| {"image_path": "./Geo170K/images/test/0.png", "question": "As shown in the figure, in triangle ABC, it is known that angle A = 80.0, angle B = 60.0, DE parallel BC, then the size of angle CED is ()", "ground_truth": "140\u00b0"} | |
| {"image_path": "./Geo170K/images/test/1.png", "question": "As shown in the figure, AB parallel CD, straight line EF intersects AB at point E, intersects CD at point F, EG bisects angle BEF, and it intersects CD at point G, angle 1 = 50.0, then angle 2 is equal to ()", "ground_truth": "65\u00b0"} | |
| {"image_path": "./Geo170K/images/test/2.png", "question": "As shown in the figure, BD bisects angle ABC, CD parallel AB, if angle BCD = 70.0, then the degree of angle CDB is ()", "ground_truth": "55\u00b0"} | |
| {"image_path": "./Geo170K/images/test/3.png", "question": "As shown in the figure, AB ia tangent to circle O at point B, and the extended line of AO intersects circle O at point C. Connect BC, if angle A = 36.0, then angle C is equal to ()", "ground_truth": "27\u00b0"} | |
| {"image_path": "./Geo170K/images/test/4.png", "question": "As shown in the figure, straight lines a and b intersect at point O. If angle 1 is equal to 50.0, then angle 2 is equal to ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/5.png", "question": "As shown in the figure, AB // CD, and EF intersects AB and CD at points E, F, angle 1 = 50.0, then the degree of angle 2 is ()", "ground_truth": "130\u00b0"} | |
| {"image_path": "./Geo170K/images/test/6.png", "question": "As shown in the figure, triangle ABC congruent triangle ADE, if angle B = 70.0, angle C = 30.0, angle DAC = 35.0, then the degree of angle EAC is ()", "ground_truth": "45\u00b0"} | |
| {"image_path": "./Geo170K/images/test/7.png", "question": "As shown in the figure, triangle ABC congruent triangle DEF, points A and D, B and E are the corresponding vertices, and the measured BC = 5.0, BF = 7.0, then the length of EC is ()", "ground_truth": "3cm"} | |
| {"image_path": "./Geo170K/images/test/8.png", "question": "As shown in the figure, in triangle ABC, angle C = 90.0, AC = BC, AD bisects angle CAB and it intersects BC at D, DE perpendicular AB at E, if AB = 6.0, then the perimeter of triangle DBE is ()", "ground_truth": "6cm"} | |
| {"image_path": "./Geo170K/images/test/9.png", "question": "As shown in the figure, in triangle ABC, AB = AC, angle A = 36.0, the perpendicular bisector of AB intersects AC at D, and intersects AB at E, then the degree of angle BDC is ()", "ground_truth": "72\u00b0"} | |
| {"image_path": "./Geo170K/images/test/10.png", "question": "As shown in the figure, in triangle ABC, angle C = 36.0, rotate triangle ABC anticlockwise around point A by 60.0 to get triangle AED, AD and BC intersect at point F, then the degree of angle AFC is ()", "ground_truth": "84\u00b0"} | |
| {"image_path": "./Geo170K/images/test/11.png", "question": "As shown in the figure, the straight line AB parallel CD, Rttriangle DEF is placed as shown, angle EDF = 90.0, if angle 1 + angle F = 70.0, then the degree of angle 2 is ()", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/12.png", "question": "As shown in the figure, AB parallel EF, CD perpendicular EF, angle BAC = 50.0, then angle ACD = ()", "ground_truth": "140\u00b0"} | |
| {"image_path": "./Geo170K/images/test/13.png", "question": "As shown in the figure, triangle ABC is the inscribed triangle of circle O, angle OAB = 35.0, then the degree of angle ACB is ()", "ground_truth": "55\u00b0"} | |
| {"image_path": "./Geo170K/images/test/14.png", "question": "Place the ruler and the right triangle board as shown in the figure (angle ACB is a right angle), it is known that angle 1 = 30.0, then the size of angle 2 is ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/15.png", "question": "As shown in the figure, the straight line a and the straight line b are intercepted by the straight line c, b perpendicular c, the foot of perpendicular is the point A, angle 1 = 70.0. If the line b is parallel to the line a, the line b can be rotated () clockwise around the point A", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/16.png", "question": "As shown in the figure, in circle O, chord AC parallel radius OB, angle BOC = 50.0, then the degree of angle OAB is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/17.png", "question": "In \u25a1ABCD, the diagonal AC and BD intersect at point O, angle DAC = 42.0, angle CBD = 23.0, then angle COD is ().", "ground_truth": "65\u00b0"} | |
| {"image_path": "./Geo170K/images/test/18.png", "question": "The positions of straight lines a, b, c, and d are shown in the figure. If angle 1 = 58.0, angle 2 = 58.0, angle 3 = 70.0, then angle 4 is equal to ()", "ground_truth": "110\u00b0"} | |
| {"image_path": "./Geo170K/images/test/19.png", "question": "As shown in the figure, a parallel b, angle 1 = 158.0, angle 2 = 42.0, angle 4 = 50.0. Then angle 3 = ()", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/20.png", "question": "As shown in the figure, AB is the diameter of circle O, C and D are two points on circle O. Connect AC, BC, CD, and OD respectively. If angle DOB = 140.0, then angle ACD = ()", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/21.png", "question": "As shown in the figure, it is known that angle 1 = angle 2 = angle 3 = 55.0, then the degree of angle 4 is ()", "ground_truth": "125\u00b0"} | |
| {"image_path": "./Geo170K/images/test/22.png", "question": "As shown in the figure, in the diamond ABCD, M and N are respectively AB and CD, and AM = CN, MN and AC intersect at point O. Connect BO. If angle DAC = 28.0, then the degree of angle OBC is ()", "ground_truth": "62\u00b0"} | |
| {"image_path": "./Geo170K/images/test/23.png", "question": "As shown in the figure, PA and PB are tangent to circle O at A and B respectively. If angle C = 65.0, then the degree of angle P is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/24.png", "question": "As shown in the figure, the line a parallel b and they intersect the line c at a and b respectively, angle 1 = 50.0, then the degree of angle 2 is ()", "ground_truth": "130\u00b0"} | |
| {"image_path": "./Geo170K/images/test/25.png", "question": "As shown in the figure, EF parallel BC, AC bisects angle BAF, angle B = 50.0, then the degree of angle C is ()", "ground_truth": "65\u00b0"} | |
| {"image_path": "./Geo170K/images/test/26.png", "question": "As shown in the figure, in order to measure the height of the school flagpole, Xiaodong uses a bamboo pole with a length of 3.2 as a measuring tool, and moves the bamboo pole so that the top of the bamboo pole and the shadow of the top of the flag pole fall on the same point on the ground. At this time, the distance between the bamboo pole and this point is 8.0 , 22.0 from the flagpole, the height of the flagpole is ().", "ground_truth": "12"} | |
| {"image_path": "./Geo170K/images/test/27.png", "question": "As shown in the figure, when planting trees on flat ground, the plant spacing (the horizontal distance between two adjacent trees) is required to be 4.0. If trees are planted on a hillside with a slope of 0.75, and the plant spacing is also required to be 4.0, then the slope distance between two adjacent trees is ()", "ground_truth": "5m"} | |
| {"image_path": "./Geo170K/images/test/28.png", "question": "As shown in the figure, the right triangle ABC and the equilateral triangle ABD are respectively drawn with the line segment AB as the edge, where angle ACB = 90.0. Connect CD, when the length of CD is the largest, the size of angle CAB is ()", "ground_truth": "45\u00b0"} | |
| {"image_path": "./Geo170K/images/test/29.png", "question": "As shown in the figure, D is the intersection point of the angular bisector BD and CD of triangle ABC. If angle A = 50.0, then angle D = ()", "ground_truth": "115\u00b0"} | |
| {"image_path": "./Geo170K/images/test/30.png", "question": "As shown in the figure, it is known that OA = OB = OC and angle ACB = 30.0, then the size of angle AOB is ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/31.png", "question": "As shown in the figure, the straight line a parallel b, the point B is on the straight line b, and AB perpendicular BC, angle 2 = 65.0, then the degree of angle 1 is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/32.png", "question": "Circle I is the inscribed circle of triangle ABC, D, E, F are 3.0 tangent points, if angle DEF = 52.0, then the degree of angle A is ()", "ground_truth": "76\u00b0"} | |
| {"image_path": "./Geo170K/images/test/33.png", "question": "As shown in the figure, the straight line AB parallel CD, angle 1 = 136.0, angle E is a right angle, then angle C is equal to ()", "ground_truth": "46\u00b0"} | |
| {"image_path": "./Geo170K/images/test/34.png", "question": "As shown in the figure, the straight lines AB and CD are intercepted by the straight line EF. If AB parallel CD, angle 1 = 100.0, then the size of angle 2 is ()", "ground_truth": "80\u00b0"} | |
| {"image_path": "./Geo170K/images/test/35.png", "question": "As shown in the figure: AB parallel DE, angle B = 30.0, angle C = 110.0, the degree of angle D is ()", "ground_truth": "100\u00b0"} | |
| {"image_path": "./Geo170K/images/test/36.png", "question": "As shown in the figure, AB is the diameter of circle O, point C is on circle O, passing point C to draw the tangent of circle O and it intersects the extended line of AB at point D. Connect AC. If angle D = 50.0, then the degree of angle A is ()", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/37.png", "question": "As shown in the figure, AB parallel CD, CP intersects AB at O, AO = PO, if angle C = 50.0, then the degree of angle A is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/38.png", "question": "As shown in the figure, in triangle ABC, AB = AC, passing point A to draw AD parallel BC. If angle 1 = 70.0, then the size of angle BAC is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/39.png", "question": "Fold a rectangular piece of paper with equal width as shown in the figure. If angle 1 = 140.0, then the degree of angle 2 is ()", "ground_truth": "110\u00b0"} | |
| {"image_path": "./Geo170K/images/test/40.png", "question": "As shown in the figure, it is known that the straight lines a and b are intercepted by the straight line c, a parallel b, angle 1 = 50.0, then angle 2 = ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/41.png", "question": "The positions of straight lines a, b, c, and d are shown in the figure. If angle 1 = 100.0, angle 2 = 100.0, angle 3 = 125.0, then angle 4 is equal to ()", "ground_truth": "55\u00b0"} | |
| {"image_path": "./Geo170K/images/test/42.png", "question": "The figure is a schematic diagram of a kite stand made by Xiao Liu. It is known that BC parallel PQ, AB: AP = 2.0:5.0, AQ = 20.0, then the length of CQ is ()", "ground_truth": "12cm"} | |
| {"image_path": "./Geo170K/images/test/43.png", "question": "As shown in the figure, triangle ODC is the figure obtained by rotating triangle OAB clockwise around point O by 30.0. If point D happens to fall on AB, and the degree of angle AOC is 100.0, then the degree of angle DOB is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/44.png", "question": "As shown in the figure, the two street lamps A and B are separated by 30.0. One night, when Xiaogang went straight 25.0 from the bottom of street lamp A to the bottom of street lamp B, he found that the top of his figure just touched the bottom of street lamp B. It is known that Xiaogang's height is 1.5, then the height of the street lamp is ()", "ground_truth": "9\u7c73"} | |
| {"image_path": "./Geo170K/images/test/45.png", "question": "As shown in the figure, C is a point on circle O, O is the center of the circle, if angle C = 35.0, then the degree of angle AOB is ()", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/46.png", "question": "As shown in the figure, if AB parallel CD, angle A = 70.0, then the degree of angle 1 is ()", "ground_truth": "110\u00b0"} | |
| {"image_path": "./Geo170K/images/test/47.png", "question": "As shown in the figure, the straight line AB parallel CD, angle C = 44.0, angle E is a right angle, then angle 1 is equal to ()", "ground_truth": "134\u00b0"} | |
| {"image_path": "./Geo170K/images/test/48.png", "question": "As shown in the figure, A, B, C are any three points on circle O, if angle BOC = 100.0, then the degree of angle BAC is ()", "ground_truth": "130\u00b0"} | |
| {"image_path": "./Geo170K/images/test/49.png", "question": "As shown in the figure, in the inscribed pentagon ABCDE of circle O, angle CAD = 35.0, angle AED = 115.0, then the degree of angle B is ()", "ground_truth": "100\u00b0"} | |
| {"image_path": "./Geo170K/images/test/50.png", "question": "As shown in the figure, in triangle ABC, angle C = 90.0, AD is the bisector of angle BAC, DE perpendicular AB at E, if DE = 8.0, DB = 10.0, then BC is equal to ()", "ground_truth": "18cm"} | |
| {"image_path": "./Geo170K/images/test/51.png", "question": "As shown in the figure, the straight lines AB and CD intersect at point O, EO perpendicular AB, and the foot of perpendicular is point O, angle BOD = 50.0, then angle COE = ()", "ground_truth": "140\u00b0"} | |
| {"image_path": "./Geo170K/images/test/52.png", "question": "As shown in the figure, the points B, E, C, and F are on the same straight line, triangle ABC congruent triangle DEF, angle B = 45.0, angle F = 65.0, then the degree of angle COE is ()", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/53.png", "question": "As shown in the figure, put the two vertices of a right triangle plate with 45.0 angles on the opposite edges of the ruler. If angle 1 = 27.5, then angle 2 is equal to ()", "ground_truth": "17.5\u00b0"} | |
| {"image_path": "./Geo170K/images/test/54.png", "question": "As shown in the figure, the straight line a parallel b, the point B is on the straight line b, and AB perpendicular BC, angle 1 = 55.0, then the degree of angle 2 is ()", "ground_truth": "35\u00b0"} | |
| {"image_path": "./Geo170K/images/test/55.png", "question": "As shown in the figure, the straight line a parallel b, the straight line c intersects a and b, angle 1 = 55.0, then angle 2 = ()", "ground_truth": "55\u00b0"} | |
| {"image_path": "./Geo170K/images/test/56.png", "question": "Place a ruler and a triangular plate as shown in the figure, angle 1 = 40.0, then the degree of angle 2 is ()", "ground_truth": "130\u00b0"} | |
| {"image_path": "./Geo170K/images/test/57.png", "question": "As shown in the figure, the straight lines AB and CD intersect at point O, and the radial OM bisects angle AOC, ON perpendicular OM. If angle AOC = 70.0, then the degree of angle CON is ()", "ground_truth": "55\u00b0"} | |
| {"image_path": "./Geo170K/images/test/58.png", "question": "As shown in the figure, the diameter CD of circle O crosses the midpoint G of chord EF, angle DCF = 20.0, then angle EOD is equal to ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/59.png", "question": "As shown in the figure, AB is parallel to CD, if angle B = 20.0, then angle C is ()", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/60.png", "question": "As shown in the figure, AB parallel CD, angle CED = 90.0, angle AEC = 35.0, then the size of angle D is ()", "ground_truth": "55\u00b0"} | |
| {"image_path": "./Geo170K/images/test/61.png", "question": "As shown in the figure, AB parallel CD, AD bisects angle BAC, and angle C = 80.0, then the degree of angle D is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/62.png", "question": "As shown in the figure, AB parallel CD, if angle 2 = 135.0, then the degree of angle 1 is ()", "ground_truth": "45\u00b0"} | |
| {"image_path": "./Geo170K/images/test/63.png", "question": "As shown in the figure, AB parallel CD, point E is on BC, and CD = CE, angle D = 74.0, then the degree of angle B is ()", "ground_truth": "32\u00b0"} | |
| {"image_path": "./Geo170K/images/test/64.png", "question": "As shown in the figure, AB parallel CD, point E is on the extended line of CA. If angle BAE = 40.0, then the size of angle ACD is ()", "ground_truth": "140\u00b0"} | |
| {"image_path": "./Geo170K/images/test/65.png", "question": "As shown in the figure, use the benchmark BE to measure the height of the tree CD. If the length of the benchmark BE is 2.0, AB = 3.0, AC = 9.0, and the points A, E, and D are on a straight line, then the tree CD is ()", "ground_truth": "6\u7c73"} | |
| {"image_path": "./Geo170K/images/test/66.png", "question": "After filling some oil in a cylindrical oil tank with a diameter of 200.0, the cross section is shown in the figure. If the width of the oil surface AB = 160.0, the maximum depth of oil is ()", "ground_truth": "40cm"} | |
| {"image_path": "./Geo170K/images/test/67.png", "question": "As shown in the figure, angle 1 = angle 2, angle 3 = 30.0, then angle 4 is equal to ()", "ground_truth": "150\u00b0"} | |
| {"image_path": "./Geo170K/images/test/68.png", "question": "As shown in the figure, AB parallel CD, angle B = 20.0, angle D = 60.0, then the degree of angle BED is ()", "ground_truth": "80\u00b0"} | |
| {"image_path": "./Geo170K/images/test/69.png", "question": "As shown in the figure, the straight line AB parallel CD, AE bisects angle CAB, angle ACD = 40.0, then the degree of angle AEC is ()", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/70.png", "question": "Xuan Xuan and Kai Kai are in the same mathematics study group. In a math activity class, they each used a square piece of paper with a side length of 12.0 to make a pair of jigsaw puzzles, and cooperated to design the work shown in the picture. Help them calculate the sum of the area of \u200b\u200bthe three figures circled in the figure, it is ()", "ground_truth": "36cm"} | |
| {"image_path": "./Geo170K/images/test/71.png", "question": "As shown in the figure, the straight line a parallel b, angle 2 = 35.0, angle 3 = 40.0, then the degree of angle 1 is ()", "ground_truth": "105\u00b0"} | |
| {"image_path": "./Geo170K/images/test/72.png", "question": "As shown in the figure, BD is the angular bisector of triangle ABC, AE perpendicular BD, and the foot of perpendicular is F. If angle ABC = 35.0, angle C = 50.0, then the degree of angle CDE is ()", "ground_truth": "45\u00b0"} | |
| {"image_path": "./Geo170K/images/test/73.png", "question": "As shown in the figure, the straight line AD parallel BC, if angle 1 = 42.0, angle BAC = 78.0, then the degree of angle 2 is ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/74.png", "question": "As shown in the figure, the perimeter of \u25a1ABCD is 16.0, AC and BD intersect at point O, and OE perpendicular AC and it intersects AD at point E, then the perimeter of triangle DCE is ()", "ground_truth": "8cm"} | |
| {"image_path": "./Geo170K/images/test/75.png", "question": "As shown in the figure, triangle ABC is the inscribed triangle of circle O. If angle ABC = 70.0, then the degree of angle AOC is equal to ()", "ground_truth": "140\u00b0"} | |
| {"image_path": "./Geo170K/images/test/76.png", "question": "As shown in the figure, AB parallel CD, radial AE intersects CD at point F, if angle 1 = 115.0, then the degree of angle 2 is ()", "ground_truth": "65\u00b0"} | |
| {"image_path": "./Geo170K/images/test/77.png", "question": "As shown in the figure, a // b, put the right-angled vertex of a triangular plate on the straight line a, angle 1 = 42.0, then the degree of angle 2 is ()", "ground_truth": "48\u00b0"} | |
| {"image_path": "./Geo170K/images/test/78.png", "question": "As shown in the figure, a parallel b, point B is on the straight line b, and AB perpendicular BC, angle 1 = 36.0, then angle 2 = ()", "ground_truth": "54\u00b0"} | |
| {"image_path": "./Geo170K/images/test/79.png", "question": "As shown in the figure, if angle 1 = angle 3, angle 2 = 60.0, then the degree of angle 4 is ()", "ground_truth": "120\u00b0"} | |
| {"image_path": "./Geo170K/images/test/80.png", "question": "As shown in the figure, AB parallel CD, AE bisects angle CAB and CD at point E, if angle C = 70.0, then the degree of angle AED is ()", "ground_truth": "125\u00b0"} | |
| {"image_path": "./Geo170K/images/test/81.png", "question": "As shown in the figure, the perimeter of parallelogram ABCD is 32.0, AC, BD intersect at point O, and OE perpendicular AC and it intersects AD at point E, then the perimeter of triangle DCE is ()", "ground_truth": "16cm"} | |
| {"image_path": "./Geo170K/images/test/82.png", "question": "As shown in the figure, a cylinder with a bottom circumference of 24.0 and a height of 5.0, the shortest route that an ant passes along the surface from point A to point B is ()", "ground_truth": "13m"} | |
| {"image_path": "./Geo170K/images/test/83.png", "question": "As shown in the figure, in triangle ABC, angle BAC = 90.0, AD perpendicular BC at point D, AE bisects angle DAC, angle B = 50.0, so the degree of angle DAE is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/84.png", "question": "As shown in the figure, the line l parallel m parallel n, the vertices B and C of the triangle ABC are on the line n and line m, the angle between BC and the line n is 25.0, and angle ACB = 60.0, then the degree of angle a is ()", "ground_truth": "35\u00b0"} | |
| {"image_path": "./Geo170K/images/test/85.png", "question": "As shown in the figure, it is known that in circle O, the central angle angle AOB = 100.0, then the angle of circumference angle ACB is equal to ().", "ground_truth": "130\u00b0"} | |
| {"image_path": "./Geo170K/images/test/86.png", "question": "As shown in the figure, triangle ABC is inscribed in circle O with radius 1.0, if angle BAC = 60.0, then the length of BC is ()", "ground_truth": "\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/87.png", "question": "As shown in the figure, the circle O is the circumscribed circle of triangle ABC, and the bisector of angle BAC and angle ABC intersects at point I. Extend AI and it intersects circle O at point D. Connect BD and DC. If the radius of circle O is 8.0, angle BAC = 120.0, then the length of DI is ()", "ground_truth": "8\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/88.png", "question": "As shown in the figure, circle O is the circumscribed circle of triangle ABC. Connect OB and OC, if the radius of circle O is 2.0, angle BAC = 60.0, then the length of BC is ()", "ground_truth": "2\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/89.png", "question": "As shown in the figure, AB and CD are the two diameters of circle O, chord DE parallel AB, arc DE is the arc of 50.0, then angle BOC is ()", "ground_truth": "115\u00b0"} | |
| {"image_path": "./Geo170K/images/test/90.png", "question": "As shown in the figure, points A, B, and C are on circle O, angle ABO = 22.0, angle ACO = 42.0, then angle BOC is equal to ()", "ground_truth": "128\u00b0"} | |
| {"image_path": "./Geo170K/images/test/91.png", "question": "As shown in the figure, A, B, C are three points on circle O, angle ACB = 25.0, then the degree of angle BAO is ()", "ground_truth": "65\u00b0"} | |
| {"image_path": "./Geo170K/images/test/92.png", "question": "As shown in the figure, it is known that in circle O, angle AOB = 50.0, then the degree of the angle of circumference angle ACB is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/93.png", "question": "As shown in the figure, AB is the diameter of circle O, C and D are two points on circle O, angle BAC = 30.0, arc AD = arc CD. Then angle DAC is equal to ()", "ground_truth": "30\u00b0"} | |
| {"image_path": "./Geo170K/images/test/94.png", "question": "As shown in the figure, AB is the diameter of circle O, C and D are two points on the circle, angle D = 34.0, then the degree of angle BOC is ()", "ground_truth": "112\u00b0"} | |
| {"image_path": "./Geo170K/images/test/95.png", "question": "As shown in the figure, points A, B, and C are all on circle O, when angle OBC = 40.0, the degree of angle A is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/96.png", "question": "As shown in the figure, the diameter AB of circle O is perpendicular to the chord CD, the foot of perpendicular is the point E, angle CAO = 22.5, OC = 6.0, then the length of CD is ()", "ground_truth": "6\u221a{2}"} | |
| {"image_path": "./Geo170K/images/test/97.png", "question": "As shown in the figure, in circle O, chord BC and radius OA intersect at point D. Connect AB and OC. If angle A = 60.0, angle ADC = 90.0, then the degree of angle C is ()", "ground_truth": "30\u00b0"} | |
| {"image_path": "./Geo170K/images/test/98.png", "question": "As shown in the figure, points A, B, and P are three points on circle O, if angle AOB = 40.0, then the degree of angle APB is ()", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/99.png", "question": "As shown in the figure, AB is the chord of circle O, OC perpendicular AB and it intersects circle O at point C. Connect OA, OB, BC, if angle ABC = 25.0, then the size of angle AOB is ()", "ground_truth": "100\u00b0"} | |
| {"image_path": "./Geo170K/images/test/100.png", "question": "As shown in the figure, given the angle of circumference angle A = 50.0, then the size of angle OBC is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/101.png", "question": "As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, angle ADC = 26.0, then the degree of angle CAB is ()", "ground_truth": "64\u00b0"} | |
| {"image_path": "./Geo170K/images/test/102.png", "question": "As shown in the figure, in circle O, AB is the diameter, CD is the chord, AB perpendicular CD, the foot of perpendicular is the point E. Connect CO and AD, if angle BOC = 30.0, then the degree of angle BAD is ()", "ground_truth": "15\u00b0"} | |
| {"image_path": "./Geo170K/images/test/103.png", "question": "As shown in the figure, AB is the diameter of circle O, points C and D are two points on the circle, and angle AOC = 126.0, then angle CDB = ()", "ground_truth": "27\u00b0"} | |
| {"image_path": "./Geo170K/images/test/104.png", "question": "As shown in the figure, AB is the diameter of circle O, points C and D are on circle O, and point C is the midpoint of arc BD, passing point C to draw the perpendicular line EF of AD and it intersects straight line AD at point E, if the radius of circle O is 2.5, the length of AC is 4.0, then the length of CE is ()", "ground_truth": "\\frac{12}{5}"} | |
| {"image_path": "./Geo170K/images/test/105.png", "question": "As shown in the figure, the points A, B, and C are on circle O, and it is known that angle ABC = 130.0, then angle AOC = ()", "ground_truth": "100\u00b0"} | |
| {"image_path": "./Geo170K/images/test/106.png", "question": "As shown in the figure, it is known that the radius of circle O is 5.0, the central angles of chords AB and CD are angle AOB, angle COD, and angle AOB is complementary to angle COD, chord CD = 8.0, then the length of chord AB is ()", "ground_truth": "6"} | |
| {"image_path": "./Geo170K/images/test/107.png", "question": "As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, and the extended lines of AB and CD intersect at point E. Given that AB = 2 DE, angle E = 16.0, then the degree of angle ABC is ()", "ground_truth": "24\u00b0"} | |
| {"image_path": "./Geo170K/images/test/108.png", "question": "This question examines the theorem of angle of circumference, the key is to answer it based on the relationship between the central angle and the angle of circumference of the same chord. 4.0. As shown in the figure, AB is the diameter of circle O, C is the point on circle O (except A and B), angle AOD = 136.0, then the degree of angle C is ()", "ground_truth": "22\u00b0"} | |
| {"image_path": "./Geo170K/images/test/109.png", "question": "As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If angle BOD = 130.0, then the degree of angle ACD is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/110.png", "question": "Shaoxing is a famous bridge township. As shown in the figure, the distance CD from the top of the round arch bridge to the water surface is 8.0, and the arch radius OC is 5.0, so the width of the water surface AB is ()", "ground_truth": "8m"} | |
| {"image_path": "./Geo170K/images/test/111.png", "question": "As shown in the figure, it is known that angle \u03b1 = 130.0, then angle \u03b2 = ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/112.png", "question": "As shown in the figure, when the width of the water surface AB in the circular bridge hole is 8.0, the arc ACB is exactly a semicircle. When the water surface rises 1.0, the water surface width A\u2032B\u2032 in the bridge hole is ()", "ground_truth": "2\u221a{15}\u7c73"} | |
| {"image_path": "./Geo170K/images/test/113.png", "question": "In the right triangle ABC, angle CAB = 90.0, angle ABC = 72.0, AD is the angle bisector of angle CAB, and the intersection BC is at point D, and crossing point C is the high line CE on the AD side in triangle ACD, then the degree of angle ECD is ()", "ground_truth": "27\u00b0"} | |
| {"image_path": "./Geo170K/images/test/114.png", "question": "As shown in the figure, AO is the height of the cone, the bottom radius of the cone OB = 0.7, the length of AB is 2.5, then the length of AO is ()", "ground_truth": "2.4"} | |
| {"image_path": "./Geo170K/images/test/115.png", "question": "As shown in the figure, in circle O, chord AC and BD intersect at point E, arc AB = arc BC = arc CD, if angle BEC = 110.0, then angle BDC = ()", "ground_truth": "35\u00b0"} | |
| {"image_path": "./Geo170K/images/test/116.png", "question": "As shown in the figure, in the sector OAB with a radius of 1.0 and a central angle of 90.0, OA and OB are the diameters respectively as a semicircle, and the area of \u200b\u200bthe shaded part in the figure is ()", "ground_truth": "\\frac{1}{2}cm\u00b2"} | |
| {"image_path": "./Geo170K/images/test/117.png", "question": "Use a sector paper sheet with a central angle of 120.0 and a radius of 6.0 to roll into a conical bottomless paper cap (as shown in the picture), then the bottom perimeter of the paper cap is ()", "ground_truth": "4\u03c0cm"} | |
| {"image_path": "./Geo170K/images/test/118.png", "question": "The picture shows a small paper cap with a conical chimney. The length of its generatrix l is 13.0 and its height h is 12.0. The area of \u200b\u200bpaper required to make this paper cap is (the seams are ignored) ()", "ground_truth": "65\u03c0"} | |
| {"image_path": "./Geo170K/images/test/119.png", "question": "Use a sector piece of paper with a central angle of 120.0 and a radius of 3.0 to roll into a cone-shaped bottomless paper cap (as shown in the picture), then the height of the paper is ()", "ground_truth": "2\u221a{2}cm"} | |
| {"image_path": "./Geo170K/images/test/120.png", "question": "As shown in the figure, the expanded figure of the lateral surface of a cone is a semicircle with a radius of 10.0, then the radius of its bottom is ()", "ground_truth": "5"} | |
| {"image_path": "./Geo170K/images/test/121.png", "question": "As shown in the figure, use a sector cardboard with a radius of 24.0 to make a conical hat (the seams are ignored). If the radius of the bottom surface of the conical hat is 10.0, then the area of \u200b\u200bthis sector cardboard is ()", "ground_truth": "240\u03c0cm^{2}"} | |
| {"image_path": "./Geo170K/images/test/122.png", "question": "As shown in the figure, the length of the generatrix of the cone is 5.0, and the length of the height line is 4.0, then the bottom area of \u200b\u200bthe cone is ()", "ground_truth": "9\u03c0cm^{2}"} | |
| {"image_path": "./Geo170K/images/test/123.png", "question": "The production process of paper umbrellas in our country is very ingenious. As shown in the figure, whether the umbrella is opened or closed, the handle AP always bisects the angle angle BAC formed by the two ribs in the same plane, and AE = AF, DE = DF, so as to ensure that the umbrella ring can slide along the handle. When a toy umbrella is opened, the BDC is on the same straight line. If AB = 50.0, AD = 14.0, then the area of \u200b\u200boil paper required to make such a paper umbrella is (don't remember the seam) ()", "ground_truth": "2400\u03c0cm^{2}"} | |
| {"image_path": "./Geo170K/images/test/124.png", "question": "As shown in the figure, a sector with a central angle of 120.0 and a radius of 6.0 encloses the side of a cone (the joints are ignored), then the height of the cone is ()", "ground_truth": "4\u221a{2}"} | |
| {"image_path": "./Geo170K/images/test/125.png", "question": "As shown in the figure, in Rttriangle ABC, angle ACB = 90.0, AC = 4.0, BC = 3.0, rotate triangle ABC around the line where AC is located to obtain a rotating body, then the lateral area of \u200b\u200bthe rotating body is ()", "ground_truth": "15\u03c0"} | |
| {"image_path": "./Geo170K/images/test/126.png", "question": "As shown in the figure, cut a circle and a sector piece of paper on the paper so that it can form a cone model. If the radius of the circle is 1.0 and the central angle of the sector is equal to 90.0, then the radius of the sector is ()", "ground_truth": "4"} | |
| {"image_path": "./Geo170K/images/test/127.png", "question": "As shown in a sector iron sheet OAB, it is known that OA = 30.0, angle AOB = 120.0, the worker master combines OA and OB to form a conical chimney cap (the joints are ignored), then the radius of the bottom circle of the chimney cap is ()", "ground_truth": "10cm"} | |
| {"image_path": "./Geo170K/images/test/128.png", "question": "As shown in the figure, it is known that the radius of the bottom surface of the cone is 6.0, and the length of the generatrix is \u200b\u200b10.0, then the lateral area of \u200b\u200bthe cone is ()", "ground_truth": "60\u03c0"} | |
| {"image_path": "./Geo170K/images/test/129.png", "question": "Lulu cuts a circle and a sector piece of paper from the paper (as shown in the picture), and uses them to form a cone model. If the radius of the circle is 1.0. The central angle of the sector is equal to 120.0, then the radius of the sector is ()", "ground_truth": "3"} | |
| {"image_path": "./Geo170K/images/test/130.png", "question": "As shown in the figure, there is a sector with a central angle of 120.0 and a radius of 6.0. If OA and OB are overlapped to form a cone side, the diameter of the bottom of the cone is ()", "ground_truth": "4cm"} | |
| {"image_path": "./Geo170K/images/test/131.png", "question": "As shown in the picture, the length of the generatrix of the cone-shaped tent roof is AB = 10.0, the bottom radius is BO = 5.0, and the lateral area of \u200b\u200bthe cone-shaped tent roof (excluding the seams) is ()", "ground_truth": "50\u03c0m^{2}"} | |
| {"image_path": "./Geo170K/images/test/132.png", "question": "As shown in the figure, in circle O, the length of chord AB is 10.0, and the angle of circumference angle ACB = 45.0, then the diameter of the circle AD is ()", "ground_truth": "10\u221a{2}"} | |
| {"image_path": "./Geo170K/images/test/133.png", "question": "As shown in the figure, in triangle ABC. angle C = 90.0, point D is a moving point on BC (point D does not coincide with point C). The circle with CD as the diameter intersects AD at point P. If AC = 6.0. The minimum length of the line segment BP is 2.0. Then the length of AB is ()", "ground_truth": "2\u221a{13}"} | |
| {"image_path": "./Geo170K/images/test/134.png", "question": "As shown in the figure, in order to measure the height AB of a pavilion (the distance from the top A to the horizontal ground BD), Xiaoming placed a step DE (DE = BC = 0.6) that is the same height as the pavilion step BC beside the pavilion, find A, B, C Three points are collinear), place a mirror horizontally at point G on the platform, and measure CG = 12.0, and then move back along the straight line CG to point E. At this time, you can see the top A of the pavilion in the mirror, and measure GE = 2.0, Xiaoming's height EF = 1.6, then the height of the pavilion AB is approximately ()", "ground_truth": "10.2\u7c73"} | |
| {"image_path": "./Geo170K/images/test/135.png", "question": "As shown in the figure, in order to estimate the width of the Jing River, a target point P is selected on the opposite bank of the Jing River, and points Q and S are taken near the bank, so that the points P, Q, and S are in a straight line, and the straight line PS is perpendicular to the river. Choose an appropriate point T on the straight line a passing point S and perpendicular to PS. The intersection of PT and the straight line b passing point Q and perpendicular to PS is R. If QS = 60.0, ST = 120.0, QR = 80.0, then the width of the river PQ is ()", "ground_truth": "120m"} | |
| {"image_path": "./Geo170K/images/test/136.png", "question": "As shown in the picture, Xiaoying designed a flashlight to measure the height of an ancient city wall. Place a horizontal plane mirror at point P. The light starts from point A and is reflected by the plane mirror and hits the top C of the ancient city wall CD. It is known that AB perpendicular BD, CD perpendicular BD. And it is measured that AB = 1.4, BP = 2.1, PD = 12.0. Then the height of the ancient city wall CD is ()", "ground_truth": "8\u7c73"} | |
| {"image_path": "./Geo170K/images/test/137.png", "question": "As shown in the figure, in circle O, point M is the midpoint of arc AB. Connect MO and extend it to intersect circle O at point N, connect BN, if angle AOB = 140.0, then the degree of angle N is ()", "ground_truth": "35\u00b0"} | |
| {"image_path": "./Geo170K/images/test/138.png", "question": "As shown in the figure, in order to measure the degree of tree AB, a certain mathematics learning interest group measured the length of the tree's shadow BC in the sun as 9.0. At the same moment, they also measured the shadow length of Xiaoliang in the sun as 1.5. Knowing that Xiaoliang's height is 1.8, then the height of tree AB is ()", "ground_truth": "10.8m"} | |
| {"image_path": "./Geo170K/images/test/139.png", "question": "As shown in the picture, it is an ancient masher in the countryside. It is known that the height of the support column AB is 0.3, the length of the pedal DE is 1.0, and the distance from the support point A to the foot D is 0.6. When foot D touches the ground, the head point E rises ()", "ground_truth": "0.5\u7c73"} | |
| {"image_path": "./Geo170K/images/test/140.png", "question": "As shown in the figure, the light source P is directly above the crossbar AB, the shadow of AB under the light is CD, AB parallel CD, AB = 2.0, CD = 5.0, the distance between point P and CD is 3.0, then the distance between AB and CD is ().", "ground_truth": "\\frac{9}{5}"} | |
| {"image_path": "./Geo170K/images/test/141.png", "question": "As shown in the figure, Xiaoqiang made a small hole imaging device in which the length of the paper tube is 15.0. He prepared a candle with a length of 20.0. To get an image with a height of 4.0, the distance between the candle and the paper tube should be ()", "ground_truth": "75cm"} | |
| {"image_path": "./Geo170K/images/test/142.png", "question": "As shown in the figure, in a badminton game, Lin Dan, the athlete standing at M in the field, clicks the request from N to point B in the opponent. It is known that the net height OA = 1.52, OB = 4.0, OM = 5.0, then when Lin Dan takes off, the distance from the hitting point to the ground NM = ()", "ground_truth": "3.42m"} | |
| {"image_path": "./Geo170K/images/test/143.png", "question": "While measuring the height of the building, Xiao Ming first measured the shadow length BA of the building on the ground as 15.0 (as shown in the figure), and then set up a benchmark with a height of 2.0 at A, and measured the shadow length AC of the benchmark as 3.0, then the height of the building is ()", "ground_truth": "10\u7c73"} | |
| {"image_path": "./Geo170K/images/test/144.png", "question": "As shown in the figure: the length of two vertical telephone poles AB is 6.0, the length of CD is 3.0, AD intersects BC at point E, then the length of the distance from E to the ground EF is ()", "ground_truth": "2"} | |
| {"image_path": "./Geo170K/images/test/145.png", "question": "As shown in the figure, a square DEFG model should be cut on a piece of triangle ABC paper. Among them, G and F are on BC, D and E are on AB and AC respectively, AH perpendicular BC and it intersects DE at M, if BC = 12.0, AH = 8.0, then the edge length of the square DEFG is ()", "ground_truth": "\\frac{24}{5}cm"} | |
| {"image_path": "./Geo170K/images/test/146.png", "question": "On 27.0 2009.0, 10.0, 2009, Shanghai team player Wu Di came to the fore in the National Games and defeated the top-seeded men's singles player Zeng Shaoxuan with a score of 2.0:0.0, and won the men's singles championship in tennis at the National Games. The picture below is a ball played by Wu Di in the final. It is known that the net height is 0.8, and the horizontal distance from the hitting point to the net is 4.0. When the ball is played, the ball can hit the net and the landing point is exactly 6.0 away from the net. Then the height h of the racket hit is ()", "ground_truth": "\\frac{4}{3}\u7c73"} | |
| {"image_path": "./Geo170K/images/test/147.png", "question": "As shown in the figure, points A, B, and C are on circle O, angle ABO = 40.0, angle ACO = 30.0, then the degree of angle BOC is ()", "ground_truth": "140\u00b0"} | |
| {"image_path": "./Geo170K/images/test/148.png", "question": "As shown in the figure, AB is a ladder leaning against the wall, the foot of the ladder is away from the wall 2.0, the point D on the ladder is away from the wall 1.8, the length of BD is 0.6, then the length of the ladder is ()", "ground_truth": "6.00\u7c73"} | |
| {"image_path": "./Geo170K/images/test/149.png", "question": "In order to measure the height of the school flagpole AC, a school math interest group erected a benchmark DF with a length of 1.5 at point F. As shown in the figure, the length of the shadow EF of DF is measured as 1.0, and then measure the length of the shadow BC of the flagpole AC to be 6.0, then the height of the flagpole AC is ()", "ground_truth": "9\u7c73"} | |
| {"image_path": "./Geo170K/images/test/150.png", "question": "As shown in the figure, Xiaodong uses a bamboo pole with a length of 3.2 as a measuring tool to measure the height of the school flagpole, and moves the bamboo pole so that the shadow on the top of the pole and the flag pole falls on the same point on the ground. At this time, the distance between the bamboo pole and this point is 8.0, and the distance from the flag pole is 22.0, then the height of the flag pole is ()", "ground_truth": "12m"} | |
| {"image_path": "./Geo170K/images/test/151.png", "question": "As shown in the figure, CD is a plane mirror, the light is emitted from point A, reflected by point E on CD, and irradiated to point B. If the incident angle is \u03b1, AC perpendicular CD, BD perpendicular CD, the feet of perpendicular are C, D, and AC = 3.0, BD = 6.0, CD = 10.0, then the length of the line segment ED is ()", "ground_truth": "\\frac{20}{3}"} | |
| {"image_path": "./Geo170K/images/test/152.png", "question": "As shown in the figure, Xiaoming designed two right angles to measure the width of the river BC, he measured AB = 2.0, BD = frac {7.0}{3.0}, CE = 9.0, then the width of the river BC is ()", "ground_truth": "\\frac{40}{7}\u7c73"} | |
| {"image_path": "./Geo170K/images/test/153.png", "question": "As shown in the figure, a student saw a tree by the lake. He visually observed that the distance between himself and the tree is 20.0, and the reflection of the top of the tree in the water is 5.0 far away from him. The student's height is 1.7, and the height of the tree is ( ).", "ground_truth": "5.1"} | |
| {"image_path": "./Geo170K/images/test/154.png", "question": "As shown in the figure, AB is a fixed climbing ladder leaning on the wall, the distance from the foot of the ladder B to the foot of the wall C is 1.6, the distance from the point D on the ladder to the wall is 1.4, and the length of the ladder is 0.5, then the length of the ladder is ()", "ground_truth": "4m"} | |
| {"image_path": "./Geo170K/images/test/155.png", "question": "As shown in the figure, the sunlight enters the room from the windows of the classroom, the length of the shadow of the window frame AB on the ground DE = 1.8, the distance from the lower eaves of the window to the ground BC = 1.0, EC = 1.2, then the height of the window AB is ()", "ground_truth": "1.5m"} | |
| {"image_path": "./Geo170K/images/test/156.png", "question": "As shown in the figure, AB is a long ladder leaning on the wall, the foot of the ladder B is away from the wall 1.6, the point D on the ladder is away from the wall 1.4, the length of BD is 0.55, then the length of the ladder is ()", "ground_truth": "4.40\u7c73"} | |
| {"image_path": "./Geo170K/images/test/157.png", "question": "As shown in the figure, the student Xiao Li whose height is 1.6 wants to measure the height of the school's flagpole. When he stands at C, the shadow of the top of his head coincides with the shadow of the top of the flagpole, and AC = 2.0, BC = 8.0, then the height of the flagpole is ()", "ground_truth": "8\u7c73"} | |
| {"image_path": "./Geo170K/images/test/158.png", "question": "As shown in the figure, the quadrilateral ABCD and A\u2032B\u2032C\u2032D\u2032 are similar figures with the similar center at point O. If OA\u2032: A\u2032A = 2.0:1.0, the area of \u200b\u200bthe quadrilateral A\u2032B\u2032C\u2032D\u2032 is 12.0 ^ 2, then the area of \u200b\u200bthe quadrilateral ABCD is ()", "ground_truth": "27cm^{2}"} | |
| {"image_path": "./Geo170K/images/test/159.png", "question": "As shown in the figure, in triangle ABC, angle C = 90.0, if AC = 4.0, BC = 3.0, then cosB is equal to ()", "ground_truth": "\\frac{3}{5}"} | |
| {"image_path": "./Geo170K/images/test/160.png", "question": "As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, BC = 3.0, then the value of sinB is equal to ()", "ground_truth": "\\frac{4}{5}"} | |
| {"image_path": "./Geo170K/images/test/161.png", "question": "As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 3.0, BC = 4.0, then the value of cosA is ()", "ground_truth": "\\frac{3}{5}"} | |
| {"image_path": "./Geo170K/images/test/162.png", "question": "As shown in the figure, it is known that in Rttriangle ABC, angle C = 90.0, AB = 10.0, AC = 8.0, then the value of tanB is ()", "ground_truth": "\\frac{4}{3}"} | |
| {"image_path": "./Geo170K/images/test/163.png", "question": "As shown in the figure, the homothetic figures are composed of a triangle ruler and its center projection under the light. If the ratio of the distance from the bulb to the vertex of the triangle ruler to the distance from the bulb to the corresponding vertex of the triangular ruler projection is 2.0:5.0, and the length of one edge of the triangle ruler is 8.0, Then the corresponding edge length of the projection triangle is ()", "ground_truth": "20cm"} | |
| {"image_path": "./Geo170K/images/test/164.png", "question": "As shown in the figure, given the angle of circumference angle BAC = 40.0, then the degree of the central angle angle BOC is ()", "ground_truth": "80\u00b0"} | |
| {"image_path": "./Geo170K/images/test/165.png", "question": "As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, AB = 5.0, then the value of cosA is ()", "ground_truth": "\\frac{4}{5}"} | |
| {"image_path": "./Geo170K/images/test/166.png", "question": "As shown in the figure, in triangle ABC, angle C = Rtangle , AB = 5.0, AC = 4.0, then the value of sinA is ()", "ground_truth": "\\frac{3}{5}"} | |
| {"image_path": "./Geo170K/images/test/167.png", "question": "In Rttriangle ABC, angle C = 90.0, AB = 2.0, BC = 1.0, then the value of sinB is ()", "ground_truth": "\\frac{\u221a{3}}{2}"} | |
| {"image_path": "./Geo170K/images/test/168.png", "question": "As shown in the figure, in Rttriangle ABC, it is known that angle A = 90.0, AC = 3.0, AB = 4.0, then sinB is equal to ()", "ground_truth": "\\frac{3}{5}"} | |
| {"image_path": "./Geo170K/images/test/169.png", "question": "In Rttriangle ACB, angle C = 90.0, BC = 5.0, AC = 12.0, then sinA = ()", "ground_truth": "\\frac{5}{13}"} | |
| {"image_path": "./Geo170K/images/test/170.png", "question": "As shown in the figure, in the rectangular coordinate system, P is the point in the first quadrant, and its coordinates are (4.0,m), and the cosine value of the angle \u03b1 between OP and the positive semi-axis of the x-axis is frac {3.0}{5.0}, then the value of tanangle \u03b1 is ()", "ground_truth": "\\frac{4}{3}"} | |
| {"image_path": "./Geo170K/images/test/171.png", "question": "As shown in the figure, it is known that in Rttriangle ABC, angle C = 90.0, AC = 6.0, BC = 8.0, then the value of tanA is ()", "ground_truth": "\\frac{4}{3}"} | |
| {"image_path": "./Geo170K/images/test/172.png", "question": "As shown in the figure: In Rttriangle ABC, angle C = 90.0, AC = 8.0, AB = 10.0, then the value of sinB is equal to ()", "ground_truth": "\\frac{4}{5}"} | |
| {"image_path": "./Geo170K/images/test/173.png", "question": "As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 1.0, BC = 2.0, then the value of cosB is ()", "ground_truth": "\\frac{2\u221a{5}}{5}"} | |
| {"image_path": "./Geo170K/images/test/174.png", "question": "As shown in the figure, in the plane rectangular coordinate system, the coordinates of point A are (2.0,3.0), then the value of tan\u03b1 is ()", "ground_truth": "\\frac{3}{2}"} | |
| {"image_path": "./Geo170K/images/test/175.png", "question": "As shown in the figure, it is known that in Rttriangle ABC, angle C = 90.0, AC = 4.0, tanA = frac {1.0}{2.0}, then the length of BC is ()", "ground_truth": "2"} | |
| {"image_path": "./Geo170K/images/test/176.png", "question": "As shown in the figure, in ABC, AB = AC = 4.0, BC = 6.0, then cosB = ()", "ground_truth": "\\frac{3}{4}"} | |
| {"image_path": "./Geo170K/images/test/177.png", "question": "As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, AB = 5.0, then the value of sinB is ()", "ground_truth": "\\frac{4}{5}"} | |
| {"image_path": "./Geo170K/images/test/178.png", "question": "As shown in the figure, the four small squares with edge length of 1.0 form a large square. A, B, and O are the vertices of the small squares, the radius of circle O is 1.0, and P is the point on circle O, and the small square is located at the upper right. , then sinangle APB is equal to ()", "ground_truth": "\\frac{\u221a{2}}{2}"} | |
| {"image_path": "./Geo170K/images/test/179.png", "question": "As shown in the figure, the hypotenuse of Rttriangle ABC AB = 10.0, cosA = frac {3.0}{5.0}, then the length of BC is ()", "ground_truth": "8cm"} | |
| {"image_path": "./Geo170K/images/test/180.png", "question": "As shown in the figure, in the quadrilateral ABCD, E and F are the midpoints of AB and AD respectively. If EF = 2.0, BC = 5.0, CD = 3.0, then tanC is equal to ()", "ground_truth": "\\frac{4}{3}"} | |
| {"image_path": "./Geo170K/images/test/181.png", "question": "In Rttriangle ABC, angle ACB = 90.0, CD perpendicular AB at point D, if AC = 3.0, BC = 4.0, then tan\u03b1 is equal to ()", "ground_truth": "\\frac{3}{4}"} | |
| {"image_path": "./Geo170K/images/test/182.png", "question": "As shown in the figure, in Rttriangle ABC, angle C = 90.0, sinA = frac {1.0}{3.0}, then the value of cosB is ()", "ground_truth": "\\frac{1}{3}"} | |
| {"image_path": "./Geo170K/images/test/183.png", "question": "We know that if the sum of two acute angles is equal to a right angle, then these two angles are complementary to each other, referred to as complementary to each other. As shown in the figure, angle A and angle B are complementary, and there are: sinA = frac angle A's opposite hypotenuse = frac ac, \\cosB = frac angle B's adjacent hypotenuse = frac ac, so we know sinA = \\cosB, notice that in triangle ABC, angle A + angle B = 90.0, that is, angle B = 90.0-angle A, angle A = 90.0-angle B, so there is: sin( 90.0-A) = \\cosA, \\ cos( 90.0-A) = sinA. Try to complete the following multiple-choice questions: If \u03b1 is an acute angle and \\cos\u03b1 = frac {4.0}{5.0}, then the value of sin(90.0-\u03b1) is equal to ()", "ground_truth": "\\frac{4}{5}"} | |
| {"image_path": "./Geo170K/images/test/184.png", "question": "As shown in the figure, it is known that AB and AD are the chords of circle O, angle BOD = 50.0, then the degree of angle BAD is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/185.png", "question": "As shown in the figure, in triangle ABC, the bisectors of the exterior angles of angle ABC and angle ACB intersects at point O, and angle BOC = 40.0, then angle A = ()", "ground_truth": "100\u00b0"} | |
| {"image_path": "./Geo170K/images/test/186.png", "question": "As shown in the figure, it is known that CD is the diameter of circle O, and the chord DE passing through the point D is parallel to the radius OA. If the angle D = 50.0, the degree of the angle C is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/187.png", "question": "As shown in the figure, point B is on circle O, chord AC parallel OB, angle BOC = 50.0, then angle OAB = ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/188.png", "question": "As shown in the figure, points A, B, and C are three points on circle O, if angle A = 40.0, then the degree of angle BOC is ()", "ground_truth": "80\u00b0"} | |
| {"image_path": "./Geo170K/images/test/189.png", "question": "In circle O, AB is the diameter, CD is the chord, angle ABD = 28.0, then the degree of angle C is ()", "ground_truth": "62\u00b0"} | |
| {"image_path": "./Geo170K/images/test/190.png", "question": "As shown in the figure, points A, B, and C are three points on circle O, if angle BOC = 80.0, then the degree of angle A is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/191.png", "question": "As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, angle CDB = 40.0, then the degree of angle CBA is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/192.png", "question": "As shown in the figure, it is known that O is a point in the quadrilateral ABCD, OA = OB = OC, angle ABC = angle ADC = 65.0, then angle DAO + angle DCO = ()", "ground_truth": "165\u00b0"} | |
| {"image_path": "./Geo170K/images/test/193.png", "question": "As shown in the figure, AB is the diameter of circle O, angle D = 33.0, then the degree of angle AOC is ()", "ground_truth": "114\u00b0"} | |
| {"image_path": "./Geo170K/images/test/194.png", "question": "As shown in the figure, in circle O, OA perpendicular BC, angle AOB = 48.0, D is a point on circle O, then the degree of angle ADC is ()", "ground_truth": "24\u00b0"} | |
| {"image_path": "./Geo170K/images/test/195.png", "question": "As shown in the figure, the three points A, B, and C are on circle O, angle ABO = 50.0, then angle ACB = ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/196.png", "question": "As shown in the figure, AC is the diameter of circle O, if angle OBC = 40.0, then the degree of angle AOB is ()", "ground_truth": "80\u00b0"} | |
| {"image_path": "./Geo170K/images/test/197.png", "question": "As shown in the figure, in circle A, the known chord BC = 8.0, DE = 6.0, angle BAC + angle EAD = 180.0, then the radius of circle A is ()", "ground_truth": "5"} | |
| {"image_path": "./Geo170K/images/test/198.png", "question": "Place the protractor on a broken piece of glass as shown in the figure, so that point A is on a semicircle, and the readings of points B and C are 105.0 and 155.0 respectively, then the size of angle BAC is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/199.png", "question": "As shown in the figure, points A and B are three points on circle O and AB = AC. Connect BO and CO, if angle ABC = 65.0, then the degree of angle BOC is ()", "ground_truth": "100\u00b0"} | |
| {"image_path": "./Geo170K/images/test/200.png", "question": "As shown in the figure, given that the degree of the central angle angle AOB is 110.0, then the angle of circumference angle ACB is equal to ()", "ground_truth": "125\u00b0"} | |
| {"image_path": "./Geo170K/images/test/201.png", "question": "As shown in the figure, the cross section of a tunnel is a semicircle with a radius of 3.4, and a truck with a width of 3.2 can pass through the tunnel.", "ground_truth": "3m"} | |
| {"image_path": "./Geo170K/images/test/202.png", "question": "As shown in the figure, AB and CD are the two diameters of circle O, the chord DE parallel AB, if the arc DE is the arc of 40.0, then angle BOC = ()", "ground_truth": "110\u00b0"} | |
| {"image_path": "./Geo170K/images/test/203.png", "question": "As shown in the figure, in circle O, if point C is the midpoint of arc AB, angle A = 50.0, then angle BOC = ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/204.png", "question": "If AB parallel CD, angle C = 60.0, then angle A + angle E is equal to ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/205.png", "question": "Known: As shown in the figure, in circle O, OA perpendicular BC, angle AOB = 70.0, then the degree of angle ADC is ()", "ground_truth": "35\u00b0"} | |
| {"image_path": "./Geo170K/images/test/206.png", "question": "As shown in the figure, CD is the chord of circle O, O is the center of the circle, fold the minor arc of circle O in half along CD, A is a point on the minor arc after folding in half, angle CAD = 110.0, then the degree of angle B is ()", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/207.png", "question": "As shown in the figure, AB is the diameter of circle O, point C is a point on circle O, angle C = 20.0, then the degree of angle BOC is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/208.png", "question": "As shown in the figure, circle O is the circumscribed circle of triangle ABC, if angle AOB = 130.0, then the degree of angle ACB is ()", "ground_truth": "115\u00b0"} | |
| {"image_path": "./Geo170K/images/test/209.png", "question": "As shown in the figure, in circle O, chord AB and CD intersect at point E, BE = DE, angle B = 40.0, then the degree of angle A is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/210.png", "question": "As shown in the figure, points A, B, C, D are on circle O, DE perpendicular OA, DF perpendicular OB, and the feet of perpendicular are E, F respectively. If angle EDF = 50.0, then the degree of angle C is ()", "ground_truth": "65\u00b0"} | |
| {"image_path": "./Geo170K/images/test/211.png", "question": "As shown in the figure, CD is the diameter of circle O, chord AB intersects CD at point M, M is the midpoint of AB, point P is at arc AD, PC and AB intersect at point N, angle PNA = 60.0, then angle PDC is equal to ( )", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/212.png", "question": "As shown in the figure, AB is the diameter of circle O, chord CD perpendicular AB at E. Connect OC and AD, and angle A = 35.0, then angle AOC = ()", "ground_truth": "110\u00b0"} | |
| {"image_path": "./Geo170K/images/test/213.png", "question": "As shown in the figure, in triangle ABC, AB = AC, draw a semicircle with BC as the diameter to intersect AB at E, and it intersects AC at D, the degree of arc CD is 40.0, then the degree of angle A is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/214.png", "question": "As shown in the figure, the points A, B, C, and P are on circle O, CD perpendicular OA, CE perpendicular OB, and the feet of perpendicular are D, E, angle DCE = 36.0, then the degree of angle P is ()", "ground_truth": "72\u00b0"} | |
| {"image_path": "./Geo170K/images/test/215.png", "question": "As shown in the figure, points A, B, C, and P are on circle O, CD perpendicular OA, CE perpendicular OB, and the feet of perpendicular are D, E, angle DCE = 40.0, then the degree of angle P is ()", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/216.png", "question": "As shown in the figure, the three points A, B, and C are on the circle. In triangle ABC, angle ABC = 70.0, angle ACB = 30.0, D is the midpoint of the arc BAC. Connect DB and DC, then the degree of angle DBC is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/217.png", "question": "As shown in the figure, AB and CD are the two chords of circle O. Connect AD and BC, if angle BCD = 50.0, then the degree of angle BAD is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/218.png", "question": "As shown in the figure, triangle ABC is inscribed in circle O, if angle OAB = 26.0, then the size of angle C is ()", "ground_truth": "64\u00b0"} | |
| {"image_path": "./Geo170K/images/test/219.png", "question": "As shown in the figure, circle O is the circumscribed circle of triangle ABC, angle A = 70.0, then the size of angle BOC is ()", "ground_truth": "140\u00b0"} | |
| {"image_path": "./Geo170K/images/test/220.png", "question": "As shown in the figure, in circle O, chord AC parallel radius OB, angle BOC = 50.0, then the degree of angle OBA is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/221.png", "question": "As shown in the figure, if angle ABC = 30.0, then the degree of angle AOC is ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/222.png", "question": "As shown in the figure, in circle O, CD is the diameter, point A, point B on circle O, connect OA, OB, AC, AB, if angle AOB = 40.0, CD parallel AB, then the size of angle BAC is ()", "ground_truth": "35\u00b0"} | |
| {"image_path": "./Geo170K/images/test/223.png", "question": "As shown in the figure, it is a circular exhibition hall. In order to monitor the entire exhibition hall, two monitors A and B are installed on the circular edge. If the monitoring angle of monitor A is 65.0, the monitoring angle of monitor B is at least ( )", "ground_truth": "115\u00b0"} | |
| {"image_path": "./Geo170K/images/test/224.png", "question": "As shown in the figure, circle O is the circumscribed circle of triangle ABC. Connect OA and OB, angle AOB = 50.0, then the degree of angle C is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/225.png", "question": "It is known that: as shown in the figure, AB is the diameter of circle O, CD is the chord,. Connect AD, AC, angle CAB = 55.0, then angle D = ()", "ground_truth": "35\u00b0"} | |
| {"image_path": "./Geo170K/images/test/226.png", "question": "As shown in the figure, points A, B, and C are on circle O, if angle C = 35.0, then angle AOB = ()", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/227.png", "question": "As shown in the figure, AB is the diameter of circle O, and the degree of angle ADC is 35.0, then the degree of angle BOC is ()", "ground_truth": "110\u00b0"} | |
| {"image_path": "./Geo170K/images/test/228.png", "question": "As shown in the figure, the quadrilateral ABCD is inscribed in circle O, AB is the diameter of circle O, and point C is the midpoint of arc BD. If angle DAB = 50.0, then the size of angle ABC is ()", "ground_truth": "65\u00b0"} | |
| {"image_path": "./Geo170K/images/test/229.png", "question": "As shown in the figure, the quadrilateral ABCD is the inscribed quadrilateral of circle O, AB is the diameter of circle O. Connect BD. If angle BCD = 120.0, then the size of angle ABD is ()", "ground_truth": "30\u00b0"} | |
| {"image_path": "./Geo170K/images/test/230.png", "question": "As shown in the figure, points A, B, C, and D are on circle O, and point E is on the extended line of AD. If angle ABC = 60.0, then the degree of angle CDE is ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/231.png", "question": "As shown in the figure, the quadrilateral ABCD is inscribed in the semicircle O, and it is known that angle ADC = 140.0, then the size of angle AOC is ()", "ground_truth": "80\u00b0"} | |
| {"image_path": "./Geo170K/images/test/232.png", "question": "As shown in the figure, the quadrilateral ABCD is inscribed in circle O. If angle BOD = 138.0, then the degree of one of its exterior angles angle DCE is ()", "ground_truth": "69\u00b0"} | |
| {"image_path": "./Geo170K/images/test/233.png", "question": "As shown in the figure, the quadrilateral ABCD is inscribed in circle O, E is a point on the BC extended line, angle A = 50.0, then the degree of angle DCE is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/234.png", "question": "As shown in the figure, the quadrilateral ABCD is inscribed in circle O, F is a point on arc CD, and arc DF = arc BC, connect CF and extend to intersects the extended line of AD at point E, connect AC. If angle ABC = 105.0, angle BAC = 25.0, then the degree of angle E is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/235.png", "question": "As shown in the figure, the quadrilateral ABCD is the inscribed quadrilateral of circle O, if angle C = 140.0, then the degree of angle BOD is ()", "ground_truth": "80\u00b0"} | |
| {"image_path": "./Geo170K/images/test/236.png", "question": "As shown in the figure, in circle O, AB parallel CD, angle BCD = 100.0, E is any point on arc DC, A, B, C, and D are the four points on circle O, then the angle of angle AEC is ()", "ground_truth": "100\u00b0"} | |
| {"image_path": "./Geo170K/images/test/237.png", "question": "As shown in the figure. Given that the three points A, B, and C are on circle O, point C is on the minor arc AB, and angle AOB = 130.0, then the degree of angle ACB is ()", "ground_truth": "115\u00b0"} | |
| {"image_path": "./Geo170K/images/test/238.png", "question": "As shown in the figure, the quadrilateral ABCD is inscribed in circle O, if angle ABC = 40.0, then the degree of angle ADC is ()", "ground_truth": "140\u00b0"} | |
| {"image_path": "./Geo170K/images/test/239.png", "question": "As shown in the figure, an exterior angle of the quadrilateral ABCD angle DCE = 70.0, then the degree of angle BAD is ()", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/240.png", "question": "As shown in the figure, the quadrilateral ABCD is inscribed in circle O, angle BOD = 70.0, then the degree of angle BCD is ()", "ground_truth": "145\u00b0"} | |
| {"image_path": "./Geo170K/images/test/241.png", "question": "As shown in the figure, the quadrilateral ABCD is inscribed in circle O, if one of its exterior angles angle DCE = 64.0, then angle BOD = ()", "ground_truth": "128\u00b0"} | |
| {"image_path": "./Geo170K/images/test/242.png", "question": "As shown in the figure, the quadrilateral ABCD is a quadrilateral inscribed in the circle, and E is a point on the extended line of AD. If angle CBA = 120.0, then the size of angle EDC is ()", "ground_truth": "120\u00b0"} | |
| {"image_path": "./Geo170K/images/test/243.png", "question": "As shown in the figure, in the circle inscribed in the quadrilateral ABCD, the central angle angle 1 = 100.0, then the angle of circumference angle ABC is equal to ()", "ground_truth": "130\u00b0"} | |
| {"image_path": "./Geo170K/images/test/244.png", "question": "As shown in the figure, in the inscribed quadrilateral ABCD of the circle, angle ABC = 120.0, then the degree of the exterior angle of the quadrilateral ABCD angle ADE is ()", "ground_truth": "120\u00b0"} | |
| {"image_path": "./Geo170K/images/test/245.png", "question": "As shown in the figure, ABCD is the inscribed quadrilateral of circle O, and angle ABC = 115.0, then angle AOC is equal to ()", "ground_truth": "130\u00b0"} | |
| {"image_path": "./Geo170K/images/test/246.png", "question": "As shown in the figure, given the angle of circumference angle BAD = 50.0, then the degree of the angle of circumference angle BCD is ()", "ground_truth": "130\u00b0"} | |
| {"image_path": "./Geo170K/images/test/247.png", "question": "As shown in the figure, circle O is the circumscribed circle of the quadrilateral ABCD, if angle O = 110.0, then the degree of angle C is ()", "ground_truth": "125\u00b0"} | |
| {"image_path": "./Geo170K/images/test/248.png", "question": "As shown in the figure, the quadrilateral ABCD is inscribed in circle O, if angle C = 36.0, then the degree of angle A is ()", "ground_truth": "144\u00b0"} | |
| {"image_path": "./Geo170K/images/test/249.png", "question": "As shown in the figure, there are four points A, B, C, D on circle O, where angle A = 80.0, then the degree of angle C is ()", "ground_truth": "100\u00b0"} | |
| {"image_path": "./Geo170K/images/test/250.png", "question": "As shown in the figure, triangle ABC is the inscribed triangle of circle O, if angle ACB = 30.0, AB = 6.0, then the radius of circle O is ()", "ground_truth": "6"} | |
| {"image_path": "./Geo170K/images/test/251.png", "question": "As shown in the figure, the line segment AB is the diameter of circle O, the chord CD \u4e04 AB, angle CAB = 20.0, then angle BOD is equal to ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/252.png", "question": "As shown in the figure, triangle ABC is the inscribed triangle of circle O, AB is the diameter of circle O, point D is a point on circle O, if angle ACD = 40.0, then the size of angle BAD is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/253.png", "question": "As shown in the figure, triangle ABC is inscribed in circle O, angle C = 20.0, then the degree of angle OAB is ()", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/254.png", "question": "As shown in the figure, triangle ABC is inscribed in circle O. Connect OA, OB, if angle C = 35.0, then the degree of angle OBA is ()", "ground_truth": "55\u00b0"} | |
| {"image_path": "./Geo170K/images/test/255.png", "question": "As shown in the figure, it is known that triangle ABC is inscribed in circle O, angle BAC = 50.0, then the degree of angle BOC is ()", "ground_truth": "100\u00b0"} | |
| {"image_path": "./Geo170K/images/test/256.png", "question": "As shown in the figure, in triangle ABC, AB = AC, angle BAC = 70.0, circle O is the circumscribed circle of triangle ABC, point D is on the minor arc arc AC, then the degree of angle D is ()", "ground_truth": "125\u00b0"} | |
| {"image_path": "./Geo170K/images/test/257.png", "question": "As shown in the figure, triangle ABC is inscribed in circle O, angle AOB = 80.0, then the size of angle ACB is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/258.png", "question": "As shown in the figure, triangle ABC is the inscribed triangle of circle O, angle C = 30.0, the radius of circle O is 5.0, if point P is a point on circle O, in triangle ABP, PB = AB, then the length of PA is ( )", "ground_truth": "5\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/259.png", "question": "As shown in the figure, triangle ABC is inscribed in circle O, OC perpendicular OB, OD perpendicular AB intersects AC at point E. Knowing that the radius of circle O is 1.0, then the value of AE^ 2 + CE^ 2 is ()", "ground_truth": "2"} | |
| {"image_path": "./Geo170K/images/test/260.png", "question": "As shown in the figure, it is known that circle O is the circumscribed circle of triangle ABC, and AB is the diameter of circle O, if OC = 5.0, AC = 6.0, then the length of BC is ()", "ground_truth": "8"} | |
| {"image_path": "./Geo170K/images/test/261.png", "question": "As shown in the figure, angle XOY = 45.0, the two vertices A and B of a right triangle ABC move on OX and OY respectively, where AB = 10.0, then the maximum value of the distance from point O to vertex A is ()", "ground_truth": "10\u221a{2}"} | |
| {"image_path": "./Geo170K/images/test/262.png", "question": "As shown in the figure, in triangle ABC, angle BAC = 70.0, angle ABC = 45.0, point O is the center of the circumscribed circle of triangle ABC, then angle AOB is equal to ()", "ground_truth": "130\u00b0"} | |
| {"image_path": "./Geo170K/images/test/263.png", "question": "As shown in the figure, circle O is the circumscribed circle of triangle ABD, if angle A = 135.0, then the degree of angle BDO is ()", "ground_truth": "45\u00b0"} | |
| {"image_path": "./Geo170K/images/test/264.png", "question": "As shown in the figure, triangle ABC is inscribed in circle O, if angle AOB = 110.0, then the degree of angle ACB is ()", "ground_truth": "55\u00b0"} | |
| {"image_path": "./Geo170K/images/test/265.png", "question": "As shown in the figure, it is known that the angle between the diameter AB of circle O and the chord AC is 30.0, the tangent PC passing through point C and the extended line of AB intersect at point P, the radius of circle O is 2.0, then PC is ()", "ground_truth": "2\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/266.png", "question": "As shown in the figure, AB cuts circle O at point B, AO intersects circle O at point C, and point D is at circle O. If angle A = 40.0, then the degree of angle BDC is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/267.png", "question": "As shown in the figure, AB is the diameter of circle O, point D is on the extended line of AB, passing point D is the tangent of circle O, and the tangent point is C, if angle A = 25.0, then angle D = ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/268.png", "question": "As shown in the figure, in the circle O with a radius of 2.0, C is a point on the extended line of the diameter AB, CD is tangent to the circle at point D. Connect AD, given that angle DAC = 30.0, the length of the line segment CD is ()", "ground_truth": "2\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/269.png", "question": "circle O is a circle with a radius of 1.0, the distance from point O to line L is 3.0, draw a tangent of circle O through any point P on the straight line L , and the tangent point is Q; if PQ is taken as the edge to make the square PQRS, then the minimum area of the square PQRS is ()", "ground_truth": "8"} | |
| {"image_path": "./Geo170K/images/test/270.png", "question": "As shown in the figure, AB is the diameter of circle O, C is the point on circle O, passing point C is the tangent of circle O and intersects the extended line of AB at point E, OD perpendicular AC at point D, if angle E = 30.0, CE = 6.0, then the value of OD is ()", "ground_truth": "\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/271.png", "question": "As shown in the figure, the straight line AB is tangent to circle O at point A, the radius of circle O is 1.0, if angle OBA = 30.0, then the length of OB is ()", "ground_truth": "2"} | |
| {"image_path": "./Geo170K/images/test/272.png", "question": "As shown in the figure, it is known that BA is the tangent of circle O, and connect OB to intersect circle O at point C. If angle B = 45.0 and the length of AB is 2.0, then the length of BC is ()", "ground_truth": "2\u221a{2}-2"} | |
| {"image_path": "./Geo170K/images/test/273.png", "question": "As shown in the figure, AB is the diameter of circle O, point P is a point outside circle O, PO intersects circle O at point C. Connect BC and PA. If angle P = 36.0, PA is tangent to circle O, then angle B is equal to ()", "ground_truth": "27\u00b0"} | |
| {"image_path": "./Geo170K/images/test/274.png", "question": "As shown in the figure, AB, AC, and BD are the tangents of circle O, and the tangent points are P, C, and D respectively. If AB = 5.0, AC = 3.0, then the length of BD is ()", "ground_truth": "2"} | |
| {"image_path": "./Geo170K/images/test/275.png", "question": "As shown in the figure, AB is the diameter of circle O, PA is tangent to circle O at point A, line segment PO intersects circle O at point C, and connect BC, if angle P = 36.0, then angle B is equal to ()", "ground_truth": "27\u00b0"} | |
| {"image_path": "./Geo170K/images/test/276.png", "question": "As shown in the figure, PA and PB are tangents of circle O, the tangent point of point A and B, AC is the diameter of circle O, given that angle P = 50.0, then the size of angle ACB is ()", "ground_truth": "65\u00b0"} | |
| {"image_path": "./Geo170K/images/test/277.png", "question": "As shown in the figure, points A, B, and C are on circle O, and the tangent line of circle O passing through point A intersects the extended line of OC at point P, angle B = 30.0, OP = 3.0, then the length of AP is ()", "ground_truth": "\\frac{3}{2}\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/278.png", "question": "As shown in the figure, in circle O, AD and CD are chords. Connect OC and extend, and it intersects the tangent of point A at point B. If angle ADC = 25.0, then the degree of angle ABO is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/279.png", "question": "As shown in the figure, the straight lines PA and PB are the two tangents of circle O. If angle APB = 120.0, the radius of circle O is 10.0, then the length of chord AB is ()", "ground_truth": "10"} | |
| {"image_path": "./Geo170K/images/test/280.png", "question": "As shown in the figure, AC is the tangent of circle O, the tangent point is C, BC is the diameter of circle O, AB intersects circle O at point D. Connect OD, if angle BAC = 50.0, then the size of angle COD is ()", "ground_truth": "80\u00b0"} | |
| {"image_path": "./Geo170K/images/test/281.png", "question": "As shown in the figure, AB is the diameter of circle O, BP is the tangent of circle O, AP and circle O intersect at point G, point D is the point on arc BC, if angle P = 40.0, then angle ADC is equal to ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/282.png", "question": "As shown in the figure, AB is the diameter of circle O, PA is tangent to circle O at point A, OP intersects circle O at point C, and connect BC. If angle P = 20.0, then the degree of angle B is ()", "ground_truth": "35\u00b0"} | |
| {"image_path": "./Geo170K/images/test/283.png", "question": "As shown in the figure, PA and PB are tangent to circle O at points A and B respectively, the tangent EF of circle O intersects PA and PB at points E and F respectively, and the tangent point C is on the arc AB. If the length of PA is 2.0, then the perimeter of triangle PEF is ()", "ground_truth": "4"} | |
| {"image_path": "./Geo170K/images/test/284.png", "question": "Put the ruler, the triangle ruler and the round nut on the desktop as shown in the figure, angle CAB = 60.0, if AD = 6.0, then the outer diameter of the round nut is ()", "ground_truth": "12\u221a{3}cm"} | |
| {"image_path": "./Geo170K/images/test/285.png", "question": "AB is the diameter of circle O, PA is tangent to circle O at point A, and PO intersects circle O at point C; connect BC, if angle P = 40.0, then angle B is equal to ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/286.png", "question": "As shown in the figure, AB is the diameter of circle O, DB and DC are respectively tangent to circle O at points B and C. If angle ACE = 25.0, then the degree of angle D is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/287.png", "question": "As shown in the figure, AB is the tangent of circle O, A is the tangent point, the extended line of BO intersects circle O at point C, angle OAC = 35.0, then the degree of angle B is ()", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/288.png", "question": "As shown in the figure, in triangle ABC, angle B = 20.0, point O is a point on the edge of BC, take O as the center and OB as the radius to make a circle, intersect the AB edge at point D, connect CD, if CD happens to be tangent of circle O , then the degree of angle DCB is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/289.png", "question": "As shown in the figure, PA and PB are the tangents of circle O, points A and B are the tangent points, and AC is the diameter of circle O. Given that angle P = 50.0, the size of angle ACB is ()", "ground_truth": "65\u00b0"} | |
| {"image_path": "./Geo170K/images/test/290.png", "question": "As shown in the figure, PA and PB are tangent to circle O at two points A and B respectively, point C is on the major arc arc ACB, angle P = 80.0, then the degree of angle C is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/291.png", "question": "As shown in the figure, circle O is the circumscribed circle of Rttriangle ABC, angle ACB = 90.0, angle A = 25.0, crossing point C to draw the tangent of circle O, and intersects the extended line of AB at point D, then the degree of angle D is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/292.png", "question": "As shown in the figure, AB is the diameter of circle O, point C is on the extended line of AB, CD is tangent to circle O, and the tangent point is D. If angle A = 35.0, then angle C = ()", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/293.png", "question": "As shown in the figure, point P is a point on the extended line AB of the diameter of circle O, passing point P to draw the tangent PC of circle O, and the tangent point is C. If AO = OB = PB = 1.0, then the length of PC is ()", "ground_truth": "\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/294.png", "question": "As shown in the figure, in triangle ABC, AB = 5.0, BC = 3.0, AC = 4.0, the circle with point C as the center is tangent to AB, then the radius of circle C is ()", "ground_truth": "2.4"} | |
| {"image_path": "./Geo170K/images/test/295.png", "question": "As shown in the figure, points A, B, and C are three points on circle O, and the straight line CD and circle O are tangent to point C. If angle DCB = 40.0, then the degree of angle CAB is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/296.png", "question": "As shown in the figure, the straight line AB and circle O are tangent to point A, the radius of circle O is 2.0, if angle OBA = 30.0, then the length of AB is ()", "ground_truth": "2\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/297.png", "question": "As shown in the figure, AB is the diameter of circle O, AC is tangent to circle O at A, BC intersects circle O at point D, if angle C = 70.0, then the degree of angle AOD is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/298.png", "question": "As shown in the figure, PA and PB are tangent to circle O at points A and B respectively, point E is a point on circle O, and angle AEB = 60.0, then angle P = ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/299.png", "question": "As shown in the figure, PA and PB are the tangents of circle O, AC is the diameter of circle O, angle c = 55.0, then angle APB is equal to ()", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/300.png", "question": "As shown in the figure, PA and PB are tangent to circle O at A and B respectively, angle P = 70.0, then angle C is ()", "ground_truth": "55\u00b0"} | |
| {"image_path": "./Geo170K/images/test/301.png", "question": "As shown in the figure, the line segment AB is the diameter of circle O, points C and D are points on circle O, and the tangent of circle O passing through point C intersects the extended line of AB at point E. If angle E = 50.0, then angle CDB is equal to ( )", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/302.png", "question": "The straight line AB and circle O are tangent to point A, as shown in the figure, if angle OBA = 60.0, AB = 1.0, then the radius of circle O is ()", "ground_truth": "\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/303.png", "question": "As shown in the figure, in Rttriangle ABC, AC = 4.0, AB = 5.0, angle C = 90.0, the circle passing through point C which is tangent to the edge AB intersects the edges CB and CA of triangle ABC at points E, F. The minimum length of the line segment EF is ()", "ground_truth": "2.4"} | |
| {"image_path": "./Geo170K/images/test/304.png", "question": "As shown in the figure, the radii of the two concentric circles are 3.0 and 5.0 respectively, and a chord AB of the great circle is tangent to the small circle, then the length of the chord AB is ()", "ground_truth": "8cm"} | |
| {"image_path": "./Geo170K/images/test/305.png", "question": "As shown in the figure, circle O is the circumscribed circle of triangle ABC, AD is the diameter of circle O, and EA is the tangent of circle O. If angle EAC = 120.0, then the degree of angle ABC is ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/306.png", "question": "As shown in the figure, the radius of circle O is 2.0, the distance from point O to line l is 3.0, and point P is a moving point on line l. If PB is tangent to circle O at point B, then the minimum value of PB is ()", "ground_truth": "\u221a{5}"} | |
| {"image_path": "./Geo170K/images/test/307.png", "question": "As shown in the figure, PA, PB, and CD are the tangents of circle O, A, B, and E are the tangent points, and CD intersects the line segments PA and PB at C and D respectively. If angle APB = 40.0, then the degree of angle COD is ( )", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/308.png", "question": "As shown in the figure, AB is the diameter of circle O, point C is on circle O, AE is the tangent of circle O, A is the tangent point, connect BC and extend to intersect AE at point D. If angle AOC = 80.0, then the degree of angle ADB is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/309.png", "question": "As shown in the figure, AC is the tangent of circle O, the tangent point is C, BC is the diameter of circle O, AB intersects circle O at point D, and connect OD. If angle BAC = 55.0, then the size of angle COD is ()", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/310.png", "question": "As shown in the figure, in triangle ABC, AB = 3.0, AC = 2.0. When angle B is the largest, the length of BC is ()", "ground_truth": "\u221a{5}"} | |
| {"image_path": "./Geo170K/images/test/311.png", "question": "As shown in the figure, AB is the diameter of the semicircle, point O is the center of the circle, point C is a point on the extended line of AB, and CD is tangent to the semicircle at point D. If AB = 6.0, CD = 4.0, then the value of sinangle C is ()", "ground_truth": "\\frac{3}{5}"} | |
| {"image_path": "./Geo170K/images/test/312.png", "question": "As shown in the figure, in Rttriangle ABC, angle C = 90.0, angle A = 30.0, BC = 2.0, the radius of circle C is 1.0, point P is the point on the hypotenuse AB, passing point P is a tangent PQ of circle C (Point Q is the tangent point), then the minimum value of the line segment PQ is ()", "ground_truth": "\u221a{2}"} | |
| {"image_path": "./Geo170K/images/test/313.png", "question": "As shown in the figure, AB and AC are the two chords of circle O. The tangent passing point B and the extended line of OC intersect at point D. If angle D = 36.0, then the degree of angle CAB is ()", "ground_truth": "27\u00b0"} | |
| {"image_path": "./Geo170K/images/test/314.png", "question": "As shown in the figure, the diameters of the two concentric circles are 6.0 and 10.0, and a chord AB of the great circle is tangent to the small circle, so the length of the chord AB is ()", "ground_truth": "8cm"} | |
| {"image_path": "./Geo170K/images/test/315.png", "question": "As shown in the figure, AP and BP are tangent to circle O at points A and B respectively, angle P = 60.0, point C is on the major arc AB, then the degree of angle C is ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/316.png", "question": "As shown in the figure, P is a point on the AB extended line of the diameter of circle O, PC is tangent to circle O at C, angle P = 50.0, angle A is ()", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/317.png", "question": "As shown in the figure, PA and PB are the tangents of circle O, and the tangent points are A and B. If angle OAB = 30.0, then the degree of angle P is ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/318.png", "question": "As shown in the figure, PA, PB are circle O is tangent, AC is the diameter of circle O, if angle BAC = 25.0, then angle P is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/319.png", "question": "As shown in the figure, the straight line BC is tangent to circle O at point A, AD is the chord of circle O. Connect OD, if angle DAC = 50.0, then the degree of angle ODA is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/320.png", "question": "As shown in the figure, a torus carpet is to be laid in the lobby of a hotel. The worker only measures the length of the chord AB of the great circle that is tangent to the small circle, and then calculates the area of \u200b\u200bthe torus. If the measured length of AB is 8.0, the area of \u200b\u200bthe torus is ()", "ground_truth": "16\u03c0\u5e73\u65b9\u7c73"} | |
| {"image_path": "./Geo170K/images/test/321.png", "question": "As shown in the figure, AB is the diameter of circle O, CD is tangent to circle O at point D, and the extended line of AB intersects CD at point C, if angle ACD = 40.0, then angle A = ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/322.png", "question": "As shown in the figure, AB is the diameter of circle O, point D is on the extended line of AB, and DC is tangent to circle O at point C, if angle A = 26.0, then angle D is equal to ()", "ground_truth": "38\u00b0"} | |
| {"image_path": "./Geo170K/images/test/323.png", "question": "As shown in the figure, in triangle ABC, AB = AC, angle BAO = 45.0, triangle ABC is inscribed in circle O, D is a point on circle O, passing point D is the tangent of circle O and the extended line of BC at E, if DE perpendicular BC, AD = 2.0\u221a{2.0}, then the length of DE is ()", "ground_truth": "\u221a{2}"} | |
| {"image_path": "./Geo170K/images/test/324.png", "question": "As shown in the figure, AB is the tangent of circle O, B is the tangent point, AO and circle O intersect at point C, if angle BAO = 40.0, then the degree of angle OCB is ()", "ground_truth": "65\u00b0"} | |
| {"image_path": "./Geo170K/images/test/325.png", "question": "As shown in the figure, circle O ia tangent to AB at point C, angle BCE = 60.0, DC = 6.0, DE = 4.0, then S_triangle CDE is ()", "ground_truth": "6\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/326.png", "question": "As shown in the figure, AB is tangent to circle O at B, and the secant ACD passes through the center O, if angle BCD = 70.0, then the degree of angle A is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/327.png", "question": "As shown in the figure, in triangle ABC, AB = 15.0, AC = 12.0, BC = 9.0, the moving circle passing through point C and tangent to AB intersects CB and CA at points E and F respectively, then the minimum value the length of the line segment EF is ()", "ground_truth": "\\frac{36}{5}"} | |
| {"image_path": "./Geo170K/images/test/328.png", "question": "As shown in the figure, BC is tangent to circle O at point C, and the extended line of BO intersects circle O at point A, connect AC, if angle ACB = 120.0, then the degree of angle A is equal to ()", "ground_truth": "30\u00b0"} | |
| {"image_path": "./Geo170K/images/test/329.png", "question": "As shown in the figure, a quadrilateral green garden, with circular fountains with a radius of 2.0 on all four corners, then the area of \u200b\u200bthe green garden occupied by these four fountains is ()", "ground_truth": "4\u03c0"} | |
| {"image_path": "./Geo170K/images/test/330.png", "question": "As shown in the figure, in the square ABCD with edge length 4.0, first draw the arc with point A as the center, the length of AD as the radius, and then draw the arc with the midpoint of the AB side as the center, and half of the AB length as the radius, then the area of the shaded part between the two arcs is () (results remain N_1)", "ground_truth": "2\u03c0"} | |
| {"image_path": "./Geo170K/images/test/331.png", "question": "As shown in the figure, in triangle ABC, DE parallel BC, AE = 3.0, AC = 9.0, AD = 4.0, then the value of AB is ()", "ground_truth": "12"} | |
| {"image_path": "./Geo170K/images/test/332.png", "question": "As shown in the figure, AB parallel CD, AD and BC intersect at point O, if AO = 2.0, DO = 4.0, BO = 3.0, then the length of BC is ()", "ground_truth": "9"} | |
| {"image_path": "./Geo170K/images/test/333.png", "question": "As shown in the figure, given that a parallel b parallel c, AB = 1.0, BC = 2.0, EF = 4.0, then DE = ()", "ground_truth": "2"} | |
| {"image_path": "./Geo170K/images/test/334.png", "question": "As shown in the figure, straight lines a, b, and c intersect straight lines and n at points A, B, C, D, E, and F respectively. Given the straight line a parallel b parallel c, if AB = 2.0, BC = 3.0, then the value of frac DEEF is ()", "ground_truth": "\\frac{2}{3}"} | |
| {"image_path": "./Geo170K/images/test/335.png", "question": "As shown in the figure, in triangle ABC, DE parallel BC, if AD = 1.0, DB = 2.0, then the value of frac AEAC is ()", "ground_truth": "\\frac{1}{3}"} | |
| {"image_path": "./Geo170K/images/test/336.png", "question": "As shown in the figure, in triangle ABC, M is the midpoint of AC, E is a point on AB, AE=frac {1.0}{4.0}AB, connect EM and extend, and it intersects the extended line of BC at D, then frac {BC}{CD} = ()", "ground_truth": "2"} | |
| {"image_path": "./Geo170K/images/test/337.png", "question": "As shown in the figure, in the rectangle ABCD, AB = 3.0, BC = 4.0, point M is on BC, and satisfies BM = 1.0, cross D to make DN perpendicular AM which intersects AM at point N, then the length of DN is ()", "ground_truth": "\\frac{6}{5}\u221a{10}"} | |
| {"image_path": "./Geo170K/images/test/338.png", "question": "As shown in the figure, in triangle ABC, point D and point E are on AB and BC respectively, and DE parallel AC, BE = 2.0, CE = 1.0, the area of \u200b\u200btriangle BDE is 4.0, then the area of \u200b\u200btriangle ABC is ( )", "ground_truth": "9"} | |
| {"image_path": "./Geo170K/images/test/339.png", "question": "As shown in the figure, in triangle ABC, DE parallel BC, if AB = 7.0, AC = 5.0, AD = 3.0, then DE = ()", "ground_truth": "\\frac{20}{7}cm"} | |
| {"image_path": "./Geo170K/images/test/340.png", "question": "As shown in the figure, in parallelogram ABCD, point E is on the edge AD, CE intersects BD at point F, if EF = frac {1.0}{3.0}FC, then frac {AE}{ED} = ()", "ground_truth": "2"} | |
| {"image_path": "./Geo170K/images/test/341.png", "question": "As shown in the figure, given that the point M is the midpoint of edge AB of the parallelogram ABCD, the line segment CM intersects BD at the point E, Striangle BEM = 2.0, then the area of \u200b\u200bthe shaded part in the figure is ()", "ground_truth": "8"} | |
| {"image_path": "./Geo170K/images/test/342.png", "question": "As shown in the figure, in the quadrilateral ABCD, AD \u2016 BC, diagonal AC and BD intersect at O, if \\\\ frac {s {\\triangle ADO} {s {\\triangle DOC}} = \\frac {1}{3}", "ground_truth": "\\frac{1}{3}"} | |
| {"image_path": "./Geo170K/images/test/343.png", "question": "As shown in the figure, in parallelogram ABCD, angle C = 120.0, AB = AE = 5.0, AE and BD intersect at point F, AF = 2 EF. Then the length of BC is ()", "ground_truth": "10"} | |
| {"image_path": "./Geo170K/images/test/344.png", "question": "As shown in the figure, D and E are the points on the edges AB and AC of triangle ABC, DE parallel BC, if AD:DB=1.0:3.0, AE = 2.0, then the length of AC is ()", "ground_truth": "8"} | |
| {"image_path": "./Geo170K/images/test/345.png", "question": "As shown in the figure, given that AB parallel CD parallel EF, AD:AF=3.0:5.0,BE=15.0, then the length of CE is equal to ()", "ground_truth": "9"} | |
| {"image_path": "./Geo170K/images/test/346.png", "question": "As shown in the figure, AD parallel BE parallel CF, straight line l2.0, l3.0 and these three parallel lines intersect at points A, B, C, D, E, F, frac {AB}{BC}=frac {2.0}{3.0},DE=6.0, then the value of EF is ( )", "ground_truth": "9"} | |
| {"image_path": "./Geo170K/images/test/347.png", "question": "As shown in the figure, it is known that a straight line a parallel b parallel c, a straight line, n and a, b, c intersect at points A, C, E, B, D, F, if AC = 4.0, AE = 10.0, BD = 3.0, then the value of DF is ()", "ground_truth": "4.5"} | |
| {"image_path": "./Geo170K/images/test/348.png", "question": "As shown in the figure, in triangle ABC, DE parallel BC, if AD = 1.0, DB = 2.0, then the value of frac ADAB is ()", "ground_truth": "\\frac{1}{3}"} | |
| {"image_path": "./Geo170K/images/test/349.png", "question": "As shown in the figure, the straight line a parallel b parallel c, the straight line, n and a, b, c intersect at the points A, C, E and B, D, F respectively, if AC = 4.0, AE = 10.0, BF =frac {15.0}{2.0}, then the length of DF is ()", "ground_truth": "\\frac{9}{2}"} | |
| {"image_path": "./Geo170K/images/test/350.png", "question": "As shown in the figure, given that a parallel b parallel c, AC = 6.0, AB = 2.0, EF = 5.0, then the value of DF is ()", "ground_truth": "\\frac{15}{2}"} | |
| {"image_path": "./Geo170K/images/test/351.png", "question": "As shown in the figure, in triangle ABC, DE parallel BC, frac {AD}{DB} = frac {1.0}{2.0}, DE = 4.0, then the length of BC is ()", "ground_truth": "12"} | |
| {"image_path": "./Geo170K/images/test/352.png", "question": "As shown in the figure, in triangle ABC, the points D and E are on the edges AB and AC respectively, DE parallel BC, given that EC = 6.0, frac {AD}{DB}=frac {2.0}{3.0}, then the length of AE is ()", "ground_truth": "4"} | |
| {"image_path": "./Geo170K/images/test/353.png", "question": "As shown in the figure, in triangle ABC, D and E are points on AB and AC respectively, which satisfy AD = 3.0, AE = 2.0, EC = 1.0, DE parallel BC, then AB = ()", "ground_truth": "4.5"} | |
| {"image_path": "./Geo170K/images/test/354.png", "question": "As shown in the figure, AB parallel CD parallel EF, AC and BD intersect at point E, if CE = 5.0, CF = 4.0, AE = BC, then the value of frac CDAB is ()", "ground_truth": "\\frac{1}{4}"} | |
| {"image_path": "./Geo170K/images/test/355.png", "question": "As shown in the figure, in triangle ABC, points D and E are on edges AB and AC respectively, DE parallel BC. If frac {AE}{AC}=frac {3.0}{4.0},AD=9.0, then AB is equal to ()", "ground_truth": "12"} | |
| {"image_path": "./Geo170K/images/test/356.png", "question": "As shown in the figure, the straight line l_{1.0}parallel l_{2.0}parallel l_{3.0}, it is known that: AB=4.0,BC=6.0,DE=3.0, then EF = ()", "ground_truth": "4.5"} | |
| {"image_path": "./Geo170K/images/test/357.png", "question": "As shown in the figure, in the parallelogram ABCD, F is a point on AB, DF intersects AC at point E, if CD = 10.0, frac {AE}{EC}=frac {2.0}{5.0}, then the length of BF is ()", "ground_truth": "6"} | |
| {"image_path": "./Geo170K/images/test/358.png", "question": "As shown in the figure, E is a point on AD of the parallelogram ABCD, passing the point E to draw EF parallel AB and it intersects BD at F, if DE:EA=2.0:3.0,EF=4.0, then the length of CD is ()", "ground_truth": "10"} | |
| {"image_path": "./Geo170K/images/test/359.png", "question": "As shown in the figure, it is known that l_ 1 parallel l_ 2 parallel l_ 3, if AB:BC=2.0:3.0,DE=4.0, then the length of EF is ()", "ground_truth": "6"} | |
| {"image_path": "./Geo170K/images/test/360.png", "question": "As shown in the figure DE parallel BC, AD = 3.0, DB = 4.0, AE = 1.5, then EC is equal to ()", "ground_truth": "2"} | |
| {"image_path": "./Geo170K/images/test/361.png", "question": "As shown in the figure, in triangle ABC, points D and E are on edges AB and AC respectively, DE parallel BC, and AE = 1.0, AC = 5.0, AB = 6.0, then the length of AD is ()", "ground_truth": "1.2"} | |
| {"image_path": "./Geo170K/images/test/362.png", "question": "As shown in the figure, D and E are points on AB and AC of triangle ABC, and DE parallel BC, if DE:BC=3.0:5.0,AD=6.0, then AB = ()", "ground_truth": "10"} | |
| {"image_path": "./Geo170K/images/test/363.png", "question": "As shown in the figure, triangle ABC similar triangle AED, angle ADE = 80.0, angle A = 60.0, then angle B is equal to ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/364.png", "question": "As shown in the figure, in Rttriangle ABC, angle C = 90.0, BC = 3.0, AC = 4.0, if triangle ABC similar triangle BDC, then CD = ()", "ground_truth": "\\frac{9}{4}"} | |
| {"image_path": "./Geo170K/images/test/365.png", "question": "As shown in the figure, triangle ABC similar triangle DEF, the scale factor of similarity is 1.0:2.0, if EF = 2.0, the length of BC is ()", "ground_truth": "1"} | |
| {"image_path": "./Geo170K/images/test/366.png", "question": "As shown in the figure, DE is the perpendicular bisector of triangle ABC. Given that the area of \u200b\u200btriangle ABC is 8.0^2, then the area of \u200b\u200btriangle ADE is ()^2.", "ground_truth": "2"} | |
| {"image_path": "./Geo170K/images/test/367.png", "question": "As shown in the figure, D is a point on BC of triangle ABC, it is known that AB = 6.0, AD = 3.0, AC = 4.0, angle DAC = angle B, then the length of BD is ()", "ground_truth": "6"} | |
| {"image_path": "./Geo170K/images/test/368.png", "question": "As shown in the figure, if triangle ABC similar triangle ACD, angle A = 60.0, angle ACD = 40.0, then the degree of angle BCD is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/369.png", "question": "As shown in the figure, two straight lines are intercepted by three parallel lines, AB = 2.0, BC = 3.0, then frac EFEG is equal to ()", "ground_truth": "\\frac{2}{5}"} | |
| {"image_path": "./Geo170K/images/test/370.png", "question": "As shown in the figure, in triangle ABC, DE parallel BC, if frac {AD}{AB}=frac {1.0}{3.0}", "ground_truth": "\\frac{1}{3}"} | |
| {"image_path": "./Geo170K/images/test/371.png", "question": "As shown in the figure, C and M are two points on the line segment AB, and the point M is the midpoint of the line segment AC. If AB = 8.0, BC = 2.0, then the length of AM is ()", "ground_truth": "3cm"} | |
| {"image_path": "./Geo170K/images/test/372.png", "question": "As shown in the figure, C and D are two points on the line segment AB. If CB = 4.0, DB = 7.0, and D is the midpoint of AC, then the length of AC is equal to ()", "ground_truth": "6cm"} | |
| {"image_path": "./Geo170K/images/test/373.png", "question": "As shown in the figure, BC=frac {1.0}{2.0}AB, D is the midpoint of AC, if DC = 3.0, then the length of AB is ()", "ground_truth": "4"} | |
| {"image_path": "./Geo170K/images/test/374.png", "question": "As shown in the figure, after Xiaolin walks straight in the direction of west from point P 12.0, turns left, the angle of rotation is \u03b1, and then walks 12.0, repeating this, Xiaolin has walked 108.0 and returned to point P, then the value of \u03b1-5.0 is ()", "ground_truth": "35\u00b0"} | |
| {"image_path": "./Geo170K/images/test/375.png", "question": "As shown in the figure, it is known that AD is the midline of triangle ABC, and the perimeter of triangle ABD is 3.0 larger than the perimeter of triangle ACD, then the difference between AB and AC is ()", "ground_truth": "3cm"} | |
| {"image_path": "./Geo170K/images/test/376.png", "question": "As shown in the figure, in triangle ABC, AB = AC, M and N are the midpoints of AB and AC respectively, D and E are points on BC. Connect DN, EM. If AB = 13.0, BC = 10.0, DE = 5.0, the area of \u200b\u200bthe shaded part in the figure is 2.0. ()", "ground_truth": "30"} | |
| {"image_path": "./Geo170K/images/test/377.png", "question": "As shown in the figure, C is a point on the semicircle O with AB as the diameter, connect AC and BC, and make square ACDE and BCFG with AC and BC as the edges respectively. The midpoints of DE, FG, arc \\athrAC, arc \\athrBC are M, N, P, Q respectively. If MP + NQ = 14.0, AC + BC = 18.0, then the length of AB is ()", "ground_truth": "13"} | |
| {"image_path": "./Geo170K/images/test/378.png", "question": "As shown in the figure, in the quadrilateral ABCD, point P is the midpoint of the diagonal BD, points E and F are the midpoints of AB and CD respectively, AD = BC, angle FPE = 136.0, then the degree of angle PFE is ()", "ground_truth": "22\u00b0"} | |
| {"image_path": "./Geo170K/images/test/379.png", "question": "As shown in the figure, it is known that the straight line a parallel b parallel c and the straight line d are perpendicular to them and intersect at the three points A, B and C. If AB = 3.0 and AC = 8.0, the distance between the parallel lines b and c is ( )", "ground_truth": "5"} | |
| {"image_path": "./Geo170K/images/test/380.png", "question": "As shown in the figure, it is known that angle 1 + angle 2 = 100.0, then angle 3 = ().", "ground_truth": "130\u00b0"} | |
| {"image_path": "./Geo170K/images/test/381.png", "question": "As shown in the figure, there is a pond. To measure the distance between A and B at both ends of the pond, firstly take a point C on the flat ground that can directly reach points A and B without passing through the pond, connect AC and extend to D, so that CD = CA , Connect BC and extend to E, make CE = CB, connect ED. If DE = 58.0 is measured, then the distance between A and B is ()", "ground_truth": "58\u7c73"} | |
| {"image_path": "./Geo170K/images/test/382.png", "question": "As shown in the figure, the parallel lines a and b are intercepted by the straight line c. If angle 1 = 50.0, then the degree of angle 2 is ()", "ground_truth": "130\u00b0"} | |
| {"image_path": "./Geo170K/images/test/383.png", "question": "As shown in the figure, it is known that angle 1 = 60.0, angle A + angle B + angle C + angle D + angle E + angle F = ()", "ground_truth": "240\u00b0"} | |
| {"image_path": "./Geo170K/images/test/384.png", "question": "As shown in the figure, in the isosceles triangle ABC, AB = AC, BD is the height on AC, if angle A = 36.0, then the size of angle DBC is ()", "ground_truth": "18\u00b0"} | |
| {"image_path": "./Geo170K/images/test/385.png", "question": "As shown in the figure, if a parallel b, angle 1 = 115.0, then angle 2 = ()", "ground_truth": "65\u00b0"} | |
| {"image_path": "./Geo170K/images/test/386.png", "question": "As shown in the figure, in triangle ABC, angle A = 80.0. Point D is a point on the extended line of BC, angle ACD = 150.0, then angle B = ()", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/387.png", "question": "As shown in the figure, a parallel b, point B is on the straight line a, and AB perpendicular BC, angle 1 = 35.0, then angle 2 = ()", "ground_truth": "55\u00b0"} | |
| {"image_path": "./Geo170K/images/test/388.png", "question": "As shown in the figure, the line AB and CD intersect at E, and there is a point F on the bisector of angle CEB, FM parallel AB. When angle 3 = 10.0, the degree of angle F is ()", "ground_truth": "85\u00b0"} | |
| {"image_path": "./Geo170K/images/test/389.png", "question": "As shown in the figure, it is known that straight lines a and b are intercepted by straight line c. If a parallel b, angle 1 = 120.0, then the degree of angle 2 is ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/390.png", "question": "As shown in the figure, C and D are two points on circle O with the line segment AB as the diameter. If CA = CD, and angle CAB = 25.0, then the degree of angle ACD is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/391.png", "question": "As shown in the figure, AB parallel EF, CD perpendicular EF at point D, if angle BCD = 140.0, then the degree of angle ABC is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/392.png", "question": "As shown in the figure, in triangle ABC, angle B = 40.0, passing point C to draw CD parallel AB, angle ACD = 65.0, then the degree of angle ACB is ()", "ground_truth": "75\u00b0"} | |
| {"image_path": "./Geo170K/images/test/393.png", "question": "Place a pair of right triangle plates as shown in the figure, so that the leg of the triangle plate with angle 30.0 and the leg of the triangle plate with angle 45.0 are on the same straight line, then the degree of angle 1 is ()", "ground_truth": "75\u00b0"} | |
| {"image_path": "./Geo170K/images/test/394.png", "question": "Given the straight line a parallel b, a right triangle plate is placed as shown in the figure, if angle 1 = 37.0, then the degree of angle 2 is ()", "ground_truth": "53\u00b0"} | |
| {"image_path": "./Geo170K/images/test/395.png", "question": "As shown in the figure, the diagonal AC and BD of the rectangle ABCD intersect at point O, CE parallel BD, DE parallel AC, if AB = 4.0, BC = 3.0, then the perimeter of the quadrilateral CODE is ()", "ground_truth": "10"} | |
| {"image_path": "./Geo170K/images/test/396.png", "question": "As shown in the figure, put the right-angled vertex of the triangle plate with 30.0 angle on one side of the ruler, if angle 1 = 35.0, then the degree of angle 2 is ()", "ground_truth": "65\u00b0"} | |
| {"image_path": "./Geo170K/images/test/397.png", "question": "As shown in the figure, in parallelogram ABCD, F is a point on AD, CF = CD. If angle B = 72.0, then the degree of angle AFC is ()", "ground_truth": "108\u00b0"} | |
| {"image_path": "./Geo170K/images/test/398.png", "question": "From a corner of the cubic blank with edge length 4.0, excavate a small cube with edge length 2.0 to obtain a part as shown in the figure, then the surface area of \u200b\u200bthis part is ()", "ground_truth": "96"} | |
| {"image_path": "./Geo170K/images/test/399.png", "question": "As shown in the figure, the points B, O, D are on the same straight line, if angle 1 = 15.0, angle 2 = 105.0, then the degree of angle AOC is ()", "ground_truth": "90"} | |
| {"image_path": "./Geo170K/images/test/400.png", "question": "As shown in the figure, the right-angled vertices of the two triangle plates are overlapped and stacked together. If angle 1 = 40.0, then the degree of angle 2 is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/401.png", "question": "As shown in the figure, after a car has turned twice through a section of road, it is the same as the original driving direction, that is, the two roads before and after turning are parallel to each other. The first turning angle angle B is equal to 142.0, and the degree of angle the second turning angle C is ()", "ground_truth": "142\u00b0"} | |
| {"image_path": "./Geo170K/images/test/402.png", "question": "As shown in triangle ABC, angle ACB = 90.0, AD bisects angle BAC and it intersects BC at D, DE is perpendicular to AB to E, if DE = 1.5, BD = 3.0, then BC = ()", "ground_truth": "4.5cm"} | |
| {"image_path": "./Geo170K/images/test/403.png", "question": "As shown in the figure, AB = AC, AD = AE, angle BAC = angle DAE, angle 1 = 25.0, angle 2 = 30.0, then angle 3 = ()", "ground_truth": "55\u00b0"} | |
| {"image_path": "./Geo170K/images/test/404.png", "question": "As shown in the figure, in triangle ABC, angle B = 46.0, angle C = 54.0, AD bisects angle BAC and it intersects BC at D, then the size of angle BAD is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/405.png", "question": "As shown in the figure, it is known that D is a point on BC, angle B = angle 1, angle BAC = 78.0, then angle 2 = ()", "ground_truth": "78\u00b0"} | |
| {"image_path": "./Geo170K/images/test/406.png", "question": "As shown in the figure, in triangle ABC, angle ACB = 90.0, fold triangle CBD along CD so that point B falls exactly at point E on the edge of AC. If angle A = 24.0, then the degree of angle BDC is ()", "ground_truth": "69\u00b0"} | |
| {"image_path": "./Geo170K/images/test/407.png", "question": "As shown in the figure, DE is the perpendicular bisector of BC of triangle ABC, and it intersects BC at E as well as intersects AB at D, and angle B = 40.0, angle A = 60.0, then the degree of angle ACD is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/408.png", "question": "As shown in the figure, in circle O with radius 5.0, AB is a chord, OC perpendicular AB at point C, and OC = 3.0, then the value of AB is ()", "ground_truth": "8cm"} | |
| {"image_path": "./Geo170K/images/test/409.png", "question": "As shown in the figure, in circle O, OA perpendicular OB, angle A = 35.0, then the degree of arc CD is ()", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/410.png", "question": "As shown in the figure, in triangle ABC, DE is the perpendicular bisector of AC, AE = 3.0, the perimeter of triangle ABD is 13.0, then the perimeter of triangle ABC is ()", "ground_truth": "19cm"} | |
| {"image_path": "./Geo170K/images/test/411.png", "question": "As shown in the figure, \u22bfABC is inscribed in circle O, if angle OAB = 28.0, then the size of angle C is ()", "ground_truth": "62\u00b0"} | |
| {"image_path": "./Geo170K/images/test/412.png", "question": "As shown in the figure, it is known that PA and PB are the tangents of circle O, A and B are the tangent points, AC is the diameter of circle O, angle P = 40.0, then the degree of angle BAC is ()", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/413.png", "question": "As shown in the figure, in Rttriangle ABC, angle B = 90.0, AB = 6.0, AC = 10.0 Fold triangle ABC along ED to make point C coincide with point A, then the perimeter of triangle ABE is equal to ()", "ground_truth": "14"} | |
| {"image_path": "./Geo170K/images/test/414.png", "question": "As shown in the figure, a rectangular ruler is broken and dislocated along a straight line, and points E, D, B, and F are on the same straight line. If angle ADE = 125.0, then the degree of angle DBC is ()", "ground_truth": "55\u00b0"} | |
| {"image_path": "./Geo170K/images/test/415.png", "question": "As shown in the figure, the central angle angle AOB = 60.0 \u2218, then the degree of the angle of circumference angle ACB is ()", "ground_truth": "30\u00b0"} | |
| {"image_path": "./Geo170K/images/test/416.png", "question": "As shown in the figure, in triangle ABC, angle A = 90.0, AB = AC, BD bisects angle ABE, DE perpendicular BC, if BC = 10.0, then the perimeter of triangle DEC is ()", "ground_truth": "10cm"} | |
| {"image_path": "./Geo170K/images/test/417.png", "question": "As shown in the figure, the perpendicular bisector of the isosceles trapezoid ABCD circumscribed by the circle EF = 15.0, then the perimeter of the isosceles trapezoid ABCD is equal to ()", "ground_truth": "60cm"} | |
| {"image_path": "./Geo170K/images/test/418.png", "question": "As shown in the figure, if CB = 4.0, DB = 7.0, and D is the midpoint of AC, then the length of AC is ()", "ground_truth": "6cm"} | |
| {"image_path": "./Geo170K/images/test/419.png", "question": "As shown in the figure, in triangle ABC, angle ABC = 120.0, if DE and FG bisect AB and BC perpendicularly, then the degree of angle EBF is ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/420.png", "question": "As shown in the figure, in Rttriangle ABC, angle BAC = 90.0, rotate triangle ABC clockwise around point A by 90.0 to obtain triangle AB\u2032C\u2032 (the corresponding point of point B is point B\u2032, and the corresponding point of point C is point C \u2032), connect CC\u2032, if angle CC\u2032B\u2032 = 33.0, then the size of angle B is ()", "ground_truth": "78\u00b0"} | |
| {"image_path": "./Geo170K/images/test/421.png", "question": "As shown in the figure, point C is on line AB, point D is the midpoint of AC, if CD = 3.0, AB = 10.0, then the length of BC is ()", "ground_truth": "4cm"} | |
| {"image_path": "./Geo170K/images/test/422.png", "question": "As shown in the figure, AD is the midline of triangle ABC, and it is known that the perimeter of triangle ABD is 22.0, and AB is longer than AC by 3.0, then the perimeter of triangle ACD is ()", "ground_truth": "19cm"} | |
| {"image_path": "./Geo170K/images/test/423.png", "question": "As shown in the figure, the line segment AB = 20.0, C is the midpoint of AB, D is the point on CB, E is the midpoint of DB, and EB = 3.0, then CD is equal to ()", "ground_truth": "4"} | |
| {"image_path": "./Geo170K/images/test/424.png", "question": "As shown in the figure, C and D are two points on the line segment AB. If CB = 4.0, DB = 7.0, and D is the midpoint of AC, then AB = ()", "ground_truth": "10cm"} | |
| {"image_path": "./Geo170K/images/test/425.png", "question": "As shown in the figure, a supermarket shopping cart is placed on a horizontal ground, and its lateral quadrilateral ABCD is in the same plane as a horizontal line on the ground, and AB parallel l, if angle A = 93.0, angle D = 111.0, then the degree of the acute angle between the straight line CD and l is ()", "ground_truth": "24\u00b0"} | |
| {"image_path": "./Geo170K/images/test/426.png", "question": "As shown in the figure, in triangle ABC, angle B = angle C, D is a point on edge BC, point E is on edge AC, angle ADE = angle AED, if angle BAD = 24.0, then angle CDE = ()", "ground_truth": "12\u00b0"} | |
| {"image_path": "./Geo170K/images/test/427.png", "question": "As shown in the figure, AB is the chord of circle O, OC perpendicular AB at point D, and it intersects circle O at point C, if the radius is 5.0, OD = 3.0, then the length of chord AB is ()", "ground_truth": "8"} | |
| {"image_path": "./Geo170K/images/test/428.png", "question": "As shown in the figure, AB is the diameter of circle O, O is the center of the circle, the chord CD perpendicular AB at E, AB = 10.0, CD = 8.0, then the length of OE is ()", "ground_truth": "3"} | |
| {"image_path": "./Geo170K/images/test/429.png", "question": "As shown in the figure, the radius of circle O is OA = 5.0, and the arc with A as the center and OA as the radius intersects circle O at the two points B and C, then the length of the chord BC is equal to ()", "ground_truth": "5\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/430.png", "question": "As shown in the figure, C and D are two points on the line segment AB. If BC = 3.0, BD = 5.0, and D is the midpoint of AC, then the length of AC is ()", "ground_truth": "4cm"} | |
| {"image_path": "./Geo170K/images/test/431.png", "question": "As shown in the figure, in circle O, AB is the chord, OC perpendicular AB, the foot of perpendicular is C, if AB = 16.0, OC = 6.0, then the diameter of circle O is equal to ()", "ground_truth": "20"} | |
| {"image_path": "./Geo170K/images/test/432.png", "question": "As shown in the figure, in the circle O with a radius of 10.0, the radius OC is perpendicular to the chord AB to the point D, AB = 16.0, then the length of CD is ()", "ground_truth": "4"} | |
| {"image_path": "./Geo170K/images/test/433.png", "question": "As shown in the figure, P is a point on the chord AB of circle O, AB = 10.0, AP = 4.0, OP = 5.0, then the radius of circle O is. ()", "ground_truth": "7"} | |
| {"image_path": "./Geo170K/images/test/434.png", "question": "As shown in the figure, the rectangle intersects with circle O, if AB = 4.0, BC = 5.0, DE = 3.0, then the length of EF is ()", "ground_truth": "7"} | |
| {"image_path": "./Geo170K/images/test/435.png", "question": "As shown in the figure, AB is the diameter of circle O, CD is the chord, AB perpendicular CD, the foot of perpendicular is point E, connect OD, CB, AC, angle DOB = 60.0, EB = 2.0, then the length of CD is ()", "ground_truth": "4\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/436.png", "question": "As shown in the figure, AB is the diameter of circle O, CD is the chord, AB perpendicular CD at point E, if the radius is 5.0, OE = 3.0, then the length of CD is ()", "ground_truth": "8"} | |
| {"image_path": "./Geo170K/images/test/437.png", "question": "As shown in the figure, in the circle O with a radius of 5.0, the length of the chord AB is 8.0, then the distance from the center O to the chord AB is ()", "ground_truth": "3"} | |
| {"image_path": "./Geo170K/images/test/438.png", "question": "As shown in the figure, AB = 8.0, AD = BC = 5.0, then CD is equal to ()", "ground_truth": "2cm"} | |
| {"image_path": "./Geo170K/images/test/439.png", "question": "As shown in the figure, C and D are two points on the line segment AB. If CB = 4.0, DB = 7.0, and D is the midpoint of AC, then the length of AB is equal to ()", "ground_truth": "10cm"} | |
| {"image_path": "./Geo170K/images/test/440.png", "question": "As shown in the figure, point C is on line AB, point E is the midpoint of AC, and point D is the midpoint of BC. If ED = 6.0, the length of the line segment AB is ()", "ground_truth": "12"} | |
| {"image_path": "./Geo170K/images/test/441.png", "question": "As shown in the figure, it is known that angle 1 = 40.0, angle A + angle B = 140.0, then the degree of angle C + angle D is ()", "ground_truth": "80\u00b0"} | |
| {"image_path": "./Geo170K/images/test/442.png", "question": "As shown in the figure, the diagonals of the quadrilateral ABCD AC perpendicular BD, the foot of perpendicular is O, and AC = 12.0, BD = 9.0, then the area of \u200b\u200bthe quadrilateral ABCD is ()", "ground_truth": "54"} | |
| {"image_path": "./Geo170K/images/test/443.png", "question": "As shown in the figure, it is known that triangle ABC, point D is on the extended line of BC, angle ACD = 140.0, angle ABC = 50.0, then the size of angle A is ()", "ground_truth": "90\u00b0"} | |
| {"image_path": "./Geo170K/images/test/444.png", "question": "As shown in the figure, point O is on the straight line AB, if angle 2 = 140.0, then the degree of angle 1 is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/445.png", "question": "As shown in the figure, line segment AB = 10.0, M is the midpoint of line segment AB, C is the midpoint of line segment MB, N is a point of line segment AM, and MN = 1.0, the length of line segment NC ()", "ground_truth": "3.5"} | |
| {"image_path": "./Geo170K/images/test/446.png", "question": "Suppose BF intersects AC at point P, AE intersects DF at point Q. If angle APB = 126.0, angle AQF = 100.0, then angle A-angle F = ()", "ground_truth": "46\u00b0"} | |
| {"image_path": "./Geo170K/images/test/447.png", "question": "As shown in the figure, BD and CE are the height and angular bisector of triangle ABC respectively, and they intersect with point O. If angle BCA = 70.0, then the degree of angle BOE is ()", "ground_truth": "55\u00b0"} | |
| {"image_path": "./Geo170K/images/test/448.png", "question": "As shown in the figure, it is known that points A, B, and C are on the same straight line, AB = 7.0, BC = 3.0, point D is the midpoint of line segment AC, and the length of line segment DB is ()", "ground_truth": "2"} | |
| {"image_path": "./Geo170K/images/test/449.png", "question": "As shown in the figure, in the quadrilateral ABCD, the angular bisector of angle DAB and the bisector of exterior angle of angle ABC intersect at point P, and angle angle D + angle C = 200.0, then angle P = ()", "ground_truth": "10\u00b0"} | |
| {"image_path": "./Geo170K/images/test/450.png", "question": "As shown in the figure, BP bisects angle ABC and it intersects CD at point F, DP bisects angle ADC and it intersects AB at point E, if angle A = 40.0, angle P = 38.0, then the degree of angle C is ()", "ground_truth": "36\u00b0"} | |
| {"image_path": "./Geo170K/images/test/451.png", "question": "As shown in the figure, extend the line segment AB to C with the length of 8.0, so that BC = 4.0, M and N are the midpoints of AB and BC respectively, then the length of MN is ()", "ground_truth": "6"} | |
| {"image_path": "./Geo170K/images/test/452.png", "question": "As shown in the figure, the four points A, B, C, and D are all on circle O, angle BOD = 110.0, then the degree of angle BCD is ()", "ground_truth": "125\u00b0"} | |
| {"image_path": "./Geo170K/images/test/453.png", "question": "As shown in the figure, the quadrilateral ABCD is an inscribed quadrilateral of circle O, angle BCD = 110.0, then the degree of angle BOD is ()", "ground_truth": "140\u00b0"} | |
| {"image_path": "./Geo170K/images/test/454.png", "question": "As shown in the figure, a cargo ship sails from point A to point D in the east direction at a speed of 24.0 nautical mile/hour. At point A, a certain island C is measured in the direction 60.0 east by north. The cargo ship arrived at point B after sailing for 30.0 minutes. At this time, it was measured that the island is in the direction 30.0 east by north. Then the shortest distance between the cargo ship and the island C is ()", "ground_truth": "6\u221a{3}\u6d77\u91cc"} | |
| {"image_path": "./Geo170K/images/test/455.png", "question": "As shown in the figure, PA, PB are tangent to circle O at points A, B, point C is a point on circle O, and angle P = 36.0, then angle ACB = ()", "ground_truth": "72\u00b0"} | |
| {"image_path": "./Geo170K/images/test/456.png", "question": "As shown in the figure, PA and PB are tangent to circle O at A and B respectively, angle C = 55.0, then angle P is equal to ()", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/457.png", "question": "As shown in the figure, in a square grid with edge length 1.0. Connect grid points D, N and E, C, DN and EC intersect at point P, then tanangle CPN is ()", "ground_truth": "2"} | |
| {"image_path": "./Geo170K/images/test/458.png", "question": "As shown in the figure, in Rttriangle ABC, angle C = 90.0, AB = 10.0, AC = 8.0, then sinB is equal to ()", "ground_truth": "\\frac{4}{5}"} | |
| {"image_path": "./Geo170K/images/test/459.png", "question": "As shown in the figure, the quadrilateral ABCD is the circumscribed quadrilateral of circle O, and AB = 10.0, CD = 12.0, then the perimeter of the quadrilateral ABCD is ()", "ground_truth": "44"} | |
| {"image_path": "./Geo170K/images/test/460.png", "question": "It is known that for a horizontally placed cylindrical drainage pipe, the radius of the pipe section is 1.0, if the water surface is high 0.2. Then the width of the water surface of the drainage pipe section is ()", "ground_truth": "1.2m"} | |
| {"image_path": "./Geo170K/images/test/461.png", "question": "As shown in the figure, A, B, C are the three points on circle O, AB, AC are on the both sides of the center O, if angle ABO = 20.0, angle ACO = 30.0, then the degree of angle BOC is ()", "ground_truth": "100\u00b0"} | |
| {"image_path": "./Geo170K/images/test/462.png", "question": "As shown in the figure, in the rectangular coordinate system xOy, point A is on the positive semi-axis of the y-axis, points B and C are on the positive semi-axis of x, and angle BAC = angle ACB = 30.0, AC = 4.0, point D is a moving point on the x-axis, the symmetrical points of point D with respect to the straight lines AB and AC are E and F, then the minimum value of the line segment EF is equal to ()", "ground_truth": "2"} | |
| {"image_path": "./Geo170K/images/test/463.png", "question": "As shown in the figure, angle BAC = 110.0, if A and B are symmetrical with respect to the line MP, A and C are symmetrical with respect to the line NQ, then the size of angle PAQ is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/464.png", "question": "As shown in the figure, AB parallel CD, BE perpendicularly bisects AD, DC = BC, if angle A = 70.0, then angle C = ()", "ground_truth": "100\u00b0"} | |
| {"image_path": "./Geo170K/images/test/465.png", "question": "As shown in the figure, in triangle ABC, AB = 10.0, AC = 18.0, point M starts from point A and moves to point B at a speed of 2.0 per second, and point N starts from point C and moves to point A at a speed of 3.0 per second. One of the moving points reaches the endpoint, and the other moving point also stops. When triangle AMN is an isosceles triangle with MN as the base, the movement time is ()", "ground_truth": "3.6\u79d2"} | |
| {"image_path": "./Geo170K/images/test/466.png", "question": "As shown in the figure, in triangle ABC, angle ABC = 110.0, AM = AN, CN = CP, then angle MNP = ()", "ground_truth": "35\u00b0"} | |
| {"image_path": "./Geo170K/images/test/467.png", "question": "As shown in the figure, it is known that the bisectors of the four inner corners of parallelogram ABCD intersect at points E, F, G, and H respectively. Connect AC. If EF = 2.0, FG = GC = 5.0, then the length of AC is ()", "ground_truth": "13"} | |
| {"image_path": "./Geo170K/images/test/468.png", "question": "As shown in the figure, parallelogram ABCD, points E and F are on AD and AB respectively, and connect EB, EC, FC, and FD in turn. The area of \u200b\u200bthe shaded part in the figure is S~ 1 ~, S~ 2 ~, S~ 3 ~ , S~ 4 ~, S~ 1 ~ = 1.0, S~ 2 ~ = 2.0, S~ 3 ~ = 3.0, then the value of S~ 4 ~ is ()", "ground_truth": "7"} | |
| {"image_path": "./Geo170K/images/test/469.png", "question": "As shown in the figure, in parallelogram ABCD, the diagonal AC and BD intersect at point O, and points E and F are the midpoints of AB and AO respectively. Connect EF. If EF = 3.0, the length of BD is ()", "ground_truth": "12"} | |
| {"image_path": "./Geo170K/images/test/470.png", "question": "As shown in the figure, parallelogram ABCD's diagonal AC, BD intersect at O, EF passes through point O, and intersects AD, BC at E, F respectively. It is known that the area of \u200b\u200bparallelogram ABCD is 20.0 ^2.0, then the area of \u200b\u200bthe shaded part in the figure is ()", "ground_truth": "5cm^2^"} | |
| {"image_path": "./Geo170K/images/test/471.png", "question": "As shown in the figure, in parallelogram ABCD, the bisector of angle BCD intersects AD at point E, and it intersects the extended line of BA at point F, BF = 4 AF, BC = 12.0, then the length of AF is ()", "ground_truth": "3"} | |
| {"image_path": "./Geo170K/images/test/472.png", "question": "As shown in the figure, in parallelogram ABCD, AB = 10.0, AD = 15.0, AC and BD intersect at point O. OE perpendicular BD and it intersects AD at E, then the perimeter of triangle ABE is ()", "ground_truth": "25cm"} | |
| {"image_path": "./Geo170K/images/test/473.png", "question": "As shown in the figure, in the parallelogram ABCD, E and F are the midpoints of AD and BC respectively, P is the moving point on the edge DC, G and H are the midpoints of PE and PF respectively, it is known that DC = 10.0, then length of GH is ()", "ground_truth": "5cm"} | |
| {"image_path": "./Geo170K/images/test/474.png", "question": "As shown in the figure, in the parallelogram ABCD, the diagonals AC and BD intersect at the point O, and the point E is the midpoint of CD. Connect OE. If the perimeter of the parallelogram ABCD is 24.0 and BD = 8.0, then the perimeter of triangle DOE is ()", "ground_truth": "10"} | |
| {"image_path": "./Geo170K/images/test/475.png", "question": "As shown in the figure, in the parallelogram ABCD, point E is a point on AB. Connect DE and CE. If DE and CE are the angular bisectors of angle ADC and angle BCD, and AB = 4.0, then the perimeter of the parallelogram ABCD is ()", "ground_truth": "12"} | |
| {"image_path": "./Geo170K/images/test/476.png", "question": "As shown in the figure, make three parallel lines through a point in the triangle. If the perimeter of the triangle is 6.0, then the sum of the perimeters of the three shaded triangles in the figure is ()", "ground_truth": "6cm"} | |
| {"image_path": "./Geo170K/images/test/477.png", "question": "As shown in the figure, in triangle ABC, the straight line DE parallel BC, angle ABC, angle ACB passing through the vertex A intersects DE at points E and D, respectively. If AC = 3.0, AB = 4.0, then the length of DE is ()", "ground_truth": "7"} | |
| {"image_path": "./Geo170K/images/test/478.png", "question": "As shown in the figure, in triangle ABC, angle B = angle C, D is on BC, angle BAD = 50.0, AE = AD, then the degree of angle EDC is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/479.png", "question": "As shown in the figure, in the quadrilateral ABCD, AD parallel BC, BF bisects angle ABC and it intersects AD at point F, CE bisects angle BCD, and it intersects AD at point E, AB = 8.0, CD = 6.0, EF = 2.0, then the length of AD is ()", "ground_truth": "12"} | |
| {"image_path": "./Geo170K/images/test/480.png", "question": "As shown in the figure, in triangle ABC, AB = 10.0, AC = 6.0, the straight line DE parallel CB passing through point A, the bisectors of angle ABC and angle ACB intersect DE at E, D respectively, then the length of DE is ()", "ground_truth": "16"} | |
| {"image_path": "./Geo170K/images/test/481.png", "question": "As shown in the figure, it is known that the length of one waist AB of the isosceles triangle ABC is 4.0 centimetres. Cross any point D on the bottom edge BC to draw two waist parallel lines, and they intersect the two waists at E and F respectively, then the perimeter of the quadrilateral AEDF is ()", "ground_truth": "8\u5398\u7c73"} | |
| {"image_path": "./Geo170K/images/test/482.png", "question": "As shown in the figure, in the equilateral triangle ABC, BD bisects angle ABC and it intersects AC at point D, and cross D to draw DE perpendicular BC at point E, and CE = 1.5, then the length of AB is ()", "ground_truth": "6"} | |
| {"image_path": "./Geo170K/images/test/483.png", "question": "A ship departs from point A on the sea level and travels 40.0 nautical miles to the west by south direction 40.0 to point B, and then travels 40.0 nautical miles from point B to the west by north 20.0 direction to point C, then the distance between A and C is ( )", "ground_truth": "40\u6d77\u91cc"} | |
| {"image_path": "./Geo170K/images/test/484.png", "question": "As shown in the figure, there is the \"herringbone\" steel frame, where the inclined beam AB = AC, the top angle angle BAC = 120.0, the span BC = 10.0, AD is the pillar (ie the center line of the bottom BC), two support frames DE perpendicular AB, DF perpendicular AC, then DE + DF is equal to ()", "ground_truth": "5m"} | |
| {"image_path": "./Geo170K/images/test/485.png", "question": "Translate triangle ABC to the right along CB to get triangle DEF. If the area of \u200b\u200bthe quadrilateral ABED is equal to 32.0, the translation distance is equal to ()", "ground_truth": "4"} | |
| {"image_path": "./Geo170K/images/test/486.png", "question": "As shown in the figure, in triangle ABC, angle ACB = 90.0, angle ABC = 60.0, BD bisects angle ABC, P point is the midpoint of BD, if BD = 6.0, the length of CP is ()", "ground_truth": "3"} | |
| {"image_path": "./Geo170K/images/test/487.png", "question": "As shown in the figure, the height of the floor of a truck compartment from the ground is frac {3.0}{2.0}. In order to facilitate the loading, a wooden board is often used to form an inclined plane. If the angle between the inclined plane and the horizontal ground is not greater than 30.0, the length of this wooden board is at least ( )", "ground_truth": "3\u7c73"} | |
| {"image_path": "./Geo170K/images/test/488.png", "question": "As shown in the figure, in Rttriangle ABC, angle ACB = 90.0, AC = 6.0, BC = 8.0, AD is the bisector of angle BAC. If P and Q are the moving points on AD and AC respectively, then the minimum value of PC + PQ is ()", "ground_truth": "\\frac{24}{5}"} | |
| {"image_path": "./Geo170K/images/test/489.png", "question": "As shown in the figure, in the quadrilateral ABCD, angle BAD = 130.0, angle B = angle D = 90.0, points E and F are the moving points on the line segments BC and DC, respectively. When the perimeter of triangle AEF is the smallest, then the degree of angle EAF is ()", "ground_truth": "80\u00b0"} | |
| {"image_path": "./Geo170K/images/test/490.png", "question": "As shown in the figure, the perimeter of triangle ABC is 16.0. Point D is the midpoint of the AB, BD = 2.0, passing point D is the vertical line l of AB, and E is any point on l, then the minimum perimeter of triangle AEC is ()", "ground_truth": "12"} | |
| {"image_path": "./Geo170K/images/test/491.png", "question": "As shown in the figure, OA and OB are the perpendicular bisectors of the line segments MC and MD respectively, MD = 5.0, MC = 7.0, CD = 10.0, a small ant starts from point M and climbs to any point E on OA, and then climbs to any point F on OB , and then climbs back to point M, the shortest path the little ant crawls can be ()", "ground_truth": "10cm"} | |
| {"image_path": "./Geo170K/images/test/492.png", "question": "As shown in the figure, in triangle ABC, BF bisects angle ABC, crossing point A to draw AF perpendicular BF, the foot of perpendicular is F and extend BC to point G, D is the midpoint of AB. Connect DF and extend to intersect AC at point E. If AB = 12.0, BC = 20.0, then the length of the line segment EF is ()", "ground_truth": "4"} | |
| {"image_path": "./Geo170K/images/test/493.png", "question": "As shown in the figure, in triangle ABC, points D and E are the midpoints of AB and AC respectively. If DE = 1.5, the length of BC is ()", "ground_truth": "3"} | |
| {"image_path": "./Geo170K/images/test/494.png", "question": "As shown in the figure, in triangle ABC, BD and CE are angular bisectors, AM perpendicular BD at point M, AN perpendicular CE at point N. The perimeter of triangle ABC is 30.0, BC = 12.0. Then the length of MN is ()", "ground_truth": "3"} | |
| {"image_path": "./Geo170K/images/test/495.png", "question": "As shown in the figure, in triangle ABC, D and E are the midpoints of BC and AC respectively. BF bisects angle ABC and intersects DE at point F. If BC = 6.0, then the length of DF is ()", "ground_truth": "3"} | |
| {"image_path": "./Geo170K/images/test/496.png", "question": "The students have all played the game of seesaw. The picture is a schematic diagram of a seesaw. The column OC is perpendicular to the ground, OA = OB. When one end of the seesaw A touches the ground, angle AOA\u2032 = 50.0, then when the other end B of the seesaw touches the ground, angle COB\u2032 is equal to ()", "ground_truth": "65\u00b0"} | |
| {"image_path": "./Geo170K/images/test/497.png", "question": "As shown in the figure, in triangle ABC, AB = AC, angle A = 40.0, DE bisects AC perpendicularly, then the degree of angle BCD is equal to ()", "ground_truth": "30\u00b0"} | |
| {"image_path": "./Geo170K/images/test/498.png", "question": "As shown in the figure, PA and PB are two tangents of circle O with radius 1.0, points A and B are tangent points respectively, angle APB = 60.0, OP intersects chord AB at point C, and intersects circle O at point D. Then the area of \u200b\u200bthe shaded part in the figure is ()", "ground_truth": "\\frac{1}{6}\u03c0"} | |
| {"image_path": "./Geo170K/images/test/499.png", "question": "As shown in the figure, in triangle ABC, angle A = 90.0, AB = AC = 3.0, now rotate triangle ABC anticlockwise around point B by a certain angle, point C\u2032 falls on the straight line where the height of side BC is located, then the area swept by BC during the rotation of edge BC is ()", "ground_truth": "3\u03c0"} | |
| {"image_path": "./Geo170K/images/test/500.png", "question": "As shown in the figure, the sector OAB and the sector OCD whose central angles are all 90.0 are stacked together, OA = 3.0, OC = 1.0, respectively connect AC and BD, then the area of \u200b\u200bthe shaded part in the figure is ()", "ground_truth": "2\u03c0"} | |
| {"image_path": "./Geo170K/images/test/501.png", "question": "As shown in the figure, in order to green the environment, four sector open spaces with a radius of 1.0 are drawn at the four corners of the rectangular open space for greening, then the total green area is ()", "ground_truth": "\u03c0"} | |
| {"image_path": "./Geo170K/images/test/502.png", "question": "The lateral surface of a staircase is shown in the figure. The measured length of AB is 3.0, and the slope ratio of the stair slope BC is 1.0:2.0, then the length of the slope BC of the staircase is ()", "ground_truth": "3\u221a{5}\u7c73"} | |
| {"image_path": "./Geo170K/images/test/503.png", "question": "At a certain moment, there is a passenger ship at sea point P, and lighthouse A is measured in the direction 30.0 north by east of P, and is 50.0 nautical miles away. The passenger ship sails at the speed of 60.0 nautical mile/hour in the direction of 60.0 from north by west for $frac {2.0}{3.0}$hours to reach point B, then tanangle BAP = ()", "ground_truth": "\\frac{4}{5}"} | |
| {"image_path": "./Geo170K/images/test/504.png", "question": "As shown in the figure, it is known that there is a laser auxiliary signal within a certain range of the lighthouse M. A ship is sailing at a constant speed from south by north at a constant speed at sea. The ship measured at A and measured that the lighthouse M was in the direction 30.0 to the east by north, and it traveled 1.0. Arrived at point B after hours, and just entered the laser signal area of \u200b\u200blighthouse M at this time. It is measured that lighthouse M is in the direction of 45.0 east by north, then the time for the ship to pass the laser signal area of \u200b\u200blighthouse M is ()", "ground_truth": "(\u221a{3}+1)\u5c0f\u65f6"} | |
| {"image_path": "./Geo170K/images/test/505.png", "question": "As shown in the figure, at 8.0 in the morning, a ship departs from point A and sails northward at a speed of 15.0 nautical miles/hour, and arrives at point B at 9.0 and 40.0 minutes. From point A, lighthouse C is measured in the direction 26.0 west by north. From point B, lighthouse C is measured in the 52.0 direction west of north, then the distance from point B to lighthouse C is ()", "ground_truth": "25\u6d77\u91cc"} | |
| {"image_path": "./Geo170K/images/test/506.png", "question": "At 9.0 in the morning, a ship departs from point A and sails in the direction due east at a speed of 40.0 nautical miles per hour, and arrives at point B at 9.0 and 30.0 minutes. As shown in the figure, the island M is measured from A and B. In the direction of 45.0 north by east and 15.0 north by east, then the distance between B and island M is ()", "ground_truth": "20\u221a{2}\u6d77\u91cc"} | |
| {"image_path": "./Geo170K/images/test/507.png", "question": "In order to measure the width of parallel river AB, angle ACB = 30.0, angle ADB = 60.0, CD = 60.0, then the width of the river AB is ()", "ground_truth": "30\u221a{3}m"} | |
| {"image_path": "./Geo170K/images/test/508.png", "question": "As shown in the figure, it is known that a fisherman on a fishing boat sees lighthouse M in the direction 60.0 east by north at point A. This fishing boat sails eastward at a speed of 28.0 nautical miles/hour, and arrives at point B in half an hour, and sees it at point B The lighthouse M is in the 15.0 direction to the east by north. At this time, the distance between the lighthouse M and the fishing boat is ()", "ground_truth": "7\u221a{2}\u6d77\u91cc"} | |
| {"image_path": "./Geo170K/images/test/509.png", "question": "As shown in the figure, it is known thatfrac {OA}{DO}=frac {BO}{CO}=frac {1.0}{2.0}, the area of \u200b\u200btriangle AOB is 100.0 ^ 2, then the area of \u200b\u200btriangle DOC is ()", "ground_truth": "400cm\u00b2"} | |
| {"image_path": "./Geo170K/images/test/510.png", "question": "As shown in the figure, in triangle ABC, angle BAC = 90.0, AD perpendicular BC at D, if AB = 3.0, BC = 5.0, then the length of DC ()", "ground_truth": "\\frac{16}{5}"} | |
| {"image_path": "./Geo170K/images/test/511.png", "question": "As shown in the figure, in the parallelogram ABCD, AE:EB=1.0:2.0,S~triangle AEF~=3.0, then S~triangle FCD~ is ()", "ground_truth": "27"} | |
| {"image_path": "./Geo170K/images/test/512.png", "question": "As shown in the figure, in the parallelogram ABCD, AE = EB, AF = 2.0, then the value of FC is ()", "ground_truth": "4"} | |
| {"image_path": "./Geo170K/images/test/513.png", "question": "As shown in the figure, in Rttriangle ABC, angle BAC = 90.0, AD perpendicular BC at D, DE perpendicular AB at E, AD = 3.0, DE = 2.0, then the length of CD is ()", "ground_truth": "\\frac{3\u221a{5}}{2}"} | |
| {"image_path": "./Geo170K/images/test/514.png", "question": "As shown in the figure, the known point D is the midpoint of AB, AF parallel BC, CG:GA=3.0:1.0,BC=8.0, then AF is equal to ()", "ground_truth": "4"} | |
| {"image_path": "./Geo170K/images/test/515.png", "question": "As shown in the figure, it is known that the radius of circle O is 6.0, M is a point outside circle O, and OM = 12.0, the line passing M and circle O intersect at A and B, the symmetrical points of points A and B with respect to OM are C, D, AD and BC intersect at point P, then the length of OP is ()", "ground_truth": "3"} | |
| {"image_path": "./Geo170K/images/test/516.png", "question": "As shown in the figure, in parallelogram ABCD, E is the midpoint of CD, AE intersects BD at point O, S~triangle DCE~ = 12.0, then S~triangle AOD~ is equal to ()", "ground_truth": "24"} | |
| {"image_path": "./Geo170K/images/test/517.png", "question": "As shown in the figure, in triangle ABC, angle ACB = 90.0, D is the point on AB, connect CD, angle ACD = angle B, if BC = 13.0, CD = 5.0, then BD = ()", "ground_truth": "12cm"} | |
| {"image_path": "./Geo170K/images/test/518.png", "question": "As shown in the figure, it is known that D and E are the points on AB and AC in triangle ABC, DE parallel BC and frac {AD}{AB}=frac {1.0}{3.0}, the perimeter of triangle ADE is 2.0, then the perimeter of triangle ABC is ()", "ground_truth": "6"} | |
| {"image_path": "./Geo170K/images/test/519.png", "question": "As shown in the figure, in triangle ABC, D is a point on AC, if angle DBC = angle A, BC = 3.0, AC = 6.0, then the length of CD is ()", "ground_truth": "\\frac{3}{2}"} | |
| {"image_path": "./Geo170K/images/test/520.png", "question": "As shown in the figure, DE parallel BC, BD, CE intersect at O, frac {EO}{OC}=frac {1.0}{3.0}, AE = N_3, then EB = ()", "ground_truth": "6"} | |
| {"image_path": "./Geo170K/images/test/521.png", "question": "As shown in the figure, a beam of light reflects from point A (-3.0, 3.0), through point C on the y axis, and then passes through point B (-1.0, 0.0), then the length of the path of the light from point A to point B is ()", "ground_truth": "5"} | |
| {"image_path": "./Geo170K/images/test/522.png", "question": "As shown in the figure, in triangle ABC, if DE parallel BC, frac {AD}{AB}=frac {1.0}{3.0}, DE = 4.0, then the length of BC is ()", "ground_truth": "12cm"} | |
| {"image_path": "./Geo170K/images/test/523.png", "question": "As shown in the figure, it is known that D, E, and F are points on the side BC, CA, and AB of isosceles triangle ABC respectively. If AB = AC, angle FDE = angle B, BD = 2.0, CD = 3.0, CE = 4.0, AE = 1.0, then the length of AF is ()", "ground_truth": "3.5"} | |
| {"image_path": "./Geo170K/images/test/524.png", "question": "As shown in the figure, the cross section of a small reservoir dam is a right trapezoid, the width of crest BC is 6.0, the height of dam is 14.0, and the slope of the slope CD is i = 1.0:2.0, then the length of the dam bottom AD is ()", "ground_truth": "34m"} | |
| {"image_path": "./Geo170K/images/test/525.png", "question": "As shown in the figure, the slope of the slope formed by the conveyor belt and the ground is 1.0:2.0, it sends the object from the ground point A to the point B higher than the ground 2.0, then the distance the object travels from A to B is ()", "ground_truth": "2\u221a{5}"} | |
| {"image_path": "./Geo170K/images/test/526.png", "question": "As shown in the figure, in triangle ABC, AB = AC = 18.0, BC = 12.0, the vertices E and F of the square DEFG are in triangle ABC, the vertices D and G are on AB and AC respectively, AD = AG, DG = 6.0, then the distance from point F to BC is ()", "ground_truth": "6\u221a{2}-6"} | |
| {"image_path": "./Geo170K/images/test/527.png", "question": "As shown in the figure, in the square ABCD with edge length 9.0, F is a point on AB. Connect CF. Pass point F to draw FE perpendicular CF which intersects AD at point E, if AF = 3.0, then AE is equal to ()", "ground_truth": "2"} | |
| {"image_path": "./Geo170K/images/test/528.png", "question": "As shown in the figure, in Rttriangle ABC, angle BAC = 90.0, AB = 2.0, AC = 3.0, D is the midpoint of BC, and moving points E and F are on AB and AC respectively, passing points to draw EG parallel AD parallel FH, and they intersect BC at points G and H, if EF parallel BC, then the value of EF + EG + FH is ()", "ground_truth": "\u221a{13}"} | |
| {"image_path": "./Geo170K/images/test/529.png", "question": "As shown in the figure, in triangle ABC, D and E are points on AB and AC respectively, and DE parallel BC, if AD = 5.0, DB = 3.0, DE = 4.0, then BC is equal to ()", "ground_truth": "\\frac{32}{5}"} | |
| {"image_path": "./Geo170K/images/test/530.png", "question": "As shown in the figure, in the parallelogram ABCD, E is the midpoint of DC, the area of \u200b\u200btriangle DEF is 2.0, then the area of \u200b\u200btriangle ABF is ()", "ground_truth": "8"} | |
| {"image_path": "./Geo170K/images/test/531.png", "question": "As shown in the figure, AB parallel CD, frac {AO}{OD}=frac {2.0}{3.0}, then the ratio of the perimeter of triangle AOB to the perimeter of triangle DOC is ()", "ground_truth": "\\frac{2}{3}"} | |
| {"image_path": "./Geo170K/images/test/532.png", "question": "As shown in the figure, AB parallel CD, AC, BD intersect at O, BO = 6.0, DO = 3.0, AC = 12.0, then the length of AO is ()", "ground_truth": "8"} | |
| {"image_path": "./Geo170K/images/test/533.png", "question": "As shown in the figure, in triangle ABC, E and F are the midpoints of AB and AC respectively. If the area of \u200b\u200btriangle AEF is 1.0, then the area of \u200b\u200bthe quadrilateral EBCF is ()", "ground_truth": "3"} | |
| {"image_path": "./Geo170K/images/test/534.png", "question": "As shown in the figure, in the trapezoidal ABCD, AD parallel BC, diagonal AC, BD intersect at point O, if S~triangle AOD~:S~triangle OCD~ = 1.0:2.0, then S~triangle AOD~:S~triangle BOC~ = ()", "ground_truth": "\\frac{1}{4}"} | |
| {"image_path": "./Geo170K/images/test/535.png", "question": "As shown in the figure, planting trees on the hillside, it is known that angle A = 30.0, AC = 3.0, the distance of slope AB of two adjacent trees is equal to ()", "ground_truth": "2\u221a{3}m"} | |
| {"image_path": "./Geo170K/images/test/536.png", "question": "As shown in the figure, the elevation angle of the top of a building is 30.0 when viewed from point A in the air by a hot air balloon, and the depression angle of this building is 60.0. The horizontal distance between the hot air balloon and the building is 120.0. The height of this building is ()", "ground_truth": "160\u221a{3}m"} | |
| {"image_path": "./Geo170K/images/test/537.png", "question": "As shown in the figure, a teaching interest group wants to measure the height of a tree CD. They firstly measured the elevation angle of the tree top C at point A as 30.0, and then proceeded 10.0 along the direction of AD to point B, and the elevation angle of tree top C measured at B is 60.0 (the three points A, B, and D are on the same straight line), then the height of the tree CD is ()", "ground_truth": "5\u221a{3}m"} | |
| {"image_path": "./Geo170K/images/test/538.png", "question": "As shown in the figure, in order to measure the height of the TV tower AB, use the goniometer CD with a height of 1.0 at D, and measure the elevation angle of the top A of the TV tower to be 30.0, and then walk 120.0 in the direction of the TV tower to F, and the elevation angle of the top A of the TV tower is 60.0, then the height of this TV tower AB (unit:) is ()", "ground_truth": "60\u221a{3}+1"} | |
| {"image_path": "./Geo170K/images/test/539.png", "question": "As shown in the figure, in a mathematics extracurricular practice activity, Xiaowen measured the elevation angle of the top A of the tree at point C to be 37.0, BC = 20.0, then the height of the tree AB is () (reference data: sin37\u00b0 approximate 0.6, cos37\u00b0 approximate 0.8, tan37\u00b0 approximate 0.75)", "ground_truth": "15m"} | |
| {"image_path": "./Geo170K/images/test/540.png", "question": "As shown in the figure, to build a highway in a certain place, a tunnel must be built from B to C (B and C are on the same level). In order to measure the distance between B and C, an engineer took a hot air balloon to start from C and rose vertically 100.0 to reach A. Observing the depression angle of B at A is 30.0, then the distance between B and C is ()", "ground_truth": "100\u221a{3}m"} | |
| {"image_path": "./Geo170K/images/test/541.png", "question": "In the mathematics practice inquiry class, the teacher arranged for the students to measure the height of the school flagpole. As shown in the figure, Xiao Ming's study group is at a distance of 10.0 from the bottom of the flagpole. The elevation angle of the top of the flagpole is measured with a goniometer as 60.0, then the height of the flagpole is ().", "ground_truth": "10\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/542.png", "question": "As shown in the figure, to measure the height AB of a tower that cannot be reached at the bottom, two students of A and B took measurements at C and D respectively. Given that the points B, C and D are on the same straight line, and AB perpendicular BD, CD = 12.0, angle ACB = 60.0, angle ADB = 30.0, the height of the tower AB is ()", "ground_truth": "6\u221a{3}\u7c73"} | |
| {"image_path": "./Geo170K/images/test/543.png", "question": "As shown in Figure 1, the clock face of a clock is fixed perpendicularly on the horizontal desktop, and there is a point A on the minute hand, and when the clock face displays 3.0 o'clock 30.0 minutes, the minute hand is perpendicular to the desktop, and the height from point A to the desktop is 10.0 cm. As shown in Figure 2, if the clock face displays 3.0 o'clock and 45.0 minutes, and the height of point A from the desktop is 16.0 cm, then the clock face displays 3.0 o'clock and 50.0 minutes, how many centimeters is the height of point A from the desktop ()", "ground_truth": "19"} | |
| {"image_path": "./Geo170K/images/test/544.png", "question": "As shown in the figure, PA and PB are the tangents of circle O, AC is the diameter of circle O, angle P = 50.0, then the degree of angle BOC is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/545.png", "question": "As shown in the figure, in Rttriangle ABC, AD perpendicular BC at D, DE perpendicular AB at E, if AD = 3.0, DE = 2.0, then AC = ()", "ground_truth": "\\frac{9}{2}"} | |
| {"image_path": "./Geo170K/images/test/546.png", "question": "As shown in the figure, in triangle ABC, AB = BC = 2.0, circle O with AB as the diameter is tangent to BC at point B, then AC is equal to ()", "ground_truth": "2\u221a{2}"} | |
| {"image_path": "./Geo170K/images/test/547.png", "question": "Definition: The minimum value of the distance between a fixed point A and any point on circle O is called the distance between point A and circle O. There is a rectangle ABCD (as shown in the figure), AB = 14.0, BC = 12.0, circle K and the edges AB, BC, and CD of the rectangle are respectively tangent to the points E, F, G, then the distance between point A and circle K is ()", "ground_truth": "4cm"} | |
| {"image_path": "./Geo170K/images/test/548.png", "question": "As shown in the figure, circle O is the circumscribed circle of triangle ABC, angle BOC = 3.0 angle AOB, if angle ACB = 20.0, then the degree of angle BAC is ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/549.png", "question": "As shown in the figure, AB is the diameter of circle O, C and D are two points on circle O, CD perpendicular AB, if angle DAB = 70.0, then angle BOC = ()", "ground_truth": "140\u00b0"} | |
| {"image_path": "./Geo170K/images/test/550.png", "question": "As shown in the figure, A, B, and C are all points on circle O, if angle ABC = 110.0, then the degree of angle AOC is ()", "ground_truth": "140\u00b0"} | |
| {"image_path": "./Geo170K/images/test/551.png", "question": "Point B is on circle O, point C is a point different from A and B on circle O, if angle AOB = 50.0, then the degree of angle ACB is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/552.png", "question": "As shown in the figure, given that points A, B, and C are on circle O, angle AOB = 100.0, then the degree of angle ACB is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/553.png", "question": "As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, angle ABD = 59.0, then angle C is equal to ()", "ground_truth": "31\u00b0"} | |
| {"image_path": "./Geo170K/images/test/554.png", "question": "As shown in the figure, in the square ABCD, AB = 8.0, Q is the midpoint of CD, set angle DAQ = \u03b1, take a point P on CD, make angle BAP = 2.0 \u03b1, then the length of CP is ()", "ground_truth": "2"} | |
| {"image_path": "./Geo170K/images/test/555.png", "question": "As shown in the figure, the intersection of the two diagonals of the rectangle is 60.0, AC + BD = 20.0, then the length of AB is ()", "ground_truth": "5cm"} | |
| {"image_path": "./Geo170K/images/test/556.png", "question": "As shown in the figure, in the diamond ABCD, angle BAD = 120.0, the length of the diagonal AC is 3.0, then the perimeter of the diamond ABCD is ()", "ground_truth": "12"} | |
| {"image_path": "./Geo170K/images/test/557.png", "question": "As shown in the figure, angle MON = 90.0, moving points A and B are respectively located on the radials OM and ON, the edge AB of the rectangle ABCD = 6.0, BC = 4.0, then the maximum length of the line segment OC is ()", "ground_truth": "8"} | |
| {"image_path": "./Geo170K/images/test/558.png", "question": "As shown in the figure, in the diamond ABCD, angle BAD = 120.0, BC = 10.0, then the length of the diagonal AC is equal to ()", "ground_truth": "10"} | |
| {"image_path": "./Geo170K/images/test/559.png", "question": "As shown in the figure, the perimeter of the diamond ABCD is 16.0, angle A = 60.0, then the length of the diagonal BD is ()", "ground_truth": "4"} | |
| {"image_path": "./Geo170K/images/test/560.png", "question": "As shown in the figure, in the diamond ABCD, AB = 5.0, angle B = 60.0, then the diagonal AC is equal to ()", "ground_truth": "5"} | |
| {"image_path": "./Geo170K/images/test/561.png", "question": "As shown in the figure, in the diamond ABCD, AB = 15.0, angle ADC = 120.0, then the distance between the two points B and D is ()", "ground_truth": "15"} | |
| {"image_path": "./Geo170K/images/test/562.png", "question": "As shown in the figure, in the diamond ABCD, two diagonal lines AC = 12.0, BD = 16.0, then the edge length of this diamond is ()", "ground_truth": "10"} | |
| {"image_path": "./Geo170K/images/test/563.png", "question": "As shown in the figure, in the diamond ABCD, angle BAD = 80.0, the perpendicular bisector of AB intersects the diagonal AC at point F, E is the foot of perpendicular. Connect DF, then angle CDF is equal to ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/564.png", "question": "As shown in the figure, in the diamond ABCD, angle B = 60.0, AB = 2.0, E and F are the midpoints of BC and CD respectively, connect AE, EF, and AF, then the perimeter of triangle AEF is ()", "ground_truth": "3\u221a{3}cm"} | |
| {"image_path": "./Geo170K/images/test/565.png", "question": "As shown in the figure, in parallelogram ABCD, BC = BD, angle C = 65.0, then the degree of angle ADB is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/566.png", "question": "As shown in the figure, in parallelogram ABCD, AB = 6.0, BC = 8.0, the bisector of angle C intersects AD at E, and intersects the extended line of BA at F, then the value of AE + AF is equal to ()", "ground_truth": "4"} | |
| {"image_path": "./Geo170K/images/test/567.png", "question": "As shown in the figure, in parallelogram ABCD, AE perpendicular BC is at E, AF perpendicular DC and it intersects the extended line of DC at point F, and angle EAF = 60.0, then angle B is equal to ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/568.png", "question": "As shown in the figure, in parallelogram ABCD, AE bisects angle BAD, if CE = 3.0, AB = 4.0, then the perimeter of parallelogram ABCD is ()", "ground_truth": "22cm"} | |
| {"image_path": "./Geo170K/images/test/569.png", "question": "As shown in the figure, in parallelogram ABCD, AE bisects angle BAD, and it is known that angle AEB = 63.0, then the degree of angle D is ()", "ground_truth": "54\u00b0"} | |
| {"image_path": "./Geo170K/images/test/570.png", "question": "As shown in the figure, in parallelogram ABCD, the diagonal AC and BD intersect at point O, AC = 10.0, BD = 6.0, AD = 4.0, then the area of \u200b\u200bparallelogram ABCD is ()", "ground_truth": "24"} | |
| {"image_path": "./Geo170K/images/test/571.png", "question": "As shown in the figure, the diagonal of the parallelogram ABCD intersects at the point O, and AB = 6.0, the perimeter of triangle OCD is 19.0, then the sum of the two diagonals of parallelogram ABCD is ()", "ground_truth": "26"} | |
| {"image_path": "./Geo170K/images/test/572.png", "question": "As shown in the figure, in the parallelogram ABCD, if angle B = 60.0, then angle D is equal to ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/573.png", "question": "As shown in the figure, in the parallelogram ABCD, it is known that angle AOB = 90.0, AC = 8.0, AD = 5.0, then the length of BD is ()", "ground_truth": "6cm"} | |
| {"image_path": "./Geo170K/images/test/574.png", "question": "As shown in the figure, in parallelogram ABCD, CE perpendicular AB, the foot of perpendicular is E, if angle A = 115.0, then angle BCE is equal to ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/575.png", "question": "As shown in the figure, in the parallelogram ABCD, CE bisects angle BCD and it intersects the AD edge at point E, and DE = 3.0, then the length of AB is ()", "ground_truth": "3"} | |
| {"image_path": "./Geo170K/images/test/576.png", "question": "In parallelogram ABCD, the diagonal AC and BD intersect at the point O, angle DAC = 42.0, angle CBD = 23.0, then angle COD is ()", "ground_truth": "65\u00b0"} | |
| {"image_path": "./Geo170K/images/test/577.png", "question": "As shown in the figure, the diagonals AC and BD of the parallelogram ABCD intersect at point O, point E is the midpoint of CD, and the perimeter of triangle ABD is 16.0, then the perimeter of triangle DOE is ()", "ground_truth": "8cm"} | |
| {"image_path": "./Geo170K/images/test/578.png", "question": "As shown in the figure, in parallelogram ABCD, BM is the bisector of angle ABC and it intersects CD at point M, and MC = 2.0, the perimeter of parallelogram ABCD is 14.0, then DM is equal to ()", "ground_truth": "3"} | |
| {"image_path": "./Geo170K/images/test/579.png", "question": "As shown in the figure, P is a point of parallelogram ABCD. Given that S~triangle ABP~ = 3.0, S~triangle PDC~ = 2.0, then the area of \u200b\u200bthe parallelogram ABCD is ()", "ground_truth": "10"} | |
| {"image_path": "./Geo170K/images/test/580.png", "question": "As shown in the figure, in parallelogram ABCD, AE bisects angle BAD and it intersects BC at point E. If AD = 8.0, EC = 2.0, then the length of AB is ()", "ground_truth": "6"} | |
| {"image_path": "./Geo170K/images/test/581.png", "question": "As shown in the figure, in the parallelogram ABCD, the straight line CE perpendicular AB passing through the point C, the foot of perpendicular is E, if angle EAD = 54.0, then the degree of angle BCE is ()", "ground_truth": "36\u00b0"} | |
| {"image_path": "./Geo170K/images/test/582.png", "question": "As shown in the figure, in parallelogram ABCD, BD = CD, angle C = 70.0, AE perpendicular BD at point E, then the degree of angle BAE is ()", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/583.png", "question": "As shown in the figure, P is a point in the parallelogram ABCD, and cross point P to draw the parallel line of AB and AD to intersect the parallelogram at the four points of E, F, G, and H. If S~AHPE~ = 3.0, S~PFCG~ = 5.0 , Then S~triangle PBD~ is ()", "ground_truth": "1"} | |
| {"image_path": "./Geo170K/images/test/584.png", "question": "As shown in the figure, in parallelogram ABCD, angle A = 120.0, then angle 1 = ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/585.png", "question": "As shown in the figure, in parallelogram ABCD, CE perpendicular AB, point E is the foot of perpendicular, if angle D = 55.0, then angle BCE = ()", "ground_truth": "35\u00b0"} | |
| {"image_path": "./Geo170K/images/test/586.png", "question": "As shown in the figure, in parallelogram ABCD, angle ABC = 60.0, AB = BC = 4.0, points M and N are on edges BC and CD respectively, and angle MAN = 60.0, then the area of \u200b\u200bthe quadrilateral AMCN is ()", "ground_truth": "4\u221a{3}cm\u00b2"} | |
| {"image_path": "./Geo170K/images/test/587.png", "question": "As shown in the figure, in the parallelogram ABCD, AB = 4.0, BC = 6.0, and the perpendicular bisector of AC intersects AD at point E, then the perimeter of triangle CDE is ()", "ground_truth": "10"} | |
| {"image_path": "./Geo170K/images/test/588.png", "question": "As shown in the figure, in parallelogram ABCD, AD = 3.0, DC = 5.0, and the perpendicular bisector of BD intersects BD at point E, then the perimeter of triangle BCE is ()", "ground_truth": "8"} | |
| {"image_path": "./Geo170K/images/test/589.png", "question": "As shown in the figure, the perimeter of parallelogram ABCD is 10.0, AC and BD intersect at point O, and OE perpendicular AC and it intersects AD at E, then the perimeter of triangle DCE is ()", "ground_truth": "5cm"} | |
| {"image_path": "./Geo170K/images/test/590.png", "question": "As shown in the figure, in the parallelogram ABCD, it is known that AB = 6.0, BC = 9.0, angle B = 30.0, then the area of \u200b\u200bthe parallelogram ABCD is ()", "ground_truth": "27"} | |
| {"image_path": "./Geo170K/images/test/591.png", "question": "As shown in the figure, in parallelogram ABCD, angle AEB = 36.0, BE bisectes angle ABC, then angle C is equal to ()", "ground_truth": "108\u00b0"} | |
| {"image_path": "./Geo170K/images/test/592.png", "question": "As shown in the figure, the diagonal of the parallelogram ABCD intersects at the point O, and AB = 5.0, the perimeter of triangle OCD is 23.0, then the sum of the two diagonals of the parallelogram ABCD is ()", "ground_truth": "36"} | |
| {"image_path": "./Geo170K/images/test/593.png", "question": "As shown in the figure, in parallelogram ABCD, the diagonal AC and BD intersect at point O, if AC = 12.0, BD = 8.0, AB = 7.0, then the perimeter of triangle OAB is ()", "ground_truth": "17"} | |
| {"image_path": "./Geo170K/images/test/594.png", "question": "The perimeter of the parallelogram ABCD is 28.0, AC and BD intersect at point O, the perimeter of triangle AOB is 4.0 larger than the perimeter of triangle OBC, then AB is equal to ()", "ground_truth": "9cm"} | |
| {"image_path": "./Geo170K/images/test/595.png", "question": "As shown in the figure, in the parallelogram ABCD, the diagonal AC and BD intersect at point O, and cross O point to draw OE parallel BC and it intersects DC at point E. If OE = 2.5, then the length of AD is ()", "ground_truth": "5"} | |
| {"image_path": "./Geo170K/images/test/596.png", "question": "As shown in the figure, the diagonal AC and BD of the parallelogram ABCD intersect at the point O, AB = 7.0, AC = 10.0, the perimeter of triangle ABO is 16.0, then the length of the diagonal BD is equal to ()", "ground_truth": "8"} | |
| {"image_path": "./Geo170K/images/test/597.png", "question": "As shown in the figure, E is any point in parallelogram ABCD, if S~quadrilateral ABCD~ = 6.0, then the area of \u200b\u200bthe shaded part in the figure is ()", "ground_truth": "3"} | |
| {"image_path": "./Geo170K/images/test/598.png", "question": "As shown in the figure, in the parallelogram ABCD, AB = 4.0, the bisector of angle BAD and the extended line of BC intersect at point E, and DC at point F, and point F is the midpoint of DC, DG perpendicular AE, foot of perpendicular is G, if DG = 1.0, then the edge length of AE is ()", "ground_truth": "4\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/599.png", "question": "As shown in the figure, AB is the chord of circle O, passing point A to draw the tangent AC of circle O. If angle BAC = 55.0, then angle AOB is equal to ()", "ground_truth": "110\u00b0"} | |
| {"image_path": "./Geo170K/images/test/600.png", "question": "As shown in the figure, the line segment AB crosses the center O, intersects circle O at points A and C, angle B = 30.0, and the straight line BD and circle O tangent to point D, then the degree of angle ADB is ()", "ground_truth": "120\u00b0"} | |
| {"image_path": "./Geo170K/images/test/601.png", "question": "As shown in the figure, in the parallelogram ABCD, AC and BD are diagonals, BC = 6.0, and the height on BC is 4.0, then the area of \u200b\u200bthe shaded part in the figure is ()", "ground_truth": "12"} | |
| {"image_path": "./Geo170K/images/test/602.png", "question": "As shown in the figure, the parallelogram ABCD is divided into 4.0 parallelograms. It is known that the three areas are 8.0, 10.0, and 30.0, then the area of \u200b\u200bthe fourth parallelogram is ()", "ground_truth": "24"} | |
| {"image_path": "./Geo170K/images/test/603.png", "question": "As shown in the figure, the diagonal AC and BD of parallelogram ABCD intersect at point O, if AC + BD = 10.0, BC = 4.0, then the perimeter of triangle BOC is ()", "ground_truth": "9"} | |
| {"image_path": "./Geo170K/images/test/604.png", "question": "As shown in the figure, in parallelogram ABCD, AC and BD intersect at point O, points E and F are on edges AD and BC respectively, and EF passes through point O. If AB = 3.0, BC = 5.0, EF = AB, then the perimeter of the quadrilateral CDEF is ()", "ground_truth": "11"} | |
| {"image_path": "./Geo170K/images/test/605.png", "question": "As shown in the figure, the perpendicular bisector of the diagonal AC of the parallelogram ABCD and the edges BC and DA intersect at E and F, respectively, and connect CF. If the perimeter of the parallelogram ABCD is equal to 18.0, then the perimeter of triangle CDF is equal to ()", "ground_truth": "9cm"} | |
| {"image_path": "./Geo170K/images/test/606.png", "question": "As shown in the figure, in triangle ABC, AB = AC, angle A = 40.0, draw an arc with C as the center and the length of CB as the radius, intersect AB at point D, connect CD, then angle ACD is equal to ()", "ground_truth": "30\u00b0"} | |
| {"image_path": "./Geo170K/images/test/607.png", "question": "As shown in the figure, in circle O, it is known that angle AOB = 110.0, C is a point on the circle, then angle ACB is ()", "ground_truth": "125\u00b0"} | |
| {"image_path": "./Geo170K/images/test/608.png", "question": "As shown in the figure, CD is the diameter of circle O, chord DE parallel OA, if the degree of angle D is 50.0, then the degree of angle C is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/609.png", "question": "As shown in the figure, BD is the diameter of circle O, points A and C are on circle O, and BD perpendicular AC, if the degree of arc AB is 60.0, then the degree of angle BDC is ()", "ground_truth": "30\u00b0"} | |
| {"image_path": "./Geo170K/images/test/610.png", "question": "As shown in the figure, it is known that AB and AD are the chords of circle O, angle B = 20.0, point C is on chord AB, connect CO and extend CO to intersect circle O at point D, angle D = 15.0, then the degree of angle BAD is ()", "ground_truth": "35\u00b0"} | |
| {"image_path": "./Geo170K/images/test/611.png", "question": "As shown in the figure, circle O is the circumscribed circle of triangle ABC, and it is known that angle C = 60.0, then the degree of angle BAO is ()", "ground_truth": "30\u00b0"} | |
| {"image_path": "./Geo170K/images/test/612.png", "question": "As shown in the figure, AB is the diameter of the semicircle, angle ABC = 50.0, point D is the midpoint of arc AC, then angle DAB is equal to ()", "ground_truth": "65\u00b0"} | |
| {"image_path": "./Geo170K/images/test/613.png", "question": "As shown in the figure, AB is the diameter of circle O, the chord CD and AB intersect, and angle ABC = 32.0, then the degree of angle CDB is ()", "ground_truth": "58\u00b0"} | |
| {"image_path": "./Geo170K/images/test/614.png", "question": "As shown in the figure, arc AB is a semicircle. Connect AB, point O is the midpoint of AB, points C and D are on arc AB, connecting AD, CO, BC, BD, OD. If angle COD = 62.0 and AD parallel OC, then the size of angle ABD is ()", "ground_truth": "28\u00b0"} | |
| {"image_path": "./Geo170K/images/test/615.png", "question": "As shown in the figure, AB is the diameter of circle O, point C and point D are on circle O. Connect AC, BC, AD, CD, if angle BAC = 50.0, then the degree of angle ADC is equal to ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/616.png", "question": "As shown in the figure, AB is the diameter of circle O, angle AOC = 140.0, then angle D is ()", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/617.png", "question": "As shown in the figure, in circle O, the diameter AB perpendicular chord CD at point H, E is the point on circle O, if angle BEC = 25.0, then the degree of angle BAD is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/618.png", "question": "As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, angle ABD = 53.0, then angle BCD is ()", "ground_truth": "37\u00b0"} | |
| {"image_path": "./Geo170K/images/test/619.png", "question": "As shown in the figure, circle O is the circumscribed circle of triangle ABC, angle AOB = 60.0, then the degree of angle C is ()", "ground_truth": "30\u00b0"} | |
| {"image_path": "./Geo170K/images/test/620.png", "question": "As shown in the figure, points A, B, and C are three points on circle O, angle AOC = 110.0, then angle ABC is equal to ()", "ground_truth": "55\u00b0"} | |
| {"image_path": "./Geo170K/images/test/621.png", "question": "As shown in the figure, AB is the diameter of circle O, CD is the chord, and AB perpendicular CD, the foot of perpendicular is the point E, it is known that angle COB = 60.0, then the degree of angle DAB is ()", "ground_truth": "30\u00b0"} | |
| {"image_path": "./Geo170K/images/test/622.png", "question": "As shown in the figure, it is known that AB is the diameter of circle O, if the degree of angle BOC is 50.0, then the degree of angle A is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/623.png", "question": "As shown in the figure, points A, B, and C are on circle O, angle AOB = 140.0, and the degree of angle ACB is ()", "ground_truth": "110\u00b0"} | |
| {"image_path": "./Geo170K/images/test/624.png", "question": "As shown in the figure, AB is the diameter of circle O, CD is a chord of circle O, and CD perpendicular AB at E, respectively connect AD and BC, it is known that angle D = 65.0, then angle OCD = ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/625.png", "question": "As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, angle ACD = 42.0, then angle BAD = ().", "ground_truth": "48"} | |
| {"image_path": "./Geo170K/images/test/626.png", "question": "As shown in the figure, AB is the diameter of circle O, angle AOC = 110.0, then angle D = ()", "ground_truth": "35\u00b0"} | |
| {"image_path": "./Geo170K/images/test/627.png", "question": "As shown in the figure, AB is the diameter of circle O, point C is on circle O, if angle ABC = 30.0, then angle CAB is ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/628.png", "question": "As shown in the figure, P is a point outside circle O, PA and PB intersect circle O at two points C and D respectively. It is known that the central angles of arc AB and arc CD are 90.0 and 50.0 respectively, then angle P = ()", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/629.png", "question": "As shown in the figure, given that the three points A, B and C are on circle O, AC perpendicular BO at D, angle B = 50.0, then the degree of angle BOC is ()", "ground_truth": "80\u00b0"} | |
| {"image_path": "./Geo170K/images/test/630.png", "question": "As shown in the figure, in circle O, the length of chord AB is 2.0, OC perpendicular AB at C, OC = 1.0, if two tangents of circle O are drawn from a point P outside circle O, the tangent points are A and B respectively, then angle APB The degree is ()", "ground_truth": "90\u00b0"} | |
| {"image_path": "./Geo170K/images/test/631.png", "question": "As shown in the figure, in triangle ABC, AB = 10.0, AC = 8.0, BC = 6.0, the moving circle passing through point C and tangent to edge AB intersects CA and CB at points P and Q respectively, then the minimum value of the length of the line segment PQ is ()", "ground_truth": "4.8"} | |
| {"image_path": "./Geo170K/images/test/632.png", "question": "As shown in the figure, in triangle ABC, AB = 2.0, AC = 1.0, the circle with AB as the diameter is tangent to AC and intersects the edge BC at point D, then the length of AD is ()", "ground_truth": "\\frac{2}{5}\u221a{5}"} | |
| {"image_path": "./Geo170K/images/test/633.png", "question": "As shown in the figure, AB is the diameter of circle O, point C is on the extended line of AB, CD is tangent to circle O, and the tangent point is D. If angle A = 35.0, then angle C is equal to ()", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/634.png", "question": "As shown in the figure, in Rttriangle ABC, angle ACB = 90.0, AC = 4.0, BC = 3.0, the circle with AC as the diameter intersects AB at D, then the length of AD is ()", "ground_truth": "\\frac{16}{5}"} | |
| {"image_path": "./Geo170K/images/test/635.png", "question": "As shown in the figure, it is known that AD and BC intersect at point O, AB parallel CD, if angle B = 40.0, angle D = 30.0, then the size of angle AOC is ()", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/636.png", "question": "As shown in the figure, in triangle ABC, AB = AC, D is the midpoint of BC, angle B = 40.0, then angle BAD = ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/637.png", "question": "As shown in the figure, angle A = 70.0, angle 2 = 130.0, then angle 1 = ()", "ground_truth": "120\u00b0"} | |
| {"image_path": "./Geo170K/images/test/638.png", "question": "As shown in the figure, in the quadrilateral ABCD, angle BAD = 120.0, angle B = angle D = 90.0, if you find a point M on BC and CD respectively, so that the perimeter of triangle AMN is the smallest, then the degree of angle AMN + angle ANM is ()", "ground_truth": "120\u00b0"} | |
| {"image_path": "./Geo170K/images/test/639.png", "question": "As shown in the figure, fold the rectangle ABCD along the line segment OG to the position of OB'C'G, angle OGC' is equal to 100.0, then the degree of angle DGC' is ()", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/640.png", "question": "As shown in the figure, AB is the diameter of circle O, if angle BDC = 40.0, then the degree of angle BOC is ()", "ground_truth": "80\u00b0"} | |
| {"image_path": "./Geo170K/images/test/641.png", "question": "As shown in the figure, fold triangle ABC so that point A coincides with point D at BC, and the crease is MN. If AB = 9.0, BC = 6.0, then the perimeter of triangle DNB is ()", "ground_truth": "12"} | |
| {"image_path": "./Geo170K/images/test/642.png", "question": "As shown in the figure, the perimeter of parallelogram ABCD is 36.0, the diagonal AC and BD intersect at point O, point E is the midpoint of CD, BD = 12.0, then the perimeter of triangle DOE is ()", "ground_truth": "15"} | |
| {"image_path": "./Geo170K/images/test/643.png", "question": "As shown in the figure, points A, B, C, D are on circle O, angle AOC = 140.0, point B is the midpoint of arc AC, then the degree of angle D is ()", "ground_truth": "35\u00b0"} | |
| {"image_path": "./Geo170K/images/test/644.png", "question": "As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If angle ABD = 50.0, then the degree of angle BCD is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/645.png", "question": "As shown in the figure, in triangle ABC, angle CAB = 30.0, rotate triangle ABC anticlockwise in the plane around point A to the position of triangle AB'C', and CC' parallel AB, then the degree of rotation angle is ()", "ground_truth": "120\u00b0"} | |
| {"image_path": "./Geo170K/images/test/646.png", "question": "As shown in the figure, O is a point on the straight line AB, angle 1 = 40.0, OD bisects angle BOC, then the degree of angle 2 is ()", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/647.png", "question": "As shown in the picture, it is a beautiful Pythagorean tree, in which all quadrilaterals are squares, and all triangles are right triangles. The areas of square A, B, C, and D are 2.0, 5.0, 1.0, 2.0, respectively. Then the area of \u200b\u200bthe largest square E is ().", "ground_truth": "10"} | |
| {"image_path": "./Geo170K/images/test/648.png", "question": "As shown in the figure, the straight lines AB and CD are cut by BC. If AB parallel CD, angle 1 = 45.0, angle 2 = 35.0, then angle 3 = ()", "ground_truth": "80\u00b0"} | |
| {"image_path": "./Geo170K/images/test/649.png", "question": "As shown in the figure, in Rttriangle ABC, angle BAC = 90.0, rotate triangle ABC clockwise around point A by 90.0 to obtain triangle AB\u2032C\u2032 (the corresponding point of point B is point B\u2032, and the corresponding point of point C is point C \u2032), connect CC\u2032. If angle CC\u2032B\u2032 = 32.0, then the size of angle AC\u2032B\u2032 is ()", "ground_truth": "13\u00b0"} | |
| {"image_path": "./Geo170K/images/test/650.png", "question": "Known: As shown in the figure, AB parallel CD, BC bisects angle ABD, and angle C = 40.0, then the degree of angle D is ()", "ground_truth": "100\u00b0"} | |
| {"image_path": "./Geo170K/images/test/651.png", "question": "Given that the straight line a parallel b, angle 1 and angle 2 are mutually complementary, angle 3 = 121.0, then angle 4 is equal to ()", "ground_truth": "149\u00b0"} | |
| {"image_path": "./Geo170K/images/test/652.png", "question": "In triangle ABC, AB = AC, D and E are respectively on BC and AC, AD = AE, angle CDE = 20.0, then the degree of angle BAD is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/653.png", "question": "As shown in the figure, the vertex A of the line parallel n, Rttriangle ABC is on the line n, angle C = 90.0, AB, CB intersect the line at point D and point E respectively, and DB = DE, if angle B = 25.0, then the degree of angle 1 is ()", "ground_truth": "65\u00b0"} | |
| {"image_path": "./Geo170K/images/test/654.png", "question": "As shown in the figure, the straight line a parallel b, the straight line c and the straight lines a, b intersect at the points A, B, AM perpendicular b, and the foot of perpendicular is the point M. If angle 1 = 58.0, then angle 2 = ()", "ground_truth": "32\u00b0"} | |
| {"image_path": "./Geo170K/images/test/655.png", "question": "As shown in the figure, put the right-angled vertex of a right triangle board on one side of the ruler, if angle 1 = 30.0, then angle 2 is ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/656.png", "question": "As shown in the figure, AB perpendicular CD at D, DE perpendicular DF, if angle BDE = 60.0, then angle CDF is equal to ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/657.png", "question": "As shown in the figure, the measured BD = 120.0, DC = 60.0, EC = 50.0, then the width of the river AB is ()", "ground_truth": "100m"} | |
| {"image_path": "./Geo170K/images/test/658.png", "question": "As shown in the figure, in triangle ABE, the perpendicular bisector of AE MN intersects BE at point C, angle E = 30.0, and AB = CE, then the degree of angle BAE is ()", "ground_truth": "90\u00b0"} | |
| {"image_path": "./Geo170K/images/test/659.png", "question": "As shown in the figure, in triangle ABC, D and E are points on edges AB and AC respectively, DE parallel BC, angle ADE = 35.0, angle C = 120.0, then angle A is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/660.png", "question": "As shown in the figure, points A, B, and C are on circle O, angle AOB = 72.0, then angle ACB is equal to ()", "ground_truth": "36\u00b0"} | |
| {"image_path": "./Geo170K/images/test/661.png", "question": "Fold a rectangular piece of paper as shown in the picture, and then unfold it. If angle 1 = 56.0, then angle 2 is equal to ()", "ground_truth": "68\u00b0"} | |
| {"image_path": "./Geo170K/images/test/662.png", "question": "As shown in the figure, the straight line a parallel b, angle 1 = 72.0, then the degree of angle 2 is ()", "ground_truth": "108\u00b0"} | |
| {"image_path": "./Geo170K/images/test/663.png", "question": "As shown in the figure, the two vertices of a right triangle with 30.0 angle are placed on the opposite side of a rectangle. If angle 1 = 25.0, then the degree of angle 2 is ()", "ground_truth": "115\u00b0"} | |
| {"image_path": "./Geo170K/images/test/664.png", "question": "As shown in the figure, it is known that AB and AD are the chords of circle O, angle ABO = 30.0, angle ADO = 20.0, then angle BAD = ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/665.png", "question": "As shown in the figure, C and D are two points on the line segment AB, if CB = 4.0, DB = 7.0, and D is the midpoint of AC, then the length of AB is equal to ()", "ground_truth": "10cm"} | |
| {"image_path": "./Geo170K/images/test/666.png", "question": "As shown in the figure, C and D are two points on the line segment AB, if AC = 3.0, C is the midpoint of AD and AB = 10.0, then DB = ()", "ground_truth": "4cm"} | |
| {"image_path": "./Geo170K/images/test/667.png", "question": "As shown in the figure, in circle O, AC is the diameter, MA and MB are tangent to circle O at points A, B, angle BAC = 25.0, then the size of angle AMB is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/668.png", "question": "Given: AB parallel CD, angle ABE = 120.0, angle C = 25.0, then the degree of angle \u03b1 is ()", "ground_truth": "85\u00b0"} | |
| {"image_path": "./Geo170K/images/test/669.png", "question": "As shown in the figure, the straight lines AB and CD intersect at point O, OD bisects angle AOE, angle BOC = 50.0, then angle EOB = ()", "ground_truth": "80\u00b0"} | |
| {"image_path": "./Geo170K/images/test/670.png", "question": "As shown in the figure, a big tree breaks at B whose height is 9.0 from the ground, and the top A of the tree falls at 12.0 from the bottom C of the tree. The height before the break is ()", "ground_truth": "24\u7c73"} | |
| {"image_path": "./Geo170K/images/test/671.png", "question": "As shown in the figure, cross point A on circle O to draw a tangent of circle O, and it intersects the extended line of diameter BC at point D, connect AB, if angle B = 25.0, then the degree of angle D is ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/672.png", "question": "As shown in the figure, place the right-angled vertex of the triangular plate (angle A = 30.0) with 30.0 angle on one of the two parallel lines. If angle 1 = 38.0, then the degree of angle 2 ()", "ground_truth": "22\u00b0"} | |
| {"image_path": "./Geo170K/images/test/673.png", "question": "As shown in the figure, Xiaoming walks from point A in the direction of 80.0 to the north by east to point B, and then from point B to the direction of 25.0 to the south by west to point C, then the degree of angle ABC is ()", "ground_truth": "55\u00b0"} | |
| {"image_path": "./Geo170K/images/test/674.png", "question": "As shown in the figure, given that the straight lines AB and CD intersect at point O, OE perpendicular AB, angle EOC = 30.0, then the degree of angle BOD is ()", "ground_truth": "120\u00b0"} | |
| {"image_path": "./Geo170K/images/test/675.png", "question": "The three views of a geometry are shown in the figure, where the front view and the left view are both equilateral triangles with edge length 2.0, then the surface area of \u200b\u200bthe geometry is ()", "ground_truth": "3\u03c0"} | |
| {"image_path": "./Geo170K/images/test/676.png", "question": "As shown in the figure, in the right triangle ABC, angle C = 90.0, AB = 5.0, AC = 4.0, then the value of sinangle B is ()", "ground_truth": "\\frac{4}{5}"} | |
| {"image_path": "./Geo170K/images/test/677.png", "question": "As shown in the figure, in Rttriangle ABC, angle C is a right angle, CD perpendicular AB at D, it is known that AC = 3.0, AB = 5.0, then tanangle BCD is equal to ()", "ground_truth": "\\frac{4}{3}"} | |
| {"image_path": "./Geo170K/images/test/678.png", "question": "As shown in the figure, in triangle ABC, DE parallel BC, if AD = 3.0, DB = 6.0, DE = 2.5, then the length of BC is ()", "ground_truth": "7.5"} | |
| {"image_path": "./Geo170K/images/test/679.png", "question": "As shown in the figure, in Rttriangle ABC, angle BAC = 90.0, AB = 3.0, AC = 4.0, point P is any point on BC, connect PA, take PA and PC as adjacent edges to make parallelogram PAQC, connect PQ, then the minimum value of PQ is ()", "ground_truth": "\\frac{12}{5}"} | |
| {"image_path": "./Geo170K/images/test/680.png", "question": "As shown in the figure, AB parallel CD, AB = 6.0, CD = 9.0, AD = 10.0, then the length of OD is ()", "ground_truth": "6"} | |
| {"image_path": "./Geo170K/images/test/681.png", "question": "As shown in the figure, in triangle ABC, DE parallel BC, intersect AB and AC at points D and E respectively. If AD = 2.0, DB = 3.0, BC = 6.0, then the length of DE is ()", "ground_truth": "\\frac{12}{5}"} | |
| {"image_path": "./Geo170K/images/test/682.png", "question": "As shown in the figure, AB is the diameter of circle O, C is the point on circle O, chord AD bisects angle BAC, intersects BC at point E, AB = 6.0, AD = 5.0, then the length of DE is ()", "ground_truth": "2.2"} | |
| {"image_path": "./Geo170K/images/test/683.png", "question": "As shown in the figure, in triangle ABC, DE parallel BC, frac {AD}{DB}=frac {1.0}{2.0},DE=4.0, then the length of BC is ()", "ground_truth": "12"} | |
| {"image_path": "./Geo170K/images/test/684.png", "question": "As shown in the figure, AD\u2022AB = AE\u2022AC, angle ADE = 80.0, angle A = 60.0, then angle B = ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/685.png", "question": "As shown in the figure, DC parallel EF parallel AB, iffrac {EG}{AB}=frac {1.0}{2.0},DC=6.0, then the length of GF is ()", "ground_truth": "3"} | |
| {"image_path": "./Geo170K/images/test/686.png", "question": "As shown on the right, in triangle ABC, DE parallel BC, frac {AD}{AB}=frac {2.0}{5.0},DE=3.0,then the length of BC is ()", "ground_truth": "7.5"} | |
| {"image_path": "./Geo170K/images/test/687.png", "question": "As shown in the figure, in the parallelogram ABCD, E is the midpoint of BC, and AE and BD intersect at point F. If the area of \u200b\u200btriangle BFE is 3.0, then the area of \u200b\u200btriangle ABF is ()", "ground_truth": "6"} | |
| {"image_path": "./Geo170K/images/test/688.png", "question": "As shown in the figure, in triangle ABC, D and E are the midpoints of AB and AC respectively. It is known that the area of \u200b\u200btriangle ADE is 1.0, then the area of \u200b\u200btriangle ABC is ()", "ground_truth": "4"} | |
| {"image_path": "./Geo170K/images/test/689.png", "question": "As shown in the figure, it is known that AB, CD, and EF are parallel to each other, and AB = 1.0, CD = 4.0, then the length of EF is ()", "ground_truth": "\\frac{4}{5}"} | |
| {"image_path": "./Geo170K/images/test/690.png", "question": "As shown in the figure, in triangle ABC, DE parallel BC, intersect AB and AC at points D and E respectively. If AE = 3.0, EC = 6.0, then the value of frac DEBC is ()", "ground_truth": "\\frac{1}{3}"} | |
| {"image_path": "./Geo170K/images/test/691.png", "question": "As shown in the figure, BE and CF are the two heights of triangle ABC. If AB = 6.0, BC = 5.0, EF = 3.0, then the length of AE is ()", "ground_truth": "\\frac{18}{5}"} | |
| {"image_path": "./Geo170K/images/test/692.png", "question": "As shown in the figure, the inclination angle angle ABD of the stairs AB with the length 4.0 is 60.0. In order to improve the safety performance of the stairs, the stairs are prepared to be rebuilt so that the inclination angle angle ACD is 45.0, then the length of the adjusted stairs AC is ()", "ground_truth": "2\u221a{6}m"} | |
| {"image_path": "./Geo170K/images/test/693.png", "question": "As shown in the figure, the cross section of the dam, the horizontal width of the slope AB is 12.0, and the slope of the slope is 1.0:2.0, then the length of the slope AB is ()", "ground_truth": "6\u221a{5}m"} | |
| {"image_path": "./Geo170K/images/test/694.png", "question": "As shown in the figure, the cable is fixed at the height of 5.0 from the ground to fix the pole, the cable and the ground form an angle 60.0, then the length of the cable AC is ()", "ground_truth": "\\frac{10\u221a{3}}{3}m"} | |
| {"image_path": "./Geo170K/images/test/695.png", "question": "As shown in the figure, in triangle ABC, points D and E are the midpoints of AB and AC respectively. If the area of \u200b\u200btriangle ADE is 4.0, then the area of \u200b\u200btriangle ABC is ()", "ground_truth": "16"} | |
| {"image_path": "./Geo170K/images/test/696.png", "question": "As shown in the figure, in the rectangle ABCD, AB = 4.0, BC = 2.0, point M is on BC, connect AM to make angle AMN = angle AMB, point N is on the straight line AD, MN intersects CD at point E, then the maximum value of BM\u2022AN is ()", "ground_truth": "10"} | |
| {"image_path": "./Geo170K/images/test/697.png", "question": "As shown in the figure, in triangle ABC, angle ACB = 90.0, CD perpendicular AB at D, CD = 4.0, BC = 5.0, then AC = ()", "ground_truth": "\\frac{20}{3}"} | |
| {"image_path": "./Geo170K/images/test/698.png", "question": "As shown in the figure, there is a square DEFG in triangle ABC, where D is on AC, E and F are on AB, and the straight line AG intersects DE and BC at M and N points respectively. If angle B = 90.0, AB = 8.0, BC = 6.0, EF = 2.0, then the length of BN is ()", "ground_truth": "\\frac{24}{7}"} | |
| {"image_path": "./Geo170K/images/test/699.png", "question": "As shown in the figure, in triangle ABC, points D and E are points on edges AB and AC respectively, and DE parallel BC, if AD = 5.0, BD = 10.0, DE = 3.0, then the length of BC is ()", "ground_truth": "9"} | |
| {"image_path": "./Geo170K/images/test/700.png", "question": "As shown in the figure, triangle ABC is inscribed in circle O, angle BAC = 120.0, AB = AC, BD is the diameter of circle O, AB = 3.0, then the value of AD is ()", "ground_truth": "3\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/701.png", "question": "As shown in the figure, in circle O, angle ABC = 130.0, then angle AOC is equal to ()", "ground_truth": "100\u00b0"} | |
| {"image_path": "./Geo170K/images/test/702.png", "question": "As shown in the figure, AC and BC are the diameters of two semicircles, angle ACP = 30.0, if AB = 20.0, the value of PQ is ()", "ground_truth": "10\u221a{3}cm"} | |
| {"image_path": "./Geo170K/images/test/703.png", "question": "As shown in the figure, in the quadrilateral ABCD, AB = AC = AD, angle CBD = 23.0, then angle CAD is ()", "ground_truth": "46\u00b0"} | |
| {"image_path": "./Geo170K/images/test/704.png", "question": "As shown in the figure, circle O is the circumscribed circle of triangle ABC, angle BCO = 40.0, then the degree of angle A is equal to ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/705.png", "question": "As shown in the figure, A, B, and C are three points on circle O, angle ABC = 25.0, then the degree of angle AOC is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/706.png", "question": "As shown in the figure, A, B, and C are points on circle O, angle ACB = 32.0, then angle AOB is equal to ()", "ground_truth": "64\u00b0"} | |
| {"image_path": "./Geo170K/images/test/707.png", "question": "As shown in the figure, points A, B, and C are on circle O, if angle ABC = 35.0, then the degree of angle AOC is ()", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/708.png", "question": "As shown in the figure, points A, B, and C are on circle O and connect AB and AC. If angle BOC = 100.0, then the degree of angle B + angle C is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/709.png", "question": "As shown in the figure, place the vertex of the right triangle 45.0 angle on the center O, the hypotenuse and the leg intersect circle O at two points A and B respectively, and C is any point on the major arc AB (not coincident with A and B) , Then the degree of angle ACB is ()", "ground_truth": "22.5\u00b0"} | |
| {"image_path": "./Geo170K/images/test/710.png", "question": "As shown in the figure, the line segment AB is the diameter of circle O, the chord CD \u4e04 AB, angle CAB = 20.0, then angle AOD is equal to ()", "ground_truth": "140\u00b0"} | |
| {"image_path": "./Geo170K/images/test/711.png", "question": "As shown in the figure, the vertices A, B, and D of parallelogram ABCD are on circle O, and the vertex C is on the diameter BE of circle O, connect AE, angle E = 36.0, then the degree of angle ADC is ()", "ground_truth": "54\u00b0"} | |
| {"image_path": "./Geo170K/images/test/712.png", "question": "The diameter of the protractor coincides with the hypotenuse AB of the right triangle ABC, where the endpoint N of the scale line of the protractor O coincides with point A, the radial CP starts from CA and rotates clockwise at a speed of 3.0 degrees per second, and CP and the semicircular arc of the protractor intersect at point E, when the 20.0 second, the corresponding reading of point E on the protractor is ()", "ground_truth": "120\u00b0"} | |
| {"image_path": "./Geo170K/images/test/713.png", "question": "As shown in the figure, the three points A, B, and C are on circle O, and angle ABO = 50.0, then angle ACB is equal to ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/714.png", "question": "AB is the diameter of circle O, point C is on circle O, if angle C = 15.0, then angle BOC = ()", "ground_truth": "30\u00b0"} | |
| {"image_path": "./Geo170K/images/test/715.png", "question": "As shown in the figure, the two chords AB and CD in the circle intersect at E, angle D = 35.0, angle AEC = 105.0, then angle C = ()", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/716.png", "question": "As shown in the figure, AB and CD are the two chords of circle O, connect AD and BC. If angle BCD = 70.0, then the degree of angle BAD is ()", "ground_truth": "70\u00b0"} | |
| {"image_path": "./Geo170K/images/test/717.png", "question": "As shown in the figure, A, B, and C are on circle O, if angle BAC = 24.0, then the degree of angle BOC is ()", "ground_truth": "48\u00b0"} | |
| {"image_path": "./Geo170K/images/test/718.png", "question": "As shown in the figure, points A, B, and C are all on circle O, if angle C = 34.0, then angle AOB is ()", "ground_truth": "68\u00b0"} | |
| {"image_path": "./Geo170K/images/test/719.png", "question": "As shown in the figure, circle A with a diameter of 10.0 passes through point C(0.0,5.0) O(0.0,0.0), B is a point on the circle A major arc on the right side of the y-axis, then the degree of angle OBC is ()", "ground_truth": "30\u00b0"} | |
| {"image_path": "./Geo170K/images/test/720.png", "question": "As shown in the figure, triangle ABC is inscribed in circle O, angle A = 15.0, connect OB, then angle OBC is equal to ()", "ground_truth": "75\u00b0"} | |
| {"image_path": "./Geo170K/images/test/721.png", "question": "As shown in the figure, in circle O, angle ABC = 40.0, then angle AOC = () degrees.", "ground_truth": "80"} | |
| {"image_path": "./Geo170K/images/test/722.png", "question": "As shown in the figure, A, B, C are the three points on circle O, and angle CAO = 25.0, angle BCO = 35.0, then the degree of angle AOB is ()", "ground_truth": "120\u00b0"} | |
| {"image_path": "./Geo170K/images/test/723.png", "question": "As shown in the figure, AB is the diameter of circle O, chord CD perpendicular AB, E is a point of arc BC, if angle CEA = 28.0, then the degree of angle ABD is ()", "ground_truth": "28\u00b0"} | |
| {"image_path": "./Geo170K/images/test/724.png", "question": "As shown in the figure, circle O is the circumscribed circle of triangle ABC, and it is known that angle B = 70.0, then the degree of angle CAO is ()", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/725.png", "question": "As shown in the figure, circle O is the circumscribed circle of triangle ABC, angle OCB = 30.0, then the degree of angle A is equal to ()", "ground_truth": "60\u00b0"} | |
| {"image_path": "./Geo170K/images/test/726.png", "question": "As shown in the figure, circle O is the circumscribed circle of triangle ABC, AB is the diameter, if angle BOC = 70.0, then angle A is equal to ()", "ground_truth": "35\u00b0"} | |
| {"image_path": "./Geo170K/images/test/727.png", "question": "As shown in the figure, in circle O, diameter AB = 5.0, chord AC = 4.0, then the distance from point O to line AC is ()", "ground_truth": "1.5cm"} | |
| {"image_path": "./Geo170K/images/test/728.png", "question": "As shown in the figure, AB is the diameter of circle O, if angle BAC = 35.0, then angle ADC = ()", "ground_truth": "55\u00b0"} | |
| {"image_path": "./Geo170K/images/test/729.png", "question": "A pair of right triangle plates are placed as shown (angle ACB = angle ADB = 90.0 ), angle CAB = 30.0, angle BAD = 45.0, AB intersects CD at E, then the degree of angle CEB is ()", "ground_truth": "75\u00b0"} | |
| {"image_path": "./Geo170K/images/test/730.png", "question": "As shown in the figure below, point C is on the semicircle O with AB as the diameter, angle BAC = 20.0, then angle BOC is equal to ()", "ground_truth": "40\u00b0"} | |
| {"image_path": "./Geo170K/images/test/731.png", "question": "As shown in the figure, AB is the diameter of circle O, angle ABC = 25.0, then the degree of angle D is ()", "ground_truth": "65\u00b0"} | |
| {"image_path": "./Geo170K/images/test/732.png", "question": "As shown in the figure, triangle ABC is the inscribed triangle of circle O, BD is the diameter, if angle DBC = 18.0, then the degree of angle A is ()", "ground_truth": "72\u00b0"} | |
| {"image_path": "./Geo170K/images/test/733.png", "question": "As shown in the figure, AB and CD are the chords of circle O, and AB parallel CD, if angle BAD = 36.0, then angle AOC is equal to ()", "ground_truth": "72\u00b0"} | |
| {"image_path": "./Geo170K/images/test/734.png", "question": "As shown in the figure, A, B, and C are the three points on circle O, if angle C = 35.0, then the degree of angle OAB is ()", "ground_truth": "55\u00b0"} | |
| {"image_path": "./Geo170K/images/test/735.png", "question": "As shown in the figure, the vertices A, B, and D of parallelogram ABCD are on circle O, and the vertex C is on the diameter BE of circle O, angle ADC = 54.0, connect AE, then the degree of angle AEB is ()", "ground_truth": "36\u00b0"} | |
| {"image_path": "./Geo170K/images/test/736.png", "question": "As shown in the figure, CD is the diameter of circle O, chord DE parallel OA, if the degree of angle D is 50.0, then the degree of angle A is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/737.png", "question": "As shown in the figure, it is known that circle O is the circumscribed circle of triangle ABC, angle AOB = 110.0, then the degree of angle C is ()", "ground_truth": "55\u00b0"} | |
| {"image_path": "./Geo170K/images/test/738.png", "question": "As shown in the figure, AB is the diameter of circle O, and point C is on circle O. If angle A = 40.0, then the degree of angle B is ()", "ground_truth": "50\u00b0"} | |
| {"image_path": "./Geo170K/images/test/739.png", "question": "As shown in the figure, if AB is the diameter of circle O, CD is the chord of circle O, angle ABD = 55.0, then the degree of angle BCD is ()", "ground_truth": "35\u00b0"} | |
| {"image_path": "./Geo170K/images/test/740.png", "question": "As shown in the figure, points A, B, and C are three points on circle O, angle BAC = 40.0, then the degree of angle BOC is ()", "ground_truth": "80\u00b0"} | |
| {"image_path": "./Geo170K/images/test/741.png", "question": "As shown in the figure, in the circle O with a radius of 5.0, if the length of the chord AB is 8.0, then its distance from the chord OC to the centre is equal to ()", "ground_truth": "3"} | |
| {"image_path": "./Geo170K/images/test/742.png", "question": "As shown in the figure, point O is the center of circle O, points A, B, and C are on circle O, AO parallel BC, angle AOB = 40.0, then the degree of angle OAC is equal to ()", "ground_truth": "20\u00b0"} | |
| {"image_path": "./Geo170K/images/test/743.png", "question": "It is known that: as shown in the figure, the diameter AB of circle O is perpendicular to the chord CD, and the foot of perpendicular is E. If AB = 10.0, CD = 6.0, then the length of BE is ()", "ground_truth": "1"} | |
| {"image_path": "./Geo170K/images/test/744.png", "question": "As shown in the figure, the radius of circle O is 10.0, AB is the chord, OC perpendicular AB, and the foot of perpendicular is E. If CE = 4.0, then the length of AB is ()", "ground_truth": "16"} | |
| {"image_path": "./Geo170K/images/test/745.png", "question": "As shown in the figure, the edge length of the square ABCD is 3.0, and the equilateral triangle PCD and equilateral triangle QCD are made on both sides of CD with CD as one edge, then the length of PQ is ()", "ground_truth": "3\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/746.png", "question": "As shown in the figure, in the square ABCD, E is a point on DC, F is a point on the extended line of BC, angle BEC = 70.0, and triangle BCE congruent triangle DCF. Connect EF, then the degree of angle EFD is ()", "ground_truth": "25\u00b0"} | |
| {"image_path": "./Geo170K/images/test/747.png", "question": "As shown in the figure, it is known that the radius of circle O is 5.0 and the chord AB = 8.0, then the distance from the center O to AB is ()", "ground_truth": "3mm"} | |
| {"image_path": "./Geo170K/images/test/748.png", "question": "As shown in the figure, MN is tangent to circle O at point A, angle AOB = 60.0, then angle BAM is equal to ()", "ground_truth": "30\u00b0"} | |
| {"image_path": "./Geo170K/images/test/749.png", "question": "As shown in the figure, the tangents PA and PB of a circle drawn from a point P outside circle O, the tangent points are A and B respectively, if angle APB = 70.0, then the degree of the minor arc AB sandwiched by these two tangents is ()", "ground_truth": "110\u00b0"} | |
| {"image_path": "./Geo170K/images/test/750.png", "question": "As shown in the figure, PB is tangent to circle O at point B, PO intersects circle O at point E, extends PO and intersects circle O at point A, connects AB, the radius of circle O OD perpendicular AB at point C, BP \u200b\u200b= 6.0, angle P = 30.0 , then the length of CD is ()", "ground_truth": "\u221a{3}"} | |
| {"image_path": "./Geo170K/images/test/751.png", "question": "As shown in the figure, PA and PB are tangent to circle O to A and B respectively. Point C and point D are the moving points on line segments PA and PB, and CD always remains tangent to circle O. If PA = 8.0, then perimeter of triangle PCD is ()", "ground_truth": "16"} | |
| {"image_path": "./Geo170K/images/test/752.png", "question": "As shown in the figure, in the two concentric circles, the chord AB of the great circle is tangent to the small circle at point C. If AB = 6.0, the area of \u200b\u200bthe ring is ()", "ground_truth": "9\u03c0"} | |
| {"image_path": "./Geo170K/images/test/753.png", "question": "As shown in the figure, the squares P and Q are sandwiched in the ABCD frame, the angle between the lower edge of the square P and AB is 15.0, and the angle between the two adjacent edges of the square P and Q is 150.0, then angle 1 is ()", "ground_truth": "15\u00b0"} | |