2462.png", "question": "Find the area of quadrilateral XYZW if XZ = 39, HW = 20, and YG = 21. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "799.500", "choices": [390.0, 409.5, 799.5, 1599.0]}
+{"prob_id": "prob_3883", "image_path": "images/img_3954.png", "question": "In \\odot B, m \\angle LBM = 3x and m \\angle LBQ = 4x+61. What is the measure of \\widehat LK? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "39.000", "choices": [39.0, 51.0, 77.571, 129.0]}
+{"prob_id": "prob_3888", "image_path": "images/img_3365.png", "question": "What is the value of \\tan Y? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.667", "choices": [0.555, 0.667, 0.832, 1.5]}
+{"prob_id": "prob_3890", "image_path": "images/img_2949.png", "question": "Find the measure of \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "45.000", "choices": [40.0, 45.0, 50.0, 95.0]}
+{"prob_id": "prob_3906", "image_path": "images/img_1262.png", "question": "m \\angle 13 = 2x+94, m \\angle 14 = 7x+49, find the measurement of \\angle 14. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "112.000", "choices": [77.778, 102.222, 112.0, 224.0]}
+{"prob_id": "prob_3915", "image_path": "images/img_3832.png", "question": "In \\triangle STR, H is the centroid, EH = 6, DH = 4, and SM = 24. What is HR? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [8.0, 12.0, 16.0, 18.0]}
+{"prob_id": "prob_3924", "image_path": "images/img_379.png", "question": "Determine the length of XY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.689", "choices": [11.0, 12.689, 24.62, 26.589]}
+{"prob_id": "prob_3931", "image_path": "images/img_2383.png", "question": "Given line a \\parallel line b, find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "79.000", "choices": [47.0, 54.0, 79.0, 101.0]}
+{"prob_id": "prob_3940", "image_path": "images/img_479.png", "question": "Find the area of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "46.765", "choices": [15.588, 46.765, 72.0, 144.0]}
+{"prob_id": "prob_3945", "image_path": "images/img_877.png", "question": "Find the perimeter of triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.324", "choices": [48.0, 51.324, 52.0, 55.324]}
+{"prob_id": "prob_3952", "image_path": "images/img_2039.png", "question": "In \\odot J, GH = 9 and KL = 4x+1. Find GR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.500", "choices": [4.5, 6.727, 9.0, 13.454]}
+{"prob_id": "prob_3964", "image_path": "images/img_3139.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_3967", "image_path": "images/img_1844.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.214", "choices": [8.7, 14.6, 22.2, 37.2]}
+{"prob_id": "prob_3975", "image_path": "images/img_345.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.798", "choices": [2.449489742783178, 2.449489742783178, 4.0, 9.797958971132712]}
+{"prob_id": "prob_3992", "image_path": "images/img_3740.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.191", "choices": [19.5, 30.2, 60.4, 120.8]}
+{"prob_id": "prob_4007", "image_path": "images/img_3241.png", "question": "What is the perimeter of the kite? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.530", "choices": [23.324, 30.53, 35.956, 37.736]}
+{"prob_id": "prob_4021", "image_path": "images/img_1285.png", "question": "Assume the segments that appear to be tangent are tangent. Find JM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [11.0, 22.0, 31.113, 44.0]}
+{"prob_id": "prob_4022", "image_path": "images/img_349.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [10.0, 15.0, 26.25, 27.857]}
+{"prob_id": "prob_4025", "image_path": "images/img_2052.png", "question": "If FG = 59, what is EF? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "102.000", "choices": [25.0, 34.0, 37.5, 102.0]}
+{"prob_id": "prob_4029", "image_path": "images/img_2064.png", "question": "Find the value of variable x in the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [9.375, 15.0, 18.562, 30.0]}
+{"prob_id": "prob_4040", "image_path": "images/img_626.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.667", "choices": [1.3333333333333333, 4.333333333333333, 6.0, 8.666666666666666]}
+{"prob_id": "prob_4044", "image_path": "images/img_9.png", "question": "In rhombus ABCD, m \\angle DAB = 2 m \\angle ADC and CB = 6. Find m \\angle ADB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_4046", "image_path": "images/img_3682.png", "question": "m \\angle 2 = 2x, m \\angle 3 = x. Find m \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 45.0, 60.0, 90.0]}
+{"prob_id": "prob_4052", "image_path": "images/img_1399.png", "question": "Determine m \\angle U. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "101.000", "choices": [32.0, 47.0, 79.0, 101.0]}
+{"prob_id": "prob_4062", "image_path": "images/img_1733.png", "question": "Find the measure of \\angle ADB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "42.379", "choices": [23.991, 26.0, 42.379, 79.901]}
+{"prob_id": "prob_4068", "image_path": "images/img_198.png", "question": "VWXY is a rhombus. Find m \\angle ZWX if m \\angle WVY = 4b+10 and m \\angle XZW = 10b-5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "66.000", "choices": [24.0, 45.0, 66.0, 90.0]}
+{"prob_id": "prob_4084", "image_path": "images/img_1665.png", "question": "EFGH is a parallelogram. Find HF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [9.0, 12.0, 18.0, 24.0]}
+{"prob_id": "prob_4088", "image_path": "images/img_1103.png", "question": "Solve for m \\angle RST. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_4097", "image_path": "images/img_2946.png", "question": "Find f. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.400", "choices": [4.286, 8.4, 29.4, 52.5]}
+{"prob_id": "prob_4100", "image_path": "images/img_2418.png", "question": "\\parallelogram ABCD \\sim \\parallelogram EFGH. Find the perimeter of \\parallelogram EFGH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [10.0, 12.0, 14.0, 18.0]}
+{"prob_id": "prob_4108", "image_path": "images/img_1890.png", "question": "Find the value of the variable x for the quadrilateral. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_4133", "image_path": "images/img_2817.png", "question": "JH is a midsegment of \\triangle KLM. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [5.0, 10.0, 11.0, 22.0]}
+{"prob_id": "prob_4138", "image_path": "images/img_1091.png", "question": "BD bisects \\angle ABC. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [6.5, 10.0, 11.5, 15.125]}
+{"prob_id": "prob_4146", "image_path": "images/img_3784.png", "question": "XY and XZ are midsegments of \\triangle RST. Find SZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [3.5, 6.5, 7.0, 13.0]}
+{"prob_id": "prob_4151", "image_path": "images/img_2071.png", "question": "What is m \\widehat EF? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "130.000", "choices": [125.0, 130.0, 235.0, 245.0]}
+{"prob_id": "prob_4153", "image_path": "images/img_3051.png", "question": "Find m \\angle Z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "143.000", "choices": [34.0, 68.0, 136.0, 143.0]}
+{"prob_id": "prob_4166", "image_path": "images/img_3752.png", "question": "JH is tangent to \\odot G at J. Find the length of GH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.000", "choices": [8.0, 8.667, 12.0, 13.0]}
+{"prob_id": "prob_4167", "image_path": "images/img_2282.png", "question": "What is GH? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.299", "choices": [10.299, 11.583, 15.858, 19.304]}
+{"prob_id": "prob_4192", "image_path": "images/img_1990.png", "question": "What is the value of k? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.364", "choices": [6.364, 9.0, 9.363, 12.728]}
+{"prob_id": "prob_4199", "image_path": "images/img_726.png", "question": "Given \\triangle EFG \\cong \\triangle GHE. Find m \\angle FEG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [34.0, 36.0, 108.0, 110.0]}
+{"prob_id": "prob_4208", "image_path": "images/img_2046.png", "question": "Find the exact circumference of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "53.407", "choices": [53.407, 66.643, 106.814, 226.98]}
+{"prob_id": "prob_4226", "image_path": "images/img_1142.png", "question": "AB \\parallel CD \\parallel EF. Find AE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.600", "choices": [10.0, 10.3, 20.0, 20.6]}
+{"prob_id": "prob_4264", "image_path": "images/img_2999.png", "question": "If ED = x+4 and DB = 3x-8, find ED. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [8.0, 10.0, 20.0, 40.0]}
+{"prob_id": "prob_4265", "image_path": "images/img_2355.png", "question": "JKMN is a rectangle. If NQ = 5x-3 and QM = 4x+6, find NK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "84.000", "choices": [21.0, 42.0, 59.397, 84.0]}
+{"prob_id": "prob_4272", "image_path": "images/img_2512.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [6.103, 7.0, 7.433, 14.0]}
+{"prob_id": "prob_4278", "image_path": "images/img_3234.png", "question": "In rhombus RSTV, m \\angle TZV = 8n+18, and m \\angle SRV = 9n+1. Find the measure of \\angle TVS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "49.000", "choices": [41.0, 49.0, 82.0, 90.0]}
+{"prob_id": "prob_4293", "image_path": "images/img_3972.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [15.0, 27.5, 41.0, 80.0]}
+{"prob_id": "prob_4299", "image_path": "images/img_533.png", "question": "What is the area of the shaded region? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.708", "choices": [5.498, 9.425, 15.708, 25.133]}
+{"prob_id": "prob_4300", "image_path": "images/img_2985.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.000", "choices": [17.0, 36.0, 74.0, 112.0]}
+{"prob_id": "prob_4302", "image_path": "images/img_1366.png", "question": "GD and FH are diameters of circle C. Solve for m \\widehat DH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [65.0, 80.0, 100.0, 145.0]}
+{"prob_id": "prob_4314", "image_path": "images/img_1867.png", "question": "The radius of \\odot P is 5 and PR = 3. Find the measure of \\widehat SQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "106.260", "choices": [53.13, 61.928, 73.74, 106.26]}
+{"prob_id": "prob_4333", "image_path": "images/img_257.png", "question": "Trapezoid MNPQ has an area of 360 square feet. Find the length of MN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [14.0, 16.0, 18.0, 20.0]}
+{"prob_id": "prob_4335", "image_path": "images/img_963.png", "question": "Find m \\widehat QS if m \\widehat QTS = 238. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "122.000", "choices": [61.0, 122.0, 238.0, 506.774]}
+{"prob_id": "prob_4360", "image_path": "images/img_2153.png", "question": "For trapezoid LMNO, P and Q are midpoints of the legs. Determine m \\angle PQN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "84.000", "choices": [36.0, 84.0, 96.0, 144.0]}
+{"prob_id": "prob_4366", "image_path": "images/img_329.png", "question": "Find m \\angle A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 90.0, 180.0, 360.0]}
+{"prob_id": "prob_4372", "image_path": "images/img_98.png", "question": "m \\angle 11 = x-4, m \\angle 12 = 2x-5, find the measure of \\angle 11. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "59.000", "choices": [43.5, 59.0, 61.0, 121.0]}
+{"prob_id": "prob_4385", "image_path": "images/img_2465.png", "question": "What is AB? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [11.0, 15.0, 18.601, 23.558]}
+{"prob_id": "prob_4391", "image_path": "images/img_1758.png", "question": "AB = DE = 8, and CD = 5. Find CF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 2.5, 3.0, 4.0]}
+{"prob_id": "prob_4395", "image_path": "images/img_2809.png", "question": "AE \\parallel BF \\parallel CG \\parallel DH, AB = BC = CD = 2, and EF = 2.25. What is EH? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.750", "choices": [2.25, 4.5, 6.0, 6.75]}
+{"prob_id": "prob_4397", "image_path": "images/img_962.png", "question": "Find the area of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [7.0, 9.093, 14.0, 28.0]}
+{"prob_id": "prob_4400", "image_path": "images/img_2943.png", "question": "Use rhombus JKLM to find m \\angle L. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "124.000", "choices": [28.0, 62.0, 76.0, 124.0]}
+{"prob_id": "prob_4414", "image_path": "images/img_1350.png", "question": "If XY = WX, YZ = WX, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [1.929, 3.0, 9.136, 10.941]}
+{"prob_id": "prob_4416", "image_path": "images/img_3886.png", "question": "Find BC if DF = 6 and FB = 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.211, 5.0, 6.325, 7.746]}
+{"prob_id": "prob_4421", "image_path": "images/img_973.png", "question": "In \\odot D, DE = EC, m \\widehat CF = 60, and DE \\perp EC. Find m \\widehat AF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_4432", "image_path": "images/img_541.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1200.000", "choices": [600.0, 900.0, 1200.0, 2400.0]}
+{"prob_id": "prob_4433", "image_path": "images/img_2325.png", "question": "Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "39.000", "choices": [39.0, 42.0, 48.0, 51.0]}
+{"prob_id": "prob_4434", "image_path": "images/img_129.png", "question": "What is BC? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.100", "choices": [16.2, 32.4, 35.1, 64.8]}
+{"prob_id": "prob_4442", "image_path": "images/img_442.png", "question": "Solve for a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "108.000", "choices": [103.5, 107.429, 108.0, 108.571]}
+{"prob_id": "prob_4453", "image_path": "images/img_1630.png", "question": "Find the exact value of DE, given AD = 12 and BD = 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.464", "choices": [3.4641016151377544, 4.898979485566356, 6.928203230275509, 9.797958971132712]}
+{"prob_id": "prob_4455", "image_path": "images/img_1930.png", "question": "If WXYZ is a kite, find WX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [10.0, 22.627, 24.739, 25.298]}
+{"prob_id": "prob_4457", "image_path": "images/img_2256.png", "question": "AD, BD, and CD are angle bisectors of \\triangle ABC. Suppose CD = 10 and EC = 8. Find the measure of \\angle BCA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "73.740", "choices": [36.87, 53.13, 73.74, 106.26]}
+{"prob_id": "prob_4458", "image_path": "images/img_2365.png", "question": "What is x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [2.217, 3.385, 6.0, 6.708]}
+{"prob_id": "prob_4463", "image_path": "images/img_1748.png", "question": "What is m \\widehat KJ? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "110.300", "choices": [110.3, 120.0, 129.246, 135.951]}
+{"prob_id": "prob_4487", "image_path": "images/img_2210.png", "question": "If ZY = 42, what is the length of ZX? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "54.000", "choices": [30.0, 42.0, 54.0, 96.0]}
+{"prob_id": "prob_4492", "image_path": "images/img_3052.png", "question": "Find the area of the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "286.000", "choices": [48.0, 143.0, 286.0, 572.0]}
+{"prob_id": "prob_4495", "image_path": "images/img_1504.png", "question": "If FK = 3x-1, KG = 4y+3, JK = 6y-2, and KH = 2x+3, find x so that the quadrilateral is a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 5.0, 10.0, 12.0]}
+{"prob_id": "prob_4504", "image_path": "images/img_378.png", "question": "Find m \\angle WYZ. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "67.380", "choices": [22.62, 24.624, 65.376, 67.38]}
+{"prob_id": "prob_4508", "image_path": "images/img_1306.png", "question": "Solve for the measure of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "73.000", "choices": [31.0, 73.0, 107.0, 109.0]}
+{"prob_id": "prob_4518", "image_path": "images/img_3773.png", "question": "m \\widehat QR = 40, and m \\widehat TS = 110. What is m \\angle 6? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [20.0, 55.0, 75.0, 105.0]}
+{"prob_id": "prob_4527", "image_path": "images/img_3001.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "82.867", "choices": [57.7, 82.9, 101.7, 108.0]}
+{"prob_id": "prob_4528", "image_path": "images/img_1346.png", "question": "What is m \\angle X? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "41.410", "choices": [36.87, 41.41, 48.59, 53.13]}
+{"prob_id": "prob_4566", "image_path": "images/img_2725.png", "question": "Determine the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "36.000", "choices": [36.0, 38.0, 52.0, 54.0]}
+{"prob_id": "prob_4573", "image_path": "images/img_3433.png", "question": "Find the length of \\widehat BDA shown in red. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "103.673", "choices": [18.85, 103.673, 131.947, 207.345]}
+{"prob_id": "prob_4574", "image_path": "images/img_2056.png", "question": "Polygon ABCD \\sim polygon AEFG, m \\angle AGF = 108, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26. Find DC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.400", "choices": [12.0, 14.0, 22.4, 26.0]}
+{"prob_id": "prob_4582", "image_path": "images/img_396.png", "question": "CA is tangent to the circle at A. If BF = 9 and CB = 3, find CA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [3.0, 6.0, 9.0, 10.392]}
+{"prob_id": "prob_4616", "image_path": "images/img_1877.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [25.0, 32.5, 33.75, 47.5]}
+{"prob_id": "prob_4618", "image_path": "images/img_37.png", "question": "PQ = RQ, m \\widehat PS = 45, and m \\widehat SR = 75. Find the measure of \\angle 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [22.5, 37.5, 52.5, 60.0]}
+{"prob_id": "prob_4619", "image_path": "images/img_1940.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.745", "choices": [5.385164807134504, 5.5677643628300215, 5.744562646538029, 5.916079783099616]}
+{"prob_id": "prob_4639", "image_path": "images/img_2475.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [1.75, 2.571, 3.111, 22.0]}
+{"prob_id": "prob_4651", "image_path": "images/img_2219.png", "question": "Determine x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.765", "choices": [7.0, 10.954, 13.0, 14.765]}
+{"prob_id": "prob_4661", "image_path": "images/img_2666.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.558", "choices": [17.643, 19.635, 34.558, 78.54]}
+{"prob_id": "prob_4663", "image_path": "images/img_3102.png", "question": "For what value of variable y must ABCD be a parallelogram? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [2.0, 5.0, 5.5, 6.0]}
+{"prob_id": "prob_4670", "image_path": "images/img_3951.png", "question": "PACE is a parallelogram and m \\angle PAC = 124. What is the measurement of \\angle CEP? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "124.000", "choices": [41.462, 48.538, 56.0, 124.0]}
+{"prob_id": "prob_4677", "image_path": "images/img_622.png", "question": "PX, PY, and PZ are the perpendicular bisectors of \\triangle RST. Find RS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "164.600", "choices": [46.7, 77.5, 82.3, 164.6]}
+{"prob_id": "prob_4684", "image_path": "images/img_2818.png", "question": "Find the length of MR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [4.0, 12.0, 16.0, 22.0]}
+{"prob_id": "prob_4700", "image_path": "images/img_3769.png", "question": "In \\odot O, m \\widehat AB = 40, m \\widehat BC = 100, and m \\widehat AD = m \\widehat DC. Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [20.0, 50.0, 55.0, 90.0]}
+{"prob_id": "prob_4714", "image_path": "images/img_3272.png", "question": "Find m \\widehat KM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "81.000", "choices": [51.0, 81.0, 99.0, 129.0]}
+{"prob_id": "prob_4715", "image_path": "images/img_1290.png", "question": "If FG = GJ = J H, and m \\angle F = 40, find m \\angle GJH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [20.0, 35.0, 70.0, 105.0]}
+{"prob_id": "prob_4716", "image_path": "images/img_2283.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.0, 4.0, 5.0, 6.0]}
+{"prob_id": "prob_4737", "image_path": "images/img_382.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.971", "choices": [6.0, 9.0, 12.0, 16.970562748477143]}
+{"prob_id": "prob_4745", "image_path": "images/img_1744.png", "question": "\\triangle WLJ \\sim \\triangle QBV. Find the scale factor of \\triangle WLJ to \\triangle QBV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [0.5, 0.625, 1.6, 2.0]}
+{"prob_id": "prob_4752", "image_path": "images/img_3247.png", "question": "Find the length of BA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.054", "choices": [6.428, 8.391, 11.918, 13.054]}
+{"prob_id": "prob_4769", "image_path": "images/img_3368.png", "question": "Determine the length of HE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 6.0, 10.0, 12.728]}
+{"prob_id": "prob_4774", "image_path": "images/img_3318.png", "question": "In rhombus LMPQ, m \\angle QLM = 2x^{2}-10, m \\angle QPM = 8x, and MP = 10. Find the perimeter of LMPQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [10.0, 40.0, 70.0, 140.0]}
+{"prob_id": "prob_4779", "image_path": "images/img_3325.png", "question": "If RU = 8, US = 14, TV = x-1, and VS = 17.5, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [3.0, 7.4, 11.0, 31.625]}
+{"prob_id": "prob_4783", "image_path": "images/img_263.png", "question": "Find m \\widehat DPA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "264.000", "choices": [168.0, 192.0, 264.0, 276.0]}
+{"prob_id": "prob_4789", "image_path": "images/img_1941.png", "question": "Find AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [12.0, 16.0, 24.0, 44.0]}
+{"prob_id": "prob_4793", "image_path": "images/img_2068.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [6.667, 10.0, 12.667, 12.857]}
+{"prob_id": "prob_4818", "image_path": "images/img_1746.png", "question": "What is the measure of \\angle K? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "165.000", "choices": [30.0, 139.149, 165.0, 201.818]}
+{"prob_id": "prob_4826", "image_path": "images/img_3309.png", "question": "Find m \\angle B. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [20.0, 30.0, 60.0, 80.0]}
+{"prob_id": "prob_4833", "image_path": "images/img_466.png", "question": "AB = DF. Find the length of FE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [9.0, 18.0, 20.125, 36.0]}
+{"prob_id": "prob_4847", "image_path": "images/img_3775.png", "question": "What is m \\widehat GE? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [120.0, 130.0, 150.0, 190.0]}
+{"prob_id": "prob_4850", "image_path": "images/img_3489.png", "question": "Find the measure of \\angle 6. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_4859", "image_path": "images/img_1921.png", "question": "The polygon circumscribes a circle. What is the perimeter of polygon? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.200", "choices": [14.2, 17.8, 21.8, 25.2]}
+{"prob_id": "prob_4862", "image_path": "images/img_2543.png", "question": "Determine the measurement of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "132.000", "choices": [46.0, 48.0, 94.0, 132.0]}
+{"prob_id": "prob_4900", "image_path": "images/img_2199.png", "question": "P is the centroid of \\triangle ABC. If SC = 6, find CP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [2.0, 4.0, 9.0, 18.0]}
+{"prob_id": "prob_4905", "image_path": "images/img_812.png", "question": "If JM = KL = JK, find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [1.0, 2.0, 3.0, 6.0]}
+{"prob_id": "prob_4909", "image_path": "images/img_1118.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [51.962, 60.0, 84.853, 120.0]}
+{"prob_id": "prob_4911", "image_path": "images/img_698.png", "question": "Find RS if PQ = 12, QR = 2, and TS = 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [2.0, 3.0, 4.0, 12.0]}
+{"prob_id": "prob_4929", "image_path": "images/img_2357.png", "question": "Find m \\angle N. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.000", "choices": [17.0, 54.0, 86.727, 108.0]}
+{"prob_id": "prob_4937", "image_path": "images/img_2376.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [40.0, 50.0, 60.0, 80.0]}
+{"prob_id": "prob_4939", "image_path": "images/img_1134.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "139.626", "choices": [15.359, 61.436, 139.626, 262.498]}
+{"prob_id": "prob_4951", "image_path": "images/img_1151.png", "question": "UV = 8. Find XY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.856", "choices": [4.0, 6.928, 13.856, 16.0]}
+{"prob_id": "prob_4954", "image_path": "images/img_1658.png", "question": "The circle is inscribed in polygon. Find the perimeter of polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "76.000", "choices": [70.0, 74.0, 76.0, 84.0]}
+{"prob_id": "prob_4968", "image_path": "images/img_734.png", "question": "Find x if AB = 6, AF = 8, BC = x, CD = y, DE = 2y-3, and FE = x+\\frac{10}{3}. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [5.459, 6.0, 10.0, 13.333]}
+{"prob_id": "prob_4969", "image_path": "images/img_482.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "142.000", "choices": [132.0, 138.0, 142.0, 148.0]}
+{"prob_id": "prob_4987", "image_path": "images/img_2397.png", "question": "Use parallelogram JKLM to find JK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [4.5, 6.0, 10.0, 12.0]}
+{"prob_id": "prob_4990", "image_path": "images/img_1225.png", "question": "Find the area of sector KLM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "26.180", "choices": [10.472, 15.355, 26.18, 52.36]}
+{"prob_id": "prob_4993", "image_path": "images/img_1124.png", "question": "Find the perimeter of \\triangle CPD if the perimeter of \\triangle BPA is 12, AP = \\sqrt{13}, and DP = 3\\sqrt{13}. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "36.000", "choices": [3.25, 4.0, 10.817, 36.0]}
+{"prob_id": "prob_4994", "image_path": "images/img_3849.png", "question": "Find ST. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.966", "choices": [8.485, 10.966, 12.5, 13.865]}
+{"prob_id": "prob_5003", "image_path": "images/img_3535.png", "question": "If AP = 1, find PD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.500", "choices": [0.333, 0.5, 0.667, 1.5]}
+{"prob_id": "prob_5014", "image_path": "images/img_762.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "727.461", "choices": [420.0, 594.0, 727.5, 840.0]}
+{"prob_id": "prob_5017", "image_path": "images/img_3694.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [10.0, 20.0, 30.0, 40.0]}
+{"prob_id": "prob_5030", "image_path": "images/img_693.png", "question": "Use parallelogram to find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 10.0, 15.0, 20.0]}
+{"prob_id": "prob_5033", "image_path": "images/img_1145.png", "question": "Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [40.0, 70.0, 90.0, 110.0]}
+{"prob_id": "prob_5034", "image_path": "images/img_3900.png", "question": "BD bisects \\angle ABF. If m \\angle ABF = 3x-8 and m \\angle ABD = x+14, find m \\angle ABD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [14.0, 36.0, 50.0, 54.0]}
+{"prob_id": "prob_5035", "image_path": "images/img_439.png", "question": "What is area of sector RST? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.524", "choices": [0.091, 0.524, 1.047, 2.618]}
+{"prob_id": "prob_5037", "image_path": "images/img_3906.png", "question": "Find DC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "53.443", "choices": [43.557, 48.247, 53.443, 107.446]}
+{"prob_id": "prob_5053", "image_path": "images/img_3869.png", "question": "Refer to rectangle QRTS. If QS = 3x+40 and RT = 16-3x, find QS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [14.0, 28.0, 32.666, 56.0]}
+{"prob_id": "prob_5055", "image_path": "images/img_2894.png", "question": "Quadrilateral ABCD is a rectangle. Find m \\angle DCA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [25.0, 34.158, 50.0, 65.0]}
+{"prob_id": "prob_5068", "image_path": "images/img_97.png", "question": "M is the midpoint of PQ. The diameter of \\odot O is 13 in, and RM = 4 in. Find PQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [4.0, 6.0, 9.0, 12.0]}
+{"prob_id": "prob_5077", "image_path": "images/img_1162.png", "question": "Find the perimeter of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.700", "choices": [12.7, 13.7, 16.7, 17.7]}
+{"prob_id": "prob_5084", "image_path": "images/img_2012.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.000", "choices": [13.5, 19.0, 23.5, 47.0]}
+{"prob_id": "prob_5103", "image_path": "images/img_737.png", "question": "PQ is the perpendicular bisector of ST. Find the value of n. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.500", "choices": [2.5, 7.0, 7.833, 8.5]}
+{"prob_id": "prob_5113", "image_path": "images/img_379.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.899", "choices": [24.62, 29.899, 65.0, 130.76]}
+{"prob_id": "prob_5121", "image_path": "images/img_2635.png", "question": "Use rhombus XYZW with m \\angle WYZ = 53, VW = 3, XV = 2a-2, and ZV = \\frac{5a+1}{4}. Find XW. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 10.0, 15.0, 20.0]}
+{"prob_id": "prob_5140", "image_path": "images/img_500.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [24.0, 56.0, 65.0, 115.0]}
+{"prob_id": "prob_5147", "image_path": "images/img_42.png", "question": "What is the measure of \\angle 10? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.000", "choices": [44.0, 46.0, 56.0, 90.0]}
+{"prob_id": "prob_5150", "image_path": "images/img_2938.png", "question": "Find the measure of \\angle TVU in rectangle STUV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.417", "choices": [35.417, 45.0, 45.325, 54.583]}
+{"prob_id": "prob_5152", "image_path": "images/img_1295.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [6.0, 9.0, 10.4, 12.7]}
+{"prob_id": "prob_5157", "image_path": "images/img_3687.png", "question": "For isosceles trapezoid ABCD, X and Y are midpoints of the legs. Find m \\angle XBC if m \\angle ADY = 78. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "102.000", "choices": [39.0, 51.0, 78.0, 102.0]}
+{"prob_id": "prob_5176", "image_path": "images/img_3731.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.600", "choices": [10.9, 13.6, 15.2, 26.6]}
+{"prob_id": "prob_5177", "image_path": "images/img_2014.png", "question": "Find the area of the shaded sector. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.036", "choices": [10.0, 27.4, 65.5, 78.5]}
+{"prob_id": "prob_5183", "image_path": "images/img_2498.png", "question": "Find PM in \\triangle JMP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "106.000", "choices": [45.0, 53.0, 90.0, 106.0]}
+{"prob_id": "prob_5211", "image_path": "images/img_2346.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.063", "choices": [7.1, 14.1, 22.1, 30.0]}
+{"prob_id": "prob_5247", "image_path": "images/img_1986.png", "question": "Find the value of variable c. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [30.0, 42.0, 50.0, 80.0]}
+{"prob_id": "prob_5257", "image_path": "images/img_927.png", "question": "Find PN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [9.0, 10.0, 11.0, 12.0]}
+{"prob_id": "prob_5289", "image_path": "images/img_1322.png", "question": "Find the length of XZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [18.0, 20.0, 24.0, 50.0]}
+{"prob_id": "prob_5291", "image_path": "images/img_2155.png", "question": "In \\odot A, m \\angle EAD = 42. Find m \\widehat BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "42.000", "choices": [42.0, 48.0, 52.0, 108.0]}
+{"prob_id": "prob_5303", "image_path": "images/img_284.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [5.0, 6.0, 7.0, 8.0]}
+{"prob_id": "prob_5314", "image_path": "images/img_3126.png", "question": "Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [10.0, 15.0, 20.0, 40.0]}
+{"prob_id": "prob_5317", "image_path": "images/img_2076.png", "question": "What is w? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "68.251", "choices": [68.251, 75.801, 91.841, 152.437]}
+{"prob_id": "prob_5319", "image_path": "images/img_1401.png", "question": "In \\odot K, MN = 16 and m \\widehat MN = 98. Find the measure of PK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [4.0, 6.0, 8.0, 15.199]}
+{"prob_id": "prob_5330", "image_path": "images/img_1545.png", "question": "Find m \\angle PQS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "42.000", "choices": [36.0, 42.0, 48.0, 63.0]}
+{"prob_id": "prob_5334", "image_path": "images/img_1733.png", "question": "Find CB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.190", "choices": [1.403, 2.876, 3.507, 7.19]}
+{"prob_id": "prob_5339", "image_path": "images/img_2930.png", "question": "What is the length of \\widehat QSR? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.944", "choices": [5.236, 10.472, 20.944, 26.18]}
+{"prob_id": "prob_5347", "image_path": "images/img_2444.png", "question": "Find m \\angle 9. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [60.0, 120.0, 240.0, 300.0]}
+{"prob_id": "prob_5367", "image_path": "images/img_3439.png", "question": "In the trapezoid, NP = 15. What is the length of KL? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [10.0, 20.0, 40.0, 65.0]}
+{"prob_id": "prob_5374", "image_path": "images/img_743.png", "question": "Chords AC and DF are equidistant from the center. If the radius of \\odot G is 26, find AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "48.000", "choices": [5.0, 10.0, 13.0, 48.0]}
+{"prob_id": "prob_5380", "image_path": "images/img_3603.png", "question": "Find b in the given parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [2.0, 8.0, 9.0, 10.0]}
+{"prob_id": "prob_5384", "image_path": "images/img_214.png", "question": "Find the area of the square. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [1.732, 3.142, 4.0, 16.0]}
+{"prob_id": "prob_5391", "image_path": "images/img_1915.png", "question": "Solve for a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "105.000", "choices": [41.0, 66.0, 91.0, 105.0]}
+{"prob_id": "prob_5397", "image_path": "images/img_2111.png", "question": "What is the perimeter of the figure? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [30.0, 35.292, 40.0, 44.0]}
+{"prob_id": "prob_5422", "image_path": "images/img_2641.png", "question": "Find the value of x for given rectangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.600", "choices": [6.6, 18.6, 24.6, 90.0]}
+{"prob_id": "prob_5424", "image_path": "images/img_2054.png", "question": "AD = 6 and DE = 7.5. What is the length of AC? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [6.0, 7.5, 12.0, 15.0]}
+{"prob_id": "prob_5427", "image_path": "images/img_170.png", "question": "BT / RT = ES / LS, find TR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.667", "choices": [1.714, 2.4, 4.286, 6.667]}
+{"prob_id": "prob_5437", "image_path": "images/img_362.png", "question": "KLMN is a rectangle. Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [5.0, 20.0, 50.0, 90.0]}
+{"prob_id": "prob_5438", "image_path": "images/img_977.png", "question": "Find the measure of \\angle 5 if PQ \\perp QR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "68.000", "choices": [12.0, 22.0, 34.0, 68.0]}
+{"prob_id": "prob_5445", "image_path": "images/img_3617.png", "question": "Find m \\angle AGE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [60.0, 120.0, 210.0, 330.0]}
+{"prob_id": "prob_5447", "image_path": "images/img_2917.png", "question": "Find the area of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 8.0, 16.0, 32.0]}
+{"prob_id": "prob_5470", "image_path": "images/img_3732.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.785", "choices": [10.392304845413264, 20.784609690826528, 25.455844122715714, 36.0]}
+{"prob_id": "prob_5475", "image_path": "images/img_1625.png", "question": "What is the length of diameter? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [3.0, 6.0, 12.0, 18.85]}
+{"prob_id": "prob_5482", "image_path": "images/img_101.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.392", "choices": [3.4641016151377544, 5.196152422706632, 8.660254037844386, 10.392304845413264]}
+{"prob_id": "prob_5484", "image_path": "images/img_219.png", "question": "Find AC, if \\triangle ABC \\sim \\triangle CBD, AD = 5, CD = 12, and BC = 31.2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.000", "choices": [10.909, 13.0, 28.8, 33.428]}
+{"prob_id": "prob_5489", "image_path": "images/img_1801.png", "question": "Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [10.0, 35.0, 55.0, 70.0]}
+{"prob_id": "prob_5494", "image_path": "images/img_2827.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 10.0, 15.0, 20.0]}
+{"prob_id": "prob_5500", "image_path": "images/img_622.png", "question": "PX, PY, and PZ are the perpendicular bisectors of \\triangle RST. Find PY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.307", "choices": [16.307, 46.7, 82.3, 83.9]}
+{"prob_id": "prob_5502", "image_path": "images/img_804.png", "question": "Find x in the given parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [38.0, 75.0, 76.0, 109.0]}
+{"prob_id": "prob_5538", "image_path": "images/img_1918.png", "question": "Find m \\angle Q. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "121.000", "choices": [50.0, 58.0, 60.0, 121.0]}
+{"prob_id": "prob_5548", "image_path": "images/img_523.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 3.0, 4.0, 6.0]}
+{"prob_id": "prob_5560", "image_path": "images/img_1646.png", "question": "Find VW. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [6.0, 8.0, 10.0, 12.0]}
+{"prob_id": "prob_5563", "image_path": "images/img_1485.png", "question": "Find the value of variable q in the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [7.167, 8.0, 9.0, 11.124]}
+{"prob_id": "prob_5591", "image_path": "images/img_3679.png", "question": "Find m \\angle 5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [32.5, 65.0, 115.0, 230.0]}
+{"prob_id": "prob_5605", "image_path": "images/img_2298.png", "question": "Find x so that line r \\parallel line s. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [30.0, 31.667, 40.0, 115.0]}
+{"prob_id": "prob_5640", "image_path": "images/img_3176.png", "question": "Find MN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "61.794", "choices": [31.872, 45.705, 53.364, 61.794]}
+{"prob_id": "prob_5642", "image_path": "images/img_3550.png", "question": "Find the area of the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.426", "choices": [16.0, 18.475, 27.713, 55.426]}
+{"prob_id": "prob_5644", "image_path": "images/img_2534.png", "question": "DB \\perp AC and BA = BC. Find CD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [12.0, 13.0, 20.0, 26.0]}
+{"prob_id": "prob_5658", "image_path": "images/img_1195.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.165", "choices": [6.0, 9.16515138991168, 10.0, 10.770329614269007]}
+{"prob_id": "prob_5662", "image_path": "images/img_2676.png", "question": "The diameters of \\odot L and \\odot M are 20 and 13 units, respectively, and QR = 4. Determine the length of RM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.500", "choices": [2.5, 6.0, 6.5, 20.0]}
+{"prob_id": "prob_5665", "image_path": "images/img_862.png", "question": "For rhombus ABCD, find AB, given that m \\angle DEC = 30y, m \\angle EDC = 8y+15, AB = 2x+8, and BC = 4x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [16.0, 22.627, 32.0, 82.0]}
+{"prob_id": "prob_5678", "image_path": "images/img_3845.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "216.000", "choices": [156.0, 216.0, 234.0, 324.0]}
+{"prob_id": "prob_5682", "image_path": "images/img_2395.png", "question": "Find m \\angle EDB if m \\widehat FE = 118, m \\widehat AB = 108, m \\angle EGB = 52, and m \\angle EFB = 30. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [15.0, 52.0, 108.0, 118.0]}
+{"prob_id": "prob_5685", "image_path": "images/img_3034.png", "question": "Use parallelogram WXYZ to find WX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [11.665, 24.0, 28.0, 203.0]}
+{"prob_id": "prob_5712", "image_path": "images/img_3655.png", "question": "What is x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [4.364, 11.25, 15.04, 16.0]}
+{"prob_id": "prob_5720", "image_path": "images/img_751.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [60.0, 80.0, 100.0, 120.0]}
+{"prob_id": "prob_5764", "image_path": "images/img_1276.png", "question": "Find WT, if ZX = 20 and TY = 15. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 15.0, 20.0, 35.0]}
+{"prob_id": "prob_5773", "image_path": "images/img_1786.png", "question": "WXYZ is a parallelogram. Solve for YZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.500", "choices": [9.5, 19.0, 36.333, 143.667]}
+{"prob_id": "prob_5776", "image_path": "images/img_1292.png", "question": "For the pair of similar figures, the area of the blue figure is 500 in^{2}, find the scale factor of the blue to the green figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.818", "choices": [0.55, 1.0, 1.818, 5.698]}
+{"prob_id": "prob_5789", "image_path": "images/img_94.png", "question": "Find the value of variable a in the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "79.000", "choices": [50.5, 79.0, 90.0, 101.0]}
+{"prob_id": "prob_5795", "image_path": "images/img_256.png", "question": "m \\angle 3 = 43. Find the measure of \\angle 10. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "137.000", "choices": [117.0, 127.0, 137.0, 147.0]}
+{"prob_id": "prob_5813", "image_path": "images/img_1907.png", "question": "Find the measure of \\widehat YXZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "166.000", "choices": [145.0, 166.0, 194.0, 215.0]}
+{"prob_id": "prob_5819", "image_path": "images/img_2935.png", "question": "If JK = 48, find the length of HJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [23.0, 25.0, 48.0, 75.0]}
+{"prob_id": "prob_5827", "image_path": "images/img_625.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.928", "choices": [3.4641016151377544, 4.0, 6.928203230275509, 8.0]}
+{"prob_id": "prob_5840", "image_path": "images/img_482.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [15.0, 34.0, 39.5, 142.0]}
+{"prob_id": "prob_5848", "image_path": "images/img_890.png", "question": "If AB = 32 and FC = 11, find DE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.238", "choices": [5.5, 11.619, 16.0, 23.238]}
+{"prob_id": "prob_5855", "image_path": "images/img_1642.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [0.8, 1.0, 2.0, 4.0]}
+{"prob_id": "prob_5881", "image_path": "images/img_3627.png", "question": "Find the measure of \\angle 2 in the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "27.000", "choices": [27.0, 63.0, 76.5, 126.0]}
+{"prob_id": "prob_5883", "image_path": "images/img_3487.png", "question": "m \\angle BZD = 107, m \\angle FZE = 2x+5, m \\angle CZD = x, what is the measure of \\angle FZE? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "73.000", "choices": [22.667, 34.0, 73.0, 107.0]}
+{"prob_id": "prob_5885", "image_path": "images/img_2784.png", "question": "Use parallelogram ABCD to find CD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 9.0, 12.0, 18.0]}
+{"prob_id": "prob_5890", "image_path": "images/img_3698.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "61.500", "choices": [13.0, 51.5, 61.5, 123.0]}
+{"prob_id": "prob_5895", "image_path": "images/img_371.png", "question": "Find m \\angle 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "56.000", "choices": [28.5, 56.0, 57.0, 123.0]}
+{"prob_id": "prob_5898", "image_path": "images/img_433.png", "question": "If m \\angle 1 = 3y-6, find the value of variable x for the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [3.333, 5.0, 10.0, 90.0]}
+{"prob_id": "prob_5900", "image_path": "images/img_2802.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "97.529", "choices": [97.53, 103.0, 108.0, 113.0]}
+{"prob_id": "prob_5909", "image_path": "images/img_1597.png", "question": "Find the measure of the altitude drawn to the hypotenuse. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.099", "choices": [1.4142135623730951, 2.5495097567963922, 3.605551275463989, 5.0990195135927845]}
+{"prob_id": "prob_5912", "image_path": "images/img_279.png", "question": "m \\angle DBE = 50. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 6.714, 9.571, 13.143]}
+{"prob_id": "prob_5922", "image_path": "images/img_219.png", "question": "Find the perimeter of the \\triangle ABC, if \\triangle ABC \\sim \\triangle CBD, AD = 5, CD = 12, and BC = 31.2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "78.000", "choices": [32.5, 72.0, 78.0, 187.2]}
+{"prob_id": "prob_5932", "image_path": "images/img_1324.png", "question": "Find x. Assume that segments that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [4.0, 6.0, 9.0, 12.0]}
+{"prob_id": "prob_5936", "image_path": "images/img_3946.png", "question": "In \\odot R, m \\widehat MN = 120. Solve for m \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 120.0, 150.0]}
+{"prob_id": "prob_5943", "image_path": "images/img_1527.png", "question": "Find the measure of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "112.000", "choices": [46.0, 67.0, 90.0, 112.0]}
+{"prob_id": "prob_5950", "image_path": "images/img_3036.png", "question": "What is the measure of \\angle 1? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 33.0, 84.0, 150.0]}
+{"prob_id": "prob_5991", "image_path": "images/img_256.png", "question": "m \\angle 3 = 43. Find the measure of \\angle 11. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.000", "choices": [43.0, 53.0, 63.0, 137.0]}
+{"prob_id": "prob_5992", "image_path": "images/img_1482.png", "question": "What is the circumference of \\odot P? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.133", "choices": [12.566, 25.133, 50.265, 7200.0]}
+{"prob_id": "prob_6001", "image_path": "images/img_3463.png", "question": "Find the area of the shaded sector. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.460", "choices": [1.5, 2.2, 3.8, 5.3]}
+{"prob_id": "prob_6007", "image_path": "images/img_695.png", "question": "Find BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.000", "choices": [5.0, 9.0, 12.0, 13.0]}
+{"prob_id": "prob_6010", "image_path": "images/img_1797.png", "question": "If m \\angle FGE = 5x+10, find the value of x so that FC \\perp AE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [4.0, 10.0, 16.0, 90.0]}
+{"prob_id": "prob_6012", "image_path": "images/img_2609.png", "question": "Polygon BGHF \\sim polygon ADEC. Determine the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [4.5, 5.25, 9.0, 18.0]}
+{"prob_id": "prob_6024", "image_path": "images/img_3053.png", "question": "What is the perimeter of the right triangle? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "33.498", "choices": [33.5, 39.1, 49.9, 55.5]}
+{"prob_id": "prob_6031", "image_path": "images/img_2035.png", "question": "QR \\parallel TS, QT \\parallel RS, and m \\angle 1 = 131. Find the measure of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "49.000", "choices": [49.0, 59.0, 69.0, 131.0]}
+{"prob_id": "prob_6051", "image_path": "images/img_1960.png", "question": "What is m \\angle 3? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [40.0, 50.0, 70.0, 90.0]}
+{"prob_id": "prob_6055", "image_path": "images/img_2903.png", "question": "What is the value of y for which line a \\parallel line b? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [32.5, 65.0, 115.0, 130.0]}
+{"prob_id": "prob_6073", "image_path": "images/img_3481.png", "question": "Find the diameter. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [5.0, 10.0, 20.0, 31.416]}
+{"prob_id": "prob_6086", "image_path": "images/img_2196.png", "question": "Determine the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [5.143, 6.75, 11.25, 12.0]}
+{"prob_id": "prob_6107", "image_path": "images/img_1009.png", "question": "If x = 14, find b. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.333", "choices": [8.083, 9.333, 12.124, 16.166]}
+{"prob_id": "prob_6112", "image_path": "images/img_130.png", "question": "AC and EB are diameters of \\odot R. What is m \\widehat DEB? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "210.000", "choices": [180.0, 210.0, 280.0, 330.0]}
+{"prob_id": "prob_6113", "image_path": "images/img_3286.png", "question": "Use the Law of Sines to find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.598", "choices": [2.142, 2.976, 3.598, 6.949]}
+{"prob_id": "prob_6117", "image_path": "images/img_1325.png", "question": "The perpendicular bisectors of \\triangle MNP meet at point Q. Find QP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [7.0, 25.0, 47.487, 48.0]}
+{"prob_id": "prob_6149", "image_path": "images/img_2408.png", "question": "Find the value of a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [0.95, 16.9, 19.45, 22.0]}
+{"prob_id": "prob_6173", "image_path": "images/img_89.png", "question": "Find m \\angle A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "51.318", "choices": [32.005, 38.682, 51.318, 57.995]}
+{"prob_id": "prob_6178", "image_path": "images/img_1867.png", "question": "The radius of \\odot P is 5 and PR = 3. Find QR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [3.0, 4.0, 5.0, 6.0]}
+{"prob_id": "prob_6183", "image_path": "images/img_2063.png", "question": "Find KL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [3.0, 6.0, 12.0, 18.0]}
+{"prob_id": "prob_6194", "image_path": "images/img_3523.png", "question": "Find the perimeter of the quadrilateral. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "98.354", "choices": [54.0, 56.785, 72.0, 98.354]}
+{"prob_id": "prob_6196", "image_path": "images/img_3847.png", "question": "Find the area of the shaded sector. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.212", "choices": [40.2, 80.4, 160.8, 201.1]}
+{"prob_id": "prob_6206", "image_path": "images/img_666.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.588", "choices": [5.196152422706632, 9.0, 12.727922061357857, 15.588457268119894]}
+{"prob_id": "prob_6215", "image_path": "images/img_802.png", "question": "What is z? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [9.0, 15.0, 18.0, 30.0]}
+{"prob_id": "prob_6218", "image_path": "images/img_1974.png", "question": "Find the perimeter of the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "124.964", "choices": [80.0, 88.0, 96.0, 124.964]}
+{"prob_id": "prob_6231", "image_path": "images/img_467.png", "question": "In the diagram, JL = 120. What is KL? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "78.000", "choices": [42.0, 66.0, 78.0, 120.0]}
+{"prob_id": "prob_6248", "image_path": "images/img_3175.png", "question": "If AC = 12 and BC = 9, what is the radius? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.937", "choices": [3.5, 7.937, 8.485, 12.5]}
+{"prob_id": "prob_6251", "image_path": "images/img_2056.png", "question": "Polygon ABCD \\sim polygon AEFG, m \\angle AGF = 108, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26. Find AG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.500", "choices": [4.5, 7.5, 12.0, 20.0]}
+{"prob_id": "prob_6254", "image_path": "images/img_3826.png", "question": "Find the measure of \\widehat WTV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "235.000", "choices": [205.0, 235.0, 280.0, 335.0]}
+{"prob_id": "prob_6260", "image_path": "images/img_2645.png", "question": "Find the area of the rectangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.890", "choices": [1.251, 2.89, 5.78, 9.079]}
+{"prob_id": "prob_6272", "image_path": "images/img_3438.png", "question": "QS is the angle bisector of \\angle PQR, find the measure of \\angle PQR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "104.000", "choices": [26.0, 52.0, 104.0, 128.0]}
+{"prob_id": "prob_6281", "image_path": "images/img_25.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.500", "choices": [37.5, 47.0, 52.5, 133.0]}
+{"prob_id": "prob_6283", "image_path": "images/img_2533.png", "question": "Find the area of the circle. Assume that all polygons that appear to be regular are regular. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "314.159", "choices": [62.832, 125.664, 314.159, 1256.637]}
+{"prob_id": "prob_6284", "image_path": "images/img_3397.png", "question": "The diameter of \\odot C is 32 units long. Find the length of \\widehat HDF if m \\angle HCF = 125. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.624", "choices": [15.359, 34.907, 65.624, 69.813]}
+{"prob_id": "prob_6286", "image_path": "images/img_2960.png", "question": "In parallelogram ABCD, BD and AC intersect at E. If AE = 9, BE = 3x-7, and DE = x+5, find DE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [9.0, 9.8, 10.333, 11.0]}
+{"prob_id": "prob_6293", "image_path": "images/img_1066.png", "question": "Tangent MP is drawn to \\odot O. Find x if MO = 20. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [5.0, 8.94427190999916, 12.0, 16.0]}
+{"prob_id": "prob_6299", "image_path": "images/img_187.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [24.249, 28.0, 39.598, 56.0]}
+{"prob_id": "prob_6300", "image_path": "images/img_3541.png", "question": "Find the area of the shaded region. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "471.239", "choices": [392.7, 471.2, 589.0, 785.4]}
+{"prob_id": "prob_6308", "image_path": "images/img_172.png", "question": "Equilateral pentagon PQRST is inscribed in \\odot U. Find m \\angle PQR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "108.000", "choices": [60.0, 72.0, 90.0, 108.0]}
+{"prob_id": "prob_6310", "image_path": "images/img_1936.png", "question": "In \\triangle ABC, CP = 30, EP = 18, and BF = 39. Find PD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [12.0, 13.0, 15.0, 26.0]}
+{"prob_id": "prob_6316", "image_path": "images/img_2389.png", "question": "Find the exact radius of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.500", "choices": [4.5, 9.0, 18.0, 28.274]}
+{"prob_id": "prob_6318", "image_path": "images/img_1414.png", "question": "Find m \\angle A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "49.000", "choices": [41.0, 49.0, 90.0, 188.0]}
+{"prob_id": "prob_6321", "image_path": "images/img_3627.png", "question": "Find the measure of \\angle 3 in the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "27.000", "choices": [27.0, 63.0, 76.5, 126.0]}
+{"prob_id": "prob_6333", "image_path": "images/img_2843.png", "question": "Find the measure of \\angle 2 in the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "55.000", "choices": [20.0, 40.0, 55.0, 70.0]}
+{"prob_id": "prob_6351", "image_path": "images/img_3322.png", "question": "Quadrilateral ABDC is a rectangle. m \\angle 2 = 40. Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [40.0, 50.0, 90.0, 130.0]}
+{"prob_id": "prob_6354", "image_path": "images/img_1841.png", "question": "Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [7.0, 9.105, 12.357, 20.75]}
+{"prob_id": "prob_6366", "image_path": "images/img_3787.png", "question": "If m \\angle RQT = 155, what is m \\angle RQS? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "72.000", "choices": [72.0, 83.0, 155.0, 581.0]}
+{"prob_id": "prob_6380", "image_path": "images/img_2092.png", "question": "Find the length of \\widehat KL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.123", "choices": [5.061, 9.076, 10.123, 15.01]}
+{"prob_id": "prob_6382", "image_path": "images/img_1185.png", "question": "Find the measure of DB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.699", "choices": [8.764, 16.43, 17.309, 23.699]}
+{"prob_id": "prob_6388", "image_path": "images/img_3706.png", "question": "Find m \\widehat SU. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [22.0, 23.0, 34.0, 68.0]}
+{"prob_id": "prob_6405", "image_path": "images/img_1965.png", "question": "Find m \\angle M. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "96.000", "choices": [62.0, 71.0, 96.0, 106.0]}
+{"prob_id": "prob_6407", "image_path": "images/img_2091.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [25.0, 40.249, 42.827, 56.25]}
+{"prob_id": "prob_6417", "image_path": "images/img_2153.png", "question": "For trapezoid LMNO, P and Q are midpoints of the legs. Find PQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.000", "choices": [13.0, 17.0, 19.0, 25.0]}
+{"prob_id": "prob_6418", "image_path": "images/img_524.png", "question": "If PB = 6, what is SB? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [2.0, 4.0, 9.0, 18.0]}
+{"prob_id": "prob_6426", "image_path": "images/img_2804.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [10.0, 25.0, 40.0, 90.0]}
+{"prob_id": "prob_6430", "image_path": "images/img_2840.png", "question": "What is the value of y? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "100.000", "choices": [80.0, 90.0, 100.0, 140.0]}
+{"prob_id": "prob_6432", "image_path": "images/img_1800.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.400", "choices": [0.8, 1.0, 1.4, 1.6]}
+{"prob_id": "prob_6434", "image_path": "images/img_347.png", "question": "Find the measure of \\angle 2 if AB \\perp BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "68.000", "choices": [64.0, 68.0, 72.0, 76.0]}
+{"prob_id": "prob_6442", "image_path": "images/img_943.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [30.0, 35.0, 45.0, 85.0]}
+{"prob_id": "prob_6449", "image_path": "images/img_2231.png", "question": "Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "145.000", "choices": [17.5, 72.5, 90.0, 145.0]}
+{"prob_id": "prob_6467", "image_path": "images/img_130.png", "question": "AC and EB are diameters of \\odot R. What is m \\widehat CB? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [30.0, 50.0, 100.0, 130.0]}
+{"prob_id": "prob_6470", "image_path": "images/img_2564.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.745", "choices": [5.657, 5.745, 8.062, 9.899]}
+{"prob_id": "prob_6472", "image_path": "images/img_1693.png", "question": "Find m \\widehat RQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [14.0, 28.0, 37.0, 51.0]}
+{"prob_id": "prob_6497", "image_path": "images/img_1949.png", "question": "Find m \\angle D. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_6512", "image_path": "images/img_391.png", "question": "Find the perimeter of \\triangle DEF if \\triangle DEF \\sim \\triangle ABC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [15.0, 16.0, 24.0, 30.0]}
+{"prob_id": "prob_6518", "image_path": "images/img_256.png", "question": "m \\angle 3 = 43. Find the measure of \\angle 16. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "137.000", "choices": [117.0, 127.0, 137.0, 147.0]}
+{"prob_id": "prob_6522", "image_path": "images/img_1305.png", "question": "Quadrilateral WXYZ is a rectangle. If PY = 3x-5 and WP = 2x+11, find ZP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.000", "choices": [8.0, 16.0, 32.0, 43.0]}
+{"prob_id": "prob_6527", "image_path": "images/img_1336.png", "question": "\\triangle WXY and \\triangle XYZ are isosceles and m \\angle XYZ = 128. Find the measure of \\angle YZX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "26.000", "choices": [22.0, 24.0, 26.0, 28.0]}
+{"prob_id": "prob_6537", "image_path": "images/img_1056.png", "question": "PQRS \\sim TVWX. Find the scale factor of PQRS to TVWX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.500", "choices": [0.667, 1.5, 1.667, 2.5]}
+{"prob_id": "prob_6566", "image_path": "images/img_3857.png", "question": "Triangles FGH and FHJ are inscribed in \\odot K with m \\widehat FG = m \\widehat FJ. Find m \\angle FHG if m \\angle 1 = 6x-5, and m \\angle 2 = 7x+4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "53.000", "choices": [37.0, 53.0, 90.0, 106.0]}
+{"prob_id": "prob_6582", "image_path": "images/img_165.png", "question": "Find the circumference of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "26.389", "choices": [13.195, 26.389, 55.418, 360.0]}
+{"prob_id": "prob_6602", "image_path": "images/img_2721.png", "question": "\\triangle ABD \\cong \\triangle CDB, m \\angle A = 2x+14, m \\angle C = 3x-15, and m \\angle DBA = 49. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.000", "choices": [17.5, 21.333, 26.4, 29.0]}
+{"prob_id": "prob_6618", "image_path": "images/img_1284.png", "question": "In \\odot X, AB = CD = 30, and m \\widehat CZ = 40. Find m \\widehat AB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [30.0, 40.0, 60.0, 80.0]}
+{"prob_id": "prob_6685", "image_path": "images/img_826.png", "question": "Find the measure of \\angle B. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "81.000", "choices": [46.0, 53.0, 81.0, 134.0]}
+{"prob_id": "prob_6691", "image_path": "images/img_546.png", "question": "Find b in the given parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [3.0, 4.0, 5.0, 13.0]}
+{"prob_id": "prob_6699", "image_path": "images/img_2532.png", "question": "Determine the measure of \\widehat JK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "108.000", "choices": [27.0, 54.0, 108.0, 126.0]}
+{"prob_id": "prob_6701", "image_path": "images/img_2110.png", "question": "Find m \\angle LMN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.694", "choices": [19.132, 21.453, 38.694, 46.547]}
+{"prob_id": "prob_6733", "image_path": "images/img_706.png", "question": "Circle A has diameters DF and PG. If DF = 10, find DA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 10.0, 20.0, 25.0]}
+{"prob_id": "prob_6743", "image_path": "images/img_2152.png", "question": "Find the measure of \\widehat TCD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "180.000", "choices": [180.0, 218.0, 270.0, 308.0]}
+{"prob_id": "prob_6749", "image_path": "images/img_2168.png", "question": "Quadrilateral DKLM is a rhombus. If DK = 8, find ML. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [4.0, 8.0, 11.314, 16.0]}
+{"prob_id": "prob_6760", "image_path": "images/img_2187.png", "question": "Solve for m \\angle AKG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "157.000", "choices": [23.0, 67.0, 113.0, 157.0]}
+{"prob_id": "prob_6770", "image_path": "images/img_1221.png", "question": "In \\triangle JKL, ZW = 7, and LX = 8.1. Determine the length of LZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.400", "choices": [2.7, 5.4, 21.0, 24.3]}
+{"prob_id": "prob_6776", "image_path": "images/img_852.png", "question": "In rectangle ABCD, CD = 18, and CE = 19.8. Find the length of BE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.800", "choices": [9.9, 18.0, 19.8, 39.6]}
+{"prob_id": "prob_6787", "image_path": "images/img_2023.png", "question": "In \\odot X, WS, VR, and QT are diameters, m \\angle WXV = 25 and m \\angle VXU = 45. Find the measure of \\angle UXR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "135.000", "choices": [45.0, 65.0, 135.0, 155.0]}
+{"prob_id": "prob_6825", "image_path": "images/img_2894.png", "question": "Quadrilateral ABCD is a rectangle. Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 10.0, 15.0, 20.0]}
+{"prob_id": "prob_6831", "image_path": "images/img_2779.png", "question": "H is the incenter of \\triangle ABC. Find HC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.910", "choices": [7.0, 12.124, 13.165, 14.91]}
+{"prob_id": "prob_6832", "image_path": "images/img_785.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.750", "choices": [6.0, 6.25, 6.5, 6.75]}
+{"prob_id": "prob_6833", "image_path": "images/img_1231.png", "question": "Find the measure of \\angle G. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "84.000", "choices": [36.0, 60.0, 84.0, 132.0]}
+{"prob_id": "prob_6834", "image_path": "images/img_2456.png", "question": "Triangle LMN is equilateral, and MP bisects LN. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [3.0, 4.0, 5.0, 6.0]}
+{"prob_id": "prob_6837", "image_path": "images/img_598.png", "question": "PA = 2.9, and HC = 10.8. Solve for the length of PC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.600", "choices": [3.6, 7.2, 8.7, 32.4]}
+{"prob_id": "prob_6868", "image_path": "images/img_2119.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "92.000", "choices": [46.0, 92.0, 184.0, 420.0]}
+{"prob_id": "prob_6869", "image_path": "images/img_3092.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.657", "choices": [10.0, 13.7, 14.9, 16.0]}
+{"prob_id": "prob_6874", "image_path": "images/img_1497.png", "question": "What is the perimeter of \\parallelogram ABCD? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "36.000", "choices": [28.0, 32.0, 36.0, 43.324]}
+{"prob_id": "prob_6882", "image_path": "images/img_1408.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [28.0, 38.0, 52.0, 62.0]}
+{"prob_id": "prob_6899", "image_path": "images/img_196.png", "question": "Find m \\widehat AE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [5.0, 90.0, 120.0, 270.0]}
+{"prob_id": "prob_6905", "image_path": "images/img_3545.png", "question": "Determine m \\widehat AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "123.000", "choices": [57.0, 114.0, 123.0, 132.0]}
+{"prob_id": "prob_6926", "image_path": "images/img_1997.png", "question": "m \\angle BDK = 3x+4, m \\angle JDR = 5x-10, find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [7.0, 12.0, 23.25, 90.0]}
+{"prob_id": "prob_6941", "image_path": "images/img_1657.png", "question": "Find the area of the polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [24.0, 30.0, 48.0, 60.0]}
+{"prob_id": "prob_6943", "image_path": "images/img_1616.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.155", "choices": [13.74772708486752, 16.15549442140351, 17.0, 21.0]}
+{"prob_id": "prob_6944", "image_path": "images/img_1462.png", "question": "ABCD \\sim EFGD. What is the value of y? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.333", "choices": [3.333, 6.0, 7.5, 13.5]}
+{"prob_id": "prob_6951", "image_path": "images/img_1869.png", "question": "GHJK is a rhombus. Find m \\angle GHJ if m \\angle JLH = 4b-6 and m \\angle JKH = 2b+11. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "118.000", "choices": [31.0, 59.0, 90.0, 118.0]}
+{"prob_id": "prob_6952", "image_path": "images/img_1104.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.077", "choices": [32.077, 33.866, 38.0, 45.509]}
+{"prob_id": "prob_6970", "image_path": "images/img_2168.png", "question": "Quadrilateral DKLM is a rhombus. If m \\angle DML = 82 find m \\angle MDK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "98.000", "choices": [41.0, 49.0, 90.0, 98.0]}
+{"prob_id": "prob_6985", "image_path": "images/img_3761.png", "question": "Solve for the measure of \\widehat NQL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "274.000", "choices": [86.0, 102.0, 180.0, 274.0]}
+{"prob_id": "prob_6986", "image_path": "images/img_1745.png", "question": "In \\odot O, EC and AB are diameters, and m \\angle BOD = m \\angle DOE = m \\angle EOF = m \\angle FOA. Find m \\widehat AE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [45.0, 90.0, 180.0, 360.0]}
+{"prob_id": "prob_6988", "image_path": "images/img_3214.png", "question": "Find the height of the parallelogram given its area with 2000 square units. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [30.0, 40.0, 50.0, 60.0]}
+{"prob_id": "prob_6991", "image_path": "images/img_2860.png", "question": "Use \\triangle MAN with right angle N to express ratio of \\cos A if m = 21, a = 28, n = 35. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.600", "choices": [0.6, 0.8, 1.0, 1.333]}
+{"prob_id": "prob_6998", "image_path": "images/img_3284.png", "question": "P is the centroid of \\triangle DEF, EH \\perp DF, DH = 9, DG = 7.5, EP = 8, and DE = FE. Find the length of FH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [4.0, 7.5, 9.0, 12.0]}
+{"prob_id": "prob_6999", "image_path": "images/img_3359.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "72.000", "choices": [30.0, 60.0, 72.0, 120.0]}
+{"prob_id": "prob_7001", "image_path": "images/img_3682.png", "question": "m \\angle 2 = 2x, m \\angle 3 = x. Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 39.0, 78.0, 114.0]}
+{"prob_id": "prob_7005", "image_path": "images/img_2735.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.274", "choices": [28.274, 32.538, 61.726, 90.0]}
+{"prob_id": "prob_7040", "image_path": "images/img_1042.png", "question": "In \\odot S, m \\angle TSR = 42. Find m \\widehat KE. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "42.000", "choices": [42.0, 84.0, 90.0, 138.0]}
+{"prob_id": "prob_7043", "image_path": "images/img_3261.png", "question": "Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "113.000", "choices": [67.0, 90.0, 113.0, 182.0]}
+{"prob_id": "prob_7046", "image_path": "images/img_720.png", "question": "WXYZ is a kite. If m \\angle WXY = 13x+24, m \\angle WZY = 35, and m \\angle ZYX = 13x+14, find m \\angle ZWX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "105.000", "choices": [35.0, 52.5, 63.333, 105.0]}
+{"prob_id": "prob_7051", "image_path": "images/img_3642.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [2.5, 5.0, 10.0, 60.0]}
+{"prob_id": "prob_7063", "image_path": "images/img_2405.png", "question": "Determine m \\angle S. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "52.000", "choices": [14.0, 52.0, 128.0, 242.0]}
+{"prob_id": "prob_7065", "image_path": "images/img_1430.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.328", "choices": [4.2, 8.3, 16.7, 69.4]}
+{"prob_id": "prob_7066", "image_path": "images/img_2953.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "130.000", "choices": [50.0, 80.0, 100.0, 130.0]}
+{"prob_id": "prob_7069", "image_path": "images/img_1959.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "37.000", "choices": [26.0, 37.0, 80.0, 89.0]}
+{"prob_id": "prob_7076", "image_path": "images/img_2451.png", "question": "Find m \\angle FEA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 45.0, 60.0, 150.0]}
+{"prob_id": "prob_7085", "image_path": "images/img_3024.png", "question": "Find the perimeter of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "100.006", "choices": [80.0, 93.438, 100.006, 104.452]}
+{"prob_id": "prob_7092", "image_path": "images/img_673.png", "question": "Find a. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.165", "choices": [4.6, 5.9, 7.2, 9.2]}
+{"prob_id": "prob_7103", "image_path": "images/img_935.png", "question": "In quadrilateral PQRS, PQ = 721, QR = 547, RS = 593, PS = 756, and m \\angle P = 58. Find m \\angle PQS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "63.448", "choices": [43.1, 56.4, 63.45, 87.4]}
+{"prob_id": "prob_7122", "image_path": "images/img_592.png", "question": "\\triangle ADB \\cong \\triangle CDB, find the length of AD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [2.0, 3.0, 4.0, 5.0]}
+{"prob_id": "prob_7124", "image_path": "images/img_100.png", "question": "GHJK is a square with diagonals intersecting at L. Given that GH = 2 and GL = \\sqrt{2}, determine the length of HJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [1.414, 2.0, 2.828, 4.0]}
+{"prob_id": "prob_7131", "image_path": "images/img_1997.png", "question": "m \\angle BDK = 3x+4, m \\angle JDR = 5x-10, find the measurement of \\angle KDR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [25.0, 40.0, 50.0, 65.0]}
+{"prob_id": "prob_7134", "image_path": "images/img_3064.png", "question": "Find m \\angle C. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "62.000", "choices": [35.0, 53.0, 62.0, 83.0]}
+{"prob_id": "prob_7135", "image_path": "images/img_3776.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.167", "choices": [10.285714285714286, 14.0, 15.833333333333334, 16.166666666666668]}
+{"prob_id": "prob_7146", "image_path": "images/img_2840.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [80.0, 90.0, 100.0, 140.0]}
+{"prob_id": "prob_7172", "image_path": "images/img_1966.png", "question": "Find \\tan R. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.333", "choices": [0.6, 0.75, 0.8, 1.3333333333333333]}
+{"prob_id": "prob_7177", "image_path": "images/img_697.png", "question": "Find m \\widehat BCA of \\odot Q. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "313.000", "choices": [47.0, 227.0, 266.0, 313.0]}
+{"prob_id": "prob_7185", "image_path": "images/img_3882.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.500", "choices": [1.714, 2.0, 4.5, 6.0]}
+{"prob_id": "prob_7187", "image_path": "images/img_3657.png", "question": "In kite PQRS, m \\angle SRT = 24, and m \\angle TSP = 53. Find m \\angle QPS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "74.000", "choices": [37.0, 66.0, 74.0, 90.0]}
+{"prob_id": "prob_7194", "image_path": "images/img_1313.png", "question": "Find the area of the shaded region. Assume that the triangle is equilateral. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.481", "choices": [20.8, 29.5, 50.3, 71.1]}
+{"prob_id": "prob_7203", "image_path": "images/img_1740.png", "question": "Quadrilateral DEFG is a rectangle. If m \\angle EDF = 5x-3 and m \\angle DFG = 3x+7, find m \\angle GDF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "68.000", "choices": [22.0, 39.25, 50.75, 68.0]}
+{"prob_id": "prob_7207", "image_path": "images/img_3063.png", "question": "PRYZ is a rhombus. If RK = 5, RY = 13 and m \\angle YRZ = 67, what is m \\angle YKZ? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [23.0, 46.0, 90.0, 134.0]}
+{"prob_id": "prob_7215", "image_path": "images/img_984.png", "question": "Points P, Q, and R are the midpoints of JK, KL, and JL, respectively. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.500", "choices": [0.83, 1.1, 2.0, 5.5]}
+{"prob_id": "prob_7229", "image_path": "images/img_920.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.500", "choices": [13.5, 14.0, 14.5, 15.0]}
+{"prob_id": "prob_7231", "image_path": "images/img_2643.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "33.941", "choices": [24.0, 33.941125496954285, 36.0, 41.569219381653056]}
+{"prob_id": "prob_7236", "image_path": "images/img_1785.png", "question": "For what value of x must ABCD be a parallelogram? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [2.0, 5.0, 13.571, 15.0]}
+{"prob_id": "prob_7253", "image_path": "images/img_1685.png", "question": "Find m \\angle T. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "68.000", "choices": [44.0, 56.0, 62.0, 68.0]}
+{"prob_id": "prob_7257", "image_path": "images/img_2036.png", "question": "Find the length of BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [7.5, 12.0, 15.0, 21.333]}
+{"prob_id": "prob_7262", "image_path": "images/img_1003.png", "question": "Find the measure of \\angle E. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "45.000", "choices": [9.899, 45.0, 90.0, 360.0]}
+{"prob_id": "prob_7274", "image_path": "images/img_662.png", "question": "For trapezoid ABDC, E and F are midpoints of the legs. Find CD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [3.0, 8.0, 10.5, 18.0]}
+{"prob_id": "prob_7280", "image_path": "images/img_1343.png", "question": "Find the value of d. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.750", "choices": [3.75, 10.293, 12.25, 18.286]}
+{"prob_id": "prob_7305", "image_path": "images/img_3118.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [5.3, 6.0, 8.0, 10.0]}
+{"prob_id": "prob_7309", "image_path": "images/img_198.png", "question": "VWXY is a rhombus. Find YX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "31.500", "choices": [15.75, 25.2, 31.5, 63.0]}
+{"prob_id": "prob_7320", "image_path": "images/img_39.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [57.5, 81.3, 99.6, 115.0]}
+{"prob_id": "prob_7337", "image_path": "images/img_1578.png", "question": "JL = 5z+3, and KM = 9z-12. Find the value of z so that JKLM is isosceles trapezoid. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.750", "choices": [2.077, 3.75, 11.333, 21.75]}
+{"prob_id": "prob_7361", "image_path": "images/img_1450.png", "question": "Find the value of the variable z for the quadrilateral. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [40.0, 45.0, 80.0, 160.0]}
+{"prob_id": "prob_7365", "image_path": "images/img_3997.png", "question": "\\angle 6 and \\angle 8 are complementary, m \\angle 8 = 47. Find the measure of \\angle 7. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [43.0, 47.0, 86.0, 90.0]}
+{"prob_id": "prob_7379", "image_path": "images/img_201.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [25.0, 40.0, 65.0, 115.0]}
+{"prob_id": "prob_7392", "image_path": "images/img_2694.png", "question": "In \\odot A, AE = 13.1 and AC \\perp BD. If BC = 6.8, what is AC? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.197", "choices": [1.827, 4.973, 11.197, 22.394]}
+{"prob_id": "prob_7396", "image_path": "images/img_3607.png", "question": "Find the area of the inscribed regular polygon shown. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "187.061", "choices": [46.765, 72.0, 187.061, 288.0]}
+{"prob_id": "prob_7399", "image_path": "images/img_3068.png", "question": "Point S is the incenter of \\triangle JPL. Find m \\angle MPQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "56.000", "choices": [24.5, 28.0, 49.0, 56.0]}
+{"prob_id": "prob_7402", "image_path": "images/img_1690.png", "question": "Find the area of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "54.000", "choices": [27.0, 36.0, 54.0, 108.0]}
+{"prob_id": "prob_7403", "image_path": "images/img_2226.png", "question": "Find DA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [2.5, 5.0, 8.0, 9.165]}
+{"prob_id": "prob_7418", "image_path": "images/img_2924.png", "question": "Find the area of the shaded region. Assume that the triangle is equilateral. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.481", "choices": [1.449, 18.265, 29.481, 48.816]}
+{"prob_id": "prob_7421", "image_path": "images/img_3482.png", "question": "\\triangle MNL \\sim \\triangle SPT. Find PT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.209", "choices": [12.0, 14.422, 15.0, 19.209]}
+{"prob_id": "prob_7429", "image_path": "images/img_1393.png", "question": "Quadrilateral JKLM is a rectangle. If m \\angle KJL = 2x+4 and m \\angle JLK = 7x+5, find m \\angle KML. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.000", "choices": [22.0, 44.0, 68.0, 136.0]}
+{"prob_id": "prob_7439", "image_path": "images/img_3444.png", "question": "The figures in the pair are similar. Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "63.000", "choices": [4.0, 27.0, 32.0, 63.0]}
+{"prob_id": "prob_7440", "image_path": "images/img_2272.png", "question": "What is x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.824", "choices": [13.824, 20.179, 43.0, 79.911]}
+{"prob_id": "prob_7466", "image_path": "images/img_2839.png", "question": "G is the incenter of \\triangle DEF, m \\angle EDF = 50. What is m \\angle EGF? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "115.000", "choices": [25.0, 50.0, 115.0, 155.0]}
+{"prob_id": "prob_7478", "image_path": "images/img_246.png", "question": "Find the area of the shaded sector. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "175.808", "choices": [37.4, 101.8, 175.8, 277.6]}
+{"prob_id": "prob_7489", "image_path": "images/img_3060.png", "question": "Find m \\angle DIG if m \\angle DGI = 24 and IG = 6. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "132.000", "choices": [24.0, 48.0, 78.0, 132.0]}
+{"prob_id": "prob_7498", "image_path": "images/img_3372.png", "question": "QS is the angle bisector of \\angle PQR, find the measure of \\angle RQS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.000", "choices": [32.0, 64.0, 116.0, 128.0]}
+{"prob_id": "prob_7500", "image_path": "images/img_3501.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.889", "choices": [11.313708498984761, 13.856406460551018, 17.88854381999832, 21.166010488516726]}
+{"prob_id": "prob_7503", "image_path": "images/img_3062.png", "question": "Find the measure of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [10.392, 12.0, 18.0, 41.569]}
+{"prob_id": "prob_7517", "image_path": "images/img_1645.png", "question": "JL / NJ = MK / PK, find JN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.857", "choices": [3.857, 4.32, 6.857, 9.143]}
+{"prob_id": "prob_7527", "image_path": "images/img_3658.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [21.7, 28.0, 38.5, 49.0]}
+{"prob_id": "prob_7530", "image_path": "images/img_2152.png", "question": "Find the measure of \\widehat BCD in \\odot P. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "270.000", "choices": [180.0, 218.0, 270.0, 308.0]}
+{"prob_id": "prob_7538", "image_path": "images/img_272.png", "question": "What is m \\widehat DF? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "129.000", "choices": [39.0, 90.0, 129.0, 141.0]}
+{"prob_id": "prob_7539", "image_path": "images/img_1007.png", "question": "The perpendicular bisectors of \\triangle RST meet at point D. Find DT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [4.68, 7.687, 9.0, 16.0]}
+{"prob_id": "prob_7544", "image_path": "images/img_1144.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [9.0, 11.0, 37.0, 47.0]}
+{"prob_id": "prob_7554", "image_path": "images/img_3610.png", "question": "Find \\sin N. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.923", "choices": [0.38, 0.42, 0.92, 2.4]}
+{"prob_id": "prob_7555", "image_path": "images/img_3474.png", "question": "Find m \\angle B. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "112.000", "choices": [112.0, 116.0, 122.0, 127.0]}
+{"prob_id": "prob_7557", "image_path": "images/img_2740.png", "question": "Express the ratio of \\tan L. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.417", "choices": [0.38, 0.42, 0.92, 2.4]}
+{"prob_id": "prob_7562", "image_path": "images/img_3615.png", "question": "Find the length of ST. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.060", "choices": [6.357, 7.06, 8.554, 12.784]}
+{"prob_id": "prob_7593", "image_path": "images/img_623.png", "question": "Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [7.429, 18.0, 21.2, 22.0]}
+{"prob_id": "prob_7594", "image_path": "images/img_1794.png", "question": "Find YZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.053", "choices": [4.592, 7.0, 8.053, 9.275]}
+{"prob_id": "prob_7602", "image_path": "images/img_2976.png", "question": "What is m \\widehat XZV? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "260.000", "choices": [80.0, 180.0, 260.0, 280.0]}
+{"prob_id": "prob_7609", "image_path": "images/img_1651.png", "question": "Use rhombus WXYZ with m \\angle XYZ = 5 m \\angle WZY and YZ = 12. Find WX. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [6.0, 12.0, 24.0, 84.0]}
+{"prob_id": "prob_7614", "image_path": "images/img_59.png", "question": "Find m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "73.000", "choices": [73.0, 82.0, 107.0, 146.0]}
+{"prob_id": "prob_7622", "image_path": "images/img_1720.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.381", "choices": [4.898979485566356, 6.6332495807108, 9.38083151964686, 9.433981132056603]}
+{"prob_id": "prob_7646", "image_path": "images/img_3388.png", "question": "Find the area of the shaded figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "27.000", "choices": [1.25, 6.0, 15.0, 27.0]}
+{"prob_id": "prob_7649", "image_path": "images/img_1934.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "56.000", "choices": [28.0, 56.0, 112.0, 164.0]}
+{"prob_id": "prob_7656", "image_path": "images/img_1239.png", "question": "Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [27.713, 36.661, 40.0, 42.332]}
+{"prob_id": "prob_7681", "image_path": "images/img_1368.png", "question": "EFGH is a parallelogram. Find w. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.500", "choices": [4.5, 6.3, 6.5, 6.7]}
+{"prob_id": "prob_7691", "image_path": "images/img_3890.png", "question": "Find the value of n. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 45.0, 60.0, 90.0]}
+{"prob_id": "prob_7695", "image_path": "images/img_1024.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "50.000", "choices": [25.0, 50.0, 100.0, 144.0]}
+{"prob_id": "prob_7716", "image_path": "images/img_1613.png", "question": "Find the area of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "280.592", "choices": [256.785, 280.592, 305.47, 374.123]}
+{"prob_id": "prob_7719", "image_path": "images/img_2289.png", "question": "Find the measure of \\angle A. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "78.463", "choices": [11.3, 11.5, 78.5, 78.7]}
+{"prob_id": "prob_7720", "image_path": "images/img_142.png", "question": "m \\widehat UY = m \\widehat XZ = m \\widehat UV = m \\widehat XW = 56. Solve for m \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "56.000", "choices": [28.0, 56.0, 96.0, 124.0]}
+{"prob_id": "prob_7728", "image_path": "images/img_1590.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [5.6, 5.667, 6.0, 13.273]}
+{"prob_id": "prob_7740", "image_path": "images/img_2967.png", "question": "Find WZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [18.0, 24.0, 30.0, 32.0]}
+{"prob_id": "prob_7748", "image_path": "images/img_3236.png", "question": "The two triangles in the diagram are similar. Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.429", "choices": [2.182, 3.429, 10.5, 16.5]}
+{"prob_id": "prob_7749", "image_path": "images/img_1806.png", "question": "Find the measure of RT for equilateral triangle SRT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [9.0, 12.0, 15.0, 18.0]}
+{"prob_id": "prob_7770", "image_path": "images/img_2698.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.485", "choices": [8.485281374238571, 10.392304845413264, 12.0, 14.696938456699067]}
+{"prob_id": "prob_7778", "image_path": "images/img_2994.png", "question": "What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "45.000", "choices": [30.0, 45.0, 60.0, 90.0]}
+{"prob_id": "prob_7781", "image_path": "images/img_2967.png", "question": "Find WU. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [8.727, 18.0, 24.0, 30.0]}
+{"prob_id": "prob_7784", "image_path": "images/img_2469.png", "question": "Find m \\angle S. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "22.363", "choices": [22.363, 23.0, 29.088, 128.549]}
+{"prob_id": "prob_7787", "image_path": "images/img_2558.png", "question": "PR and QT are diameters of \\odot A. Solve for the measure of \\widehat PQS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "230.000", "choices": [140.0, 180.0, 230.0, 320.0]}
+{"prob_id": "prob_7795", "image_path": "images/img_3562.png", "question": "EG and FG are angle bisectors of \\triangle DEF. Find the distance from G to EF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.700", "choices": [3.7, 7.4, 25.0, 42.0]}
+{"prob_id": "prob_7799", "image_path": "images/img_1096.png", "question": "Use rectangle LMNP, parallelogram LKMJ. If MK = 6x, KL = 3x+2y, and JN = 14-x, find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.000", "choices": [2.0, 3.0, 6.0, 12.0]}
+{"prob_id": "prob_7803", "image_path": "images/img_652.png", "question": "Find the perimeter of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [8.0, 12.0, 20.785, 25.133]}
+{"prob_id": "prob_7836", "image_path": "images/img_3650.png", "question": "Lines that appear to be tangent are tangent. O is the center of the circle. What is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [30.0, 60.0, 120.0, 210.0]}
+{"prob_id": "prob_7840", "image_path": "images/img_1042.png", "question": "In \\odot S, m \\angle TSR = 42. Find m \\widehat KT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "138.000", "choices": [21.0, 42.0, 63.0, 138.0]}
+{"prob_id": "prob_7860", "image_path": "images/img_1444.png", "question": "QRST is a rectangle. If m \\angle QTR = 2x^{2}-7 and m \\angle SRT = x^{2}+18, find m \\angle PSR. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.000", "choices": [43.0, 44.333, 45.667, 86.0]}
+{"prob_id": "prob_7866", "image_path": "images/img_157.png", "question": "What is the length of QP? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [11.18, 12.166, 14.0, 22.0]}
+{"prob_id": "prob_7869", "image_path": "images/img_3308.png", "question": "What is c? Lines that appear to be tangent are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "47.500", "choices": [47.5, 62.5, 70.0, 132.5]}
+{"prob_id": "prob_7907", "image_path": "images/img_451.png", "question": "WXYZ is a square. If WT = 3, find m \\angle WTZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [15.0, 30.0, 45.0, 90.0]}
+{"prob_id": "prob_7913", "image_path": "images/img_2655.png", "question": "Find the area of the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "106.066", "choices": [75.0, 106.1, 150.0, 212.1]}
+{"prob_id": "prob_7914", "image_path": "images/img_3702.png", "question": "Find m \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [26.0, 52.0, 64.0, 90.0]}
+{"prob_id": "prob_7923", "image_path": "images/img_2101.png", "question": "Find the value of q. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "27.500", "choices": [11.136, 14.583, 27.5, 39.6]}
+{"prob_id": "prob_7925", "image_path": "images/img_2464.png", "question": "BD = x-1, CE = x+2. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.800", "choices": [1.0, 2.8, 4.623, 9.0]}
+{"prob_id": "prob_7934", "image_path": "images/img_47.png", "question": "Find the area of the shaded region of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "53.014", "choices": [13.894, 50.364, 53.014, 201.455]}
+{"prob_id": "prob_7940", "image_path": "images/img_1594.png", "question": "If DB = 6, AD = 2, and CB = 20, find EB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [5.0, 6.667, 15.0, 60.0]}
+{"prob_id": "prob_7941", "image_path": "images/img_813.png", "question": "In kite EFGH, m \\angle FEJ = 25, and m \\angle FGJ = 57. Find the measure of \\angle GFJ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "33.000", "choices": [25.0, 33.0, 65.0, 90.0]}
+{"prob_id": "prob_7946", "image_path": "images/img_2293.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.385", "choices": [1.0, 2.217, 2.25, 3.385]}
+{"prob_id": "prob_7967", "image_path": "images/img_1132.png", "question": "If QRST is a parallelogram, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.400", "choices": [5.4, 9.0, 11.0, 13.0]}
+{"prob_id": "prob_7969", "image_path": "images/img_3902.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [30.0, 45.0, 60.0, 90.0]}
+{"prob_id": "prob_7977", "image_path": "images/img_2354.png", "question": "Find the area of \\odot K. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "283.487", "choices": [27.387, 59.686, 283.487, 2136.283]}
+{"prob_id": "prob_7990", "image_path": "images/img_793.png", "question": "Find y if m \\angle 5 = 68 and m \\angle 3 = 3y-2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "38.000", "choices": [22.0, 23.3, 38.0, 82.0]}
+{"prob_id": "prob_7996", "image_path": "images/img_184.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.000", "choices": [3.0, 20.333, 29.0, 81.0]}
+{"prob_id": "prob_8003", "image_path": "images/img_42.png", "question": "What is the measure of \\angle 8? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.000", "choices": [34.0, 44.0, 46.0, 90.0]}
+{"prob_id": "prob_8015", "image_path": "images/img_1156.png", "question": "Use parallelogram ABCD to find m \\angle BAD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "103.000", "choices": [49.0, 54.0, 77.0, 103.0]}
+{"prob_id": "prob_8018", "image_path": "images/img_3026.png", "question": "Find m \\angle 1 in the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "57.000", "choices": [57.0, 61.5, 66.0, 114.0]}
+{"prob_id": "prob_8022", "image_path": "images/img_3288.png", "question": "For the pair of similar figures, the area of the blue figure is 400 mm^{2} and the green figure is 64 mm^{2}, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [6.4, 16.0, 100.0, 250.0]}
+{"prob_id": "prob_8035", "image_path": "images/img_3162.png", "question": "Find RV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.000", "choices": [1.667, 2.333, 5.0, 7.0]}
+{"prob_id": "prob_8045", "image_path": "images/img_3356.png", "question": "In \\odot A, m \\widehat PQ = m \\widehat RS. Find y if m \\angle 1 = 6x+11, m \\angle 2 = 9x+19, m \\angle 3 = 4y-25, and m \\angle 4 = 3y-9. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "16.000", "choices": [16.0, 17.714, 30.571, 33.0]}
+{"prob_id": "prob_8069", "image_path": "images/img_1705.png", "question": "Use \\odot P to find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [30.0, 40.0, 70.0, 130.0]}
+{"prob_id": "prob_8078", "image_path": "images/img_3082.png", "question": "Find m \\widehat ABE for \\odot O. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "230.000", "choices": [50.0, 160.0, 230.0, 260.0]}
+{"prob_id": "prob_8116", "image_path": "images/img_3015.png", "question": "m \\angle 17 = 2x+7, m \\angle 18 = x+30, find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "23.000", "choices": [23.0, 47.667, 53.0, 60.0]}
+{"prob_id": "prob_8120", "image_path": "images/img_1221.png", "question": "In \\triangle JKL, ZW = 7, and LX = 8.1. Determine the length of XZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.700", "choices": [2.7, 5.4, 21.0, 24.3]}
+{"prob_id": "prob_8125", "image_path": "images/img_538.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "93.923", "choices": [91.9, 93.9, 95.9, 97.9]}
+{"prob_id": "prob_8162", "image_path": "images/img_1297.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.738", "choices": [17.7, 36.6, 57.7, 66.0]}
+{"prob_id": "prob_8163", "image_path": "images/img_3589.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "44.091", "choices": [22.045407685048602, 44.090815370097204, 54.0, 62.35382907247958]}
+{"prob_id": "prob_8166", "image_path": "images/img_1997.png", "question": "m \\angle BDJ = 7y+2, m \\angle JDR = 2y+7, find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [1.0, 9.0, 19.0, 41.5]}
+{"prob_id": "prob_8168", "image_path": "images/img_1127.png", "question": "What is the circumference of \\odot T? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.841", "choices": [37.2, 39.6, 40.8, 42.4]}
+{"prob_id": "prob_8186", "image_path": "images/img_3724.png", "question": "Given m \\angle GFI = 128, what is the value of x? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [4.154, 10.0, 14.444, 26.0]}
+{"prob_id": "prob_8187", "image_path": "images/img_889.png", "question": "For the pair of similar figures, the area of the blue figure is 72 m^{2} and the green figure is 50 m^{2}, find the scale factor of the blue to the green figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.200", "choices": [0.6944444444444444, 0.8333333333333334, 1.2, 1.44]}
+{"prob_id": "prob_8199", "image_path": "images/img_892.png", "question": "Solve for t. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "1.250", "choices": [0.5, 0.714, 0.833, 1.25]}
+{"prob_id": "prob_8211", "image_path": "images/img_1973.png", "question": "If m \\angle BNC = 20, find m \\widehat BC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [20.0, 30.0, 40.0, 50.0]}
+{"prob_id": "prob_8222", "image_path": "images/img_3073.png", "question": "Find RQ if AU = 15, QU = 25, AD = 3x+6, DR = 8x-2, and UD = 15. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "40.000", "choices": [6.75, 18.0, 30.0, 40.0]}
+{"prob_id": "prob_8228", "image_path": "images/img_1180.png", "question": "Find the measure of \\angle 1 for the parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "95.000", "choices": [37.0, 48.0, 85.0, 95.0]}
+{"prob_id": "prob_8232", "image_path": "images/img_1381.png", "question": "CG, EH, and FJ are midsegments of \\triangle ABD, \\triangle GCD, and \\triangle GHE, respectively. What is m \\angle GHE? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "57.000", "choices": [28.5, 57.0, 66.0, 123.0]}
+{"prob_id": "prob_8240", "image_path": "images/img_2371.png", "question": "The perpendicular bisectors of \\triangle ABC meet at point G. Find BF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.708", "choices": [2.0, 4.899, 6.708, 7.0]}
+{"prob_id": "prob_8258", "image_path": "images/img_1975.png", "question": "Find the value of variable x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.800", "choices": [2.333, 10.714, 25.8, 53.0]}
+{"prob_id": "prob_8270", "image_path": "images/img_3034.png", "question": "Use parallelogram WXYZ to find m \\angle XYZ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "105.000", "choices": [30.0, 75.0, 105.0, 180.0]}
+{"prob_id": "prob_8273", "image_path": "images/img_1675.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.028", "choices": [6.0, 15.905973720586866, 17.0, 18.027756377319946]}
+{"prob_id": "prob_8274", "image_path": "images/img_2470.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [1.647, 7.765, 10.0, 16.118]}
+{"prob_id": "prob_8275", "image_path": "images/img_1130.png", "question": "CE bisects \\angle DCF, and CG bisects \\angle FCB. If m \\angle DCE = 4x+15 and m \\angle ECF = 6x-5, find m \\angle GCB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "35.000", "choices": [35.0, 55.0, 70.0, 125.0]}
+{"prob_id": "prob_8276", "image_path": "images/img_1879.png", "question": "Find the value of y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [9.798, 10.0, 10.667, 12.649]}
+{"prob_id": "prob_8282", "image_path": "images/img_2024.png", "question": "Find the area of the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [22.0, 30.0, 60.0, 120.0]}
+{"prob_id": "prob_8292", "image_path": "images/img_2779.png", "question": "H is the incenter of \\triangle ABC. Find m \\angle DHG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "120.000", "choices": [60.0, 100.0, 120.0, 150.0]}
+{"prob_id": "prob_8303", "image_path": "images/img_3831.png", "question": "\\triangle DFG and \\triangle FGH are isosceles. Find the measure of \\angle FGH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "56.000", "choices": [56.0, 58.0, 64.0, 68.0]}
+{"prob_id": "prob_8313", "image_path": "images/img_2565.png", "question": "Find m \\angle K. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "49.000", "choices": [16.0, 49.0, 82.0, 98.0]}
+{"prob_id": "prob_8320", "image_path": "images/img_2284.png", "question": "What is the measure of \\widehat PQR in \\odot T? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "180.000", "choices": [120.0, 180.0, 220.0, 240.0]}
+{"prob_id": "prob_8325", "image_path": "images/img_1712.png", "question": "Find the area of the segment. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.540", "choices": [3.915, 28.54, 114.159, 310.245]}
+{"prob_id": "prob_8333", "image_path": "images/img_2345.png", "question": "m \\angle UOW = 50, and OV bisects \\angle UOW. What is m \\angle VOY? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "155.000", "choices": [25.0, 65.0, 90.0, 155.0]}
+{"prob_id": "prob_8337", "image_path": "images/img_2867.png", "question": "Solve for m \\angle FGH. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "90.000", "choices": [12.5, 25.0, 90.0, 155.0]}
+{"prob_id": "prob_8342", "image_path": "images/img_508.png", "question": "m \\angle 5 = 72 and m \\angle 9 = 102. Find the measure of \\angle 1. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "102.000", "choices": [72.0, 78.0, 102.0, 108.0]}
+{"prob_id": "prob_8346", "image_path": "images/img_591.png", "question": "Find the perimeter of the regular polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "27.713", "choices": [23.511, 24.0, 27.713, 29.062]}
+{"prob_id": "prob_8348", "image_path": "images/img_3693.png", "question": "\\triangle RST \\cong \\triangle XYZ. Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "15.000", "choices": [5.0, 14.0, 15.0, 35.0]}
+{"prob_id": "prob_8376", "image_path": "images/img_2815.png", "question": "Find the measure of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [34.0, 56.0, 68.0, 146.0]}
+{"prob_id": "prob_8379", "image_path": "images/img_3506.png", "question": "Find the length of AD if AB = DC, AD = DC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "25.000", "choices": [6.25, 25.0, 50.0, 64.375]}
+{"prob_id": "prob_8386", "image_path": "images/img_1513.png", "question": "Find x if \\triangle JMN is an isosceles triangle with JM = MN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.000", "choices": [2.0, 3.0, 4.0, 4.0]}
+{"prob_id": "prob_8398", "image_path": "images/img_3795.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [7.0, 9.0, 12.0, 15.0]}
+{"prob_id": "prob_8399", "image_path": "images/img_2961.png", "question": "Find m \\angle D of quadrilateral ABCD. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "45.000", "choices": [45.0, 90.0, 135.0, 180.0]}
+{"prob_id": "prob_8414", "image_path": "images/img_3699.png", "question": "Quadrilateral WXYZ is a rectangle. If XZ = 2c and ZY = 6, and XY = 8, find WY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [6.0, 8.0, 10.0, 20.0]}
+{"prob_id": "prob_8415", "image_path": "images/img_3234.png", "question": "In rhombus RSTV, m \\angle TZV = 8n+18, and m \\angle SRV = 9n+1. Find the measure of \\angle RSV. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "49.000", "choices": [41.0, 49.0, 82.0, 164.0]}
+{"prob_id": "prob_8427", "image_path": "images/img_1751.png", "question": "Find the measure of \\angle 1 in special parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "58.000", "choices": [32.0, 58.0, 74.0, 90.0]}
+{"prob_id": "prob_8428", "image_path": "images/img_1193.png", "question": "Find the measure of \\angle 2. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.000", "choices": [23.0, 24.0, 28.0, 33.0]}
+{"prob_id": "prob_8438", "image_path": "images/img_3820.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "125.000", "choices": [55.0, 115.0, 125.0, 135.0]}
+{"prob_id": "prob_8450", "image_path": "images/img_1216.png", "question": "What is m \\angle A? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "71.000", "choices": [71.0, 76.0, 80.0, 133.0]}
+{"prob_id": "prob_8468", "image_path": "images/img_1493.png", "question": "Find the measure of XT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [3.5, 7.0, 14.0, 28.0]}
+{"prob_id": "prob_8489", "image_path": "images/img_862.png", "question": "For rhombus ABCD, find m \\angle BAD, given that m \\angle DEC = 30y, m \\angle EDC = 8y+15, AB = 2x+8, and BC = 4x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "102.000", "choices": [51.0, 78.0, 90.0, 102.0]}
+{"prob_id": "prob_8491", "image_path": "images/img_993.png", "question": "Find the value of b that would make the quadrilateral a parallelogram. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [19.286, 19.615, 20.0, 71.667]}
+{"prob_id": "prob_8494", "image_path": "images/img_1253.png", "question": "m \\widehat AB = 176, and m \\widehat BC = 42. Solve for the measure of \\angle 3. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "88.000", "choices": [21.0, 71.0, 88.0, 109.0]}
+{"prob_id": "prob_8501", "image_path": "images/img_3821.png", "question": "Find the measure of \\angle DFB on \\odot F with diameter AC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "165.000", "choices": [163.0, 165.0, 167.0, 169.0]}
+{"prob_id": "prob_8502", "image_path": "images/img_103.png", "question": "The angle bisectors of \\triangle XYZ intersect at W. Find WB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [6.0, 8.0, 10.0, 12.0]}
+{"prob_id": "prob_8503", "image_path": "images/img_1524.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.806", "choices": [6.0, 8.0, 10.0, 12.806248474865697]}
+{"prob_id": "prob_8506", "image_path": "images/img_3407.png", "question": "Find the perimeter of the figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "32.000", "choices": [26.472, 31.165, 32.0, 40.0]}
+{"prob_id": "prob_8511", "image_path": "images/img_3992.png", "question": "Solve for the diameter of \\odot S. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [7.5, 30.0, 47.124, 133.5]}
+{"prob_id": "prob_8516", "image_path": "images/img_361.png", "question": "Find the area of the kite. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [15.0, 17.5, 18.0, 21.0]}
+{"prob_id": "prob_8517", "image_path": "images/img_1172.png", "question": "Find z. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [18.0, 20.0, 22.0, 24.0]}
+{"prob_id": "prob_8519", "image_path": "images/img_1733.png", "question": "Find the measure of \\angle C. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "26.000", "choices": [9.946, 26.0, 47.621, 66.009]}
+{"prob_id": "prob_8523", "image_path": "images/img_1379.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.314", "choices": [8.0, 11.314, 12.649, 36.0]}
+{"prob_id": "prob_8534", "image_path": "images/img_1905.png", "question": "In \\odot T, ZV = 1, and TW = 13. Find VT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.000", "choices": [5.0, 10.0, 12.0, 13.0]}
+{"prob_id": "prob_8548", "image_path": "images/img_2928.png", "question": "m \\angle 3 = x-12 and m \\angle 6 = 72. Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "84.000", "choices": [6.0, 18.0, 72.0, 84.0]}
+{"prob_id": "prob_8562", "image_path": "images/img_2421.png", "question": "If CD = 3 and AD = 12, what is BA? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.416", "choices": [6.0, 6.708, 12.369, 13.416]}
+{"prob_id": "prob_8567", "image_path": "images/img_748.png", "question": "\\angle 6 and \\angle 8 are complementary, m \\angle 8 = 47. Find the measure of \\angle 6. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "43.000", "choices": [43.0, 47.0, 86.0, 90.0]}
+{"prob_id": "prob_8582", "image_path": "images/img_2146.png", "question": "What is the measure of \\angle E? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "135.000", "choices": [81.0, 108.0, 113.684, 135.0]}
+{"prob_id": "prob_8584", "image_path": "images/img_2464.png", "question": "BD = x-1, CE = x+2. Find CF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.330", "choices": [1.8, 3.499, 4.8, 9.33]}
+{"prob_id": "prob_8594", "image_path": "images/img_3305.png", "question": "Rhombus MNPQ has an area of 375 square inches. If MP is 25 inches, find PQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "19.526", "choices": [15.0, 19.526, 30.0, 375.0]}
+{"prob_id": "prob_8600", "image_path": "images/img_1753.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.000", "choices": [17.0, 24.041630560342618, 34.0, 41.641325627314025]}
+{"prob_id": "prob_8623", "image_path": "images/img_3869.png", "question": "Refer to rectangle QRTS. If RU = 3x-6 and UT = x+9, find RS. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "33.000", "choices": [8.25, 16.5, 19.25, 33.0]}
+{"prob_id": "prob_8628", "image_path": "images/img_505.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.071", "choices": [5.0, 7.0710678118654755, 10.0, 14.142135623730951]}
+{"prob_id": "prob_8634", "image_path": "images/img_3254.png", "question": "Find m \\angle 4. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "64.000", "choices": [26.0, 32.0, 64.0, 78.0]}
+{"prob_id": "prob_8635", "image_path": "images/img_3419.png", "question": "Find the height of the trapezoid, in which Area = 280 cm^{2}. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "20.000", "choices": [20.0, 35.0, 50.0, 160.0]}
+{"prob_id": "prob_8644", "image_path": "images/img_173.png", "question": "For the pair of similar figures, the area of the blue figure is 32 cm^{2}, find the area of the green figure. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "12.500", "choices": [12.5, 20.0, 51.2, 81.9]}
+{"prob_id": "prob_8648", "image_path": "images/img_630.png", "question": "Find the area of the triangle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "84.000", "choices": [40.0, 84.0, 85.0, 105.0]}
+{"prob_id": "prob_8665", "image_path": "images/img_1417.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.657", "choices": [5.656854249492381, 6.928203230275509, 8.0, 8.94427190999916]}
+{"prob_id": "prob_8676", "image_path": "images/img_860.png", "question": "In rectangle PLCM, LC = 19, and LM = 23. Find TC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.500", "choices": [9.5, 11.5, 12.961, 19.0]}
+{"prob_id": "prob_8677", "image_path": "images/img_2185.png", "question": "Find the measure of \\angle 3 in the rhombus. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [30.0, 60.0, 75.0, 90.0]}
+{"prob_id": "prob_8679", "image_path": "images/img_1720.png", "question": "Find y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.745", "choices": [4.898979485566356, 5.744562646538029, 5.830951894845301, 6.6332495807108]}
+{"prob_id": "prob_8680", "image_path": "images/img_1831.png", "question": "If MNPQ \\sim XYZW, find the perimeter of XYZW. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.000", "choices": [17.0, 18.0, 20.0, 34.0]}
+{"prob_id": "prob_8682", "image_path": "images/img_3192.png", "question": "What is the measure of \\widehat FA? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "58.000", "choices": [58.0, 140.0, 158.0, 182.0]}
+{"prob_id": "prob_8685", "image_path": "images/img_3679.png", "question": "Find m \\angle 7. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "65.000", "choices": [32.5, 65.0, 115.0, 230.0]}
+{"prob_id": "prob_8699", "image_path": "images/img_2198.png", "question": "In \\triangle PQR, NQ = 6, RK = 3, and PK = 4. Solve for the length of NK. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "2.000", "choices": [2.0, 2.667, 6.0, 9.0]}
+{"prob_id": "prob_8701", "image_path": "images/img_1617.png", "question": "Find the value of x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [3.5, 7.0, 14.0, 86.5]}
+{"prob_id": "prob_8702", "image_path": "images/img_404.png", "question": "AE, BF, and CG are medians. Find CG. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.000", "choices": [6.0, 12.0, 12.0, 18.0]}
+{"prob_id": "prob_8713", "image_path": "images/img_640.png", "question": "Find x. Perimeter = 41 yards. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "6.000", "choices": [5.375, 6.0, 6.833, 7.0]}
+{"prob_id": "prob_8724", "image_path": "images/img_2984.png", "question": "Find the length of \\widehat WN if \\triangle IWN is equilateral and WN = 5. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "5.236", "choices": [1.8849555921538759, 5.235987755982989, 15.707963267948966, 31.41592653589793]}
+{"prob_id": "prob_8740", "image_path": "images/img_2562.png", "question": "Determine the area of the circle. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "314.159", "choices": [62.832, 314.159, 1186.824, 1256.637]}
+{"prob_id": "prob_8742", "image_path": "images/img_1042.png", "question": "In \\odot S, m \\angle TSR = 42. Find m \\widehat ERT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "180.000", "choices": [42.0, 84.0, 138.0, 180.0]}
+{"prob_id": "prob_8746", "image_path": "images/img_2355.png", "question": "JKMN is a rectangle. If NQ = 2x+3 and QK = 5x-9, find QM. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "11.000", "choices": [5.5, 11.0, 15.556, 22.0]}
+{"prob_id": "prob_8749", "image_path": "images/img_2588.png", "question": "Find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "28.168", "choices": [22.1, 23.4, 26.3, 28.2]}
+{"prob_id": "prob_8750", "image_path": "images/img_2528.png", "question": "If MD = 7, find RI. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "14.000", "choices": [7.0, 14.0, 21.0, 28.0]}
+{"prob_id": "prob_8759", "image_path": "images/img_2015.png", "question": "isosceles trapezoid TWYZ with m \\angle Z = m \\angle Y, m \\angle Z = 30x, m \\angle T = m \\angle W, and m \\angle T = 20x, find m \\angle T. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "72.000", "choices": [62.0, 72.0, 108.0, 118.0]}
+{"prob_id": "prob_8778", "image_path": "images/img_3951.png", "question": "PACE is a parallelogram and m \\angle PAC = 124. What is the measurement of \\angle ECA? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "56.000", "choices": [41.462, 48.538, 56.0, 124.0]}
+{"prob_id": "prob_8802", "image_path": "images/img_2094.png", "question": "Find the perimeter of \\triangle STU. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "31.000", "choices": [31.0, 62.0, 76.0, 77.0]}
+{"prob_id": "prob_8805", "image_path": "images/img_3764.png", "question": "Quadrilateral ABCD is a rhombus. If m \\angle BCD = 120, find m \\angle DAC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "60.000", "choices": [30.0, 60.0, 90.0, 120.0]}
+{"prob_id": "prob_8809", "image_path": "images/img_3951.png", "question": "PACE is a parallelogram and m \\angle PAC = 124. What is the length of RE? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "3.500", "choices": [3.5, 6.6, 7.47, 14.94]}
+{"prob_id": "prob_8812", "image_path": "images/img_79.png", "question": "Find the value of variable y. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.962", "choices": [3.611, 4.792, 7.962, 9.97]}
+{"prob_id": "prob_8831", "image_path": "images/img_2513.png", "question": "Find the value of b. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "70.000", "choices": [55.0, 70.0, 110.0, 125.0]}
+{"prob_id": "prob_8832", "image_path": "images/img_1415.png", "question": "PQ = QR = RS. Solve for the length of XW. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "4.500", "choices": [3.0, 4.5, 6.75, 9.0]}
+{"prob_id": "prob_8853", "image_path": "images/img_1087.png", "question": "Find m \\angle N. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "102.000", "choices": [78.0, 86.4, 102.0, 108.857]}
+{"prob_id": "prob_8854", "image_path": "images/img_3098.png", "question": "Find CA. Assume that segments that appear tangent to circles are tangent. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "29.000", "choices": [14.5, 29.0, 41.012, 58.0]}
+{"prob_id": "prob_8858", "image_path": "images/img_3597.png", "question": "If RS = 15 and ST = 9, find RT. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "24.000", "choices": [6.0, 15.0, 21.0, 24.0]}
+{"prob_id": "prob_8887", "image_path": "images/img_1555.png", "question": "RP = 3.5 and JP = 9. Find PL. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.000", "choices": [3.5, 4.5, 7.0, 9.0]}
+{"prob_id": "prob_8894", "image_path": "images/img_627.png", "question": "In \\odot E, EG = EF. Find FC. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "13.500", "choices": [13.5, 27.0, 30.187, 54.0]}
+{"prob_id": "prob_8900", "image_path": "images/img_2869.png", "question": "Find PN. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [25.0, 30.0, 50.0, 60.0]}
+{"prob_id": "prob_8904", "image_path": "images/img_3900.png", "question": "BD bisects \\angle ABF. If m \\angle ABF = 3x-8 and m \\angle ABD = x+14, find m \\angle CBF. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "80.000", "choices": [50.0, 80.0, 100.0, 130.0]}
+{"prob_id": "prob_8926", "image_path": "images/img_1795.png", "question": "In ABCD, m \\angle ABC = 79, BC = 62.4, and BD = 75. Find the measurement of \\angle CDA. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "79.000", "choices": [11.0, 79.0, 101.0, 158.0]}
+{"prob_id": "prob_8928", "image_path": "images/img_1131.png", "question": "Find TY. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "7.500", "choices": [5.0, 7.5, 10.0, 12.5]}
+{"prob_id": "prob_8930", "image_path": "images/img_2221.png", "question": "Find m \\angle MNP. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "130.000", "choices": [40.0, 50.0, 130.0, 140.0]}
+{"prob_id": "prob_8946", "image_path": "images/img_176.png", "question": "Find the perimeter of the polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "17.534", "choices": [16.0, 17.534, 17.602, 19.602]}
+{"prob_id": "prob_8948", "image_path": "images/img_1479.png", "question": "What is the length of \\widehat BD? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "18.064", "choices": [10.21, 15.551, 18.064, 22.934]}
+{"prob_id": "prob_8952", "image_path": "images/img_2065.png", "question": "MN \\parallel BC. Solve for x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "9.000", "choices": [6.0, 9.0, 12.0, 15.0]}
+{"prob_id": "prob_8963", "image_path": "images/img_2860.png", "question": "Use \\triangle MAN with right angle N to express ratio of \\tan M if m = 21, a = 28, n = 35. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "0.750", "choices": [0.6, 0.75, 1.0, 1.333]}
+{"prob_id": "prob_8965", "image_path": "images/img_1410.png", "question": "m \\angle 11 = x+40, m \\angle 12 = x+10, m \\angle 13 = 3x+30, what is the measure of \\angle 12? Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "30.000", "choices": [15.0, 30.0, 60.0, 90.0]}
+{"prob_id": "prob_8968", "image_path": "images/img_2558.png", "question": "PR and QT are diameters of \\odot A. Solve for the measure of \\widehat UPQ. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "130.000", "choices": [130.0, 140.0, 180.0, 320.0]}
+{"prob_id": "prob_8988", "image_path": "images/img_1204.png", "question": "Circle O has a radius of 13 inches. Radius OB is perpendicular to chord CD which is 24 inches long. Find XB. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "8.000", "choices": [5.0, 8.0, 10.0, 12.0]}
+{"prob_id": "prob_8994", "image_path": "images/img_889.png", "question": "For the pair of similar figures, the area of the blue figure is 72 m^{2} and the green figure is 50 m^{2}, find x. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "10.000", "choices": [8.3, 10.0, 14.4, 17.3]}
+{"prob_id": "prob_9003", "image_path": "images/img_552.png", "question": "Find the perimeter of the polygon. Please first convert the diagram to sematic sequences. Then, solve the problem.", "dataset_name": "PGPS9k", "ground_truth": "34.409", "choices": [20.0, 24.0, 28.0, 34.409]}