pid string | question string | image string | decoded_image image | choices list | unit string | precision float64 | answer string | question_type string | answer_type string | metadata dict | query string |
|---|---|---|---|---|---|---|---|---|---|---|---|
3 | △ABC的两内角平分线OB、OC相交于点O，若∠A＝110°，则∠BOC＝（） | images/3.jpg | [
"135°",
"140°",
"145°",
"150°"
] | null | null | 145° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 60,
"img_width": 131,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: △ABC的两内角平分线OB、OC相交于点O，若∠A＝110°，则∠BOC＝（）
Choices:
(A) 135°
(B) 140°
(C) 145°
(D) 150° | |
5 | Find $m\angle H$ | images/5.jpg | [
"97",
"102",
"107",
"122"
] | null | null | 97 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 245,
"img_width": 322,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find $m\angle H$
Choices:
(A) 97
(B) 102
(C) 107
(D) 122 | |
6 | 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 () | images/6.jpg | [
"6cm",
"7cm",
"4cm",
"5cm"
] | null | null | 6cm | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 30,
"img_width": 203,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
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 ()
Choices:
(A) 6cm
(B) 7cm
(C) 4cm
(D) 5cm | |
9 | 如图是一株美丽的勾股树，其中所有四边形都是正方形，所有的三角形都是直角三角形，若正方形A、B的面积分别为5、3，则最大正方形C的面积是（） | images/9.jpg | [
"15",
"13",
"11",
"8"
] | null | null | 8 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 155,
"img_width": 134,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图是一株美丽的勾股树，其中所有四边形都是正方形，所有的三角形都是直角三角形，若正方形A、B的面积分别为5、3，则最大正方形C的面积是（）
Choices:
(A) 15
(B) 13
(C) 11
(D) 8 | |
17 | 如图，在Rt△ABC中，∠ACB＝90°，D是AB的中点，AB＝10，则CD的长为（） | images/17.jpg | [
"5",
"6",
"8",
"10"
] | null | null | 5 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 172,
"img_width": 125,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在Rt△ABC中，∠ACB＝90°，D是AB的中点，AB＝10，则CD的长为（）
Choices:
(A) 5
(B) 6
(C) 8
(D) 10 | |
28 | $\overline{AB}$ is a diameter, $AC=8$ inches, and $BC=15$ inches. Find the radius of the circle. | images/28.jpg | [
"7.5",
"8",
"8.5",
"17"
] | null | null | 8.5 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 431,
"img_width": 519,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: $\overline{AB}$ is a diameter, $AC=8$ inches, and $BC=15$ inches. Find the radius of the circle.
Choices:
(A) 7.5
(B) 8
(C) 8.5
(D) 17 | |
30 | As shown in the figure, the two chords AB and CD in the circle intersect at E, ∠D = 35.0, ∠AEC = 105.0, then ∠C = () | images/30.jpg | [
"60°",
"70°",
"80°",
"85°"
] | null | null | 70° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 113,
"img_width": 117,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, the two chords AB and CD in the circle intersect at E, ∠D = 35.0, ∠AEC = 105.0, then ∠C = ()
Choices:
(A) 60°
(B) 70°
(C) 80°
(D) 85° | |
32 | 如图，在ABCD中，AB＝AC，∠CAB＝40°，则∠D的度数是（） | images/32.jpg | [
"40°",
"50°",
"60°",
"70°"
] | null | null | 70° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 100,
"img_width": 168,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在ABCD中，AB＝AC，∠CAB＝40°，则∠D的度数是（）
Choices:
(A) 40°
(B) 50°
(C) 60°
(D) 70° | |
33 | 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 () | images/33.jpg | [
"2πcm",
"3πcm",
"4πcm",
"5πcm"
] | null | null | 4πcm | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 95,
"img_width": 331,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
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 ()
Choices:
(A) 2πcm
(B) 3πcm
(C) 4πcm
(D) 5πcm | |
35 | 如图，AB是⊙O的直径，EF，EB是⊙O的弦，点E是FEB的中点，EF与AB交于点C，连接OF，若∠AOF＝40°，则∠F的度数是（） | images/35.jpg | [
"20°",
"35°",
"40°",
"55°"
] | null | null | 35° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 141,
"img_width": 151,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，AB是⊙O的直径，EF，EB是⊙O的弦，点E是FEB的中点，EF与AB交于点C，连接OF，若∠AOF＝40°，则∠F的度数是（）
Choices:
(A) 20°
(B) 35°
(C) 40°
(D) 55° | |
48 | Find $m \angle 3$. | images/48.jpg | [
"28",
"38",
"52",
"62"
] | null | null | 38 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 426,
"img_width": 596,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find $m \angle 3$.
Choices:
(A) 28
(B) 38
(C) 52
(D) 62 | |
54 | In the figure above, the ratio of the length of line AB to the length of line AC is 2 : 5. If AC = 25, what is the length of line AB? | images/54.jpg | [
"8",
"10",
"15",
"18",
"20"
] | null | null | 10 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 310,
"img_width": 433,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In the figure above, the ratio of the length of line AB to the length of line AC is 2 : 5. If AC = 25, what is the length of line AB?
Choices:
(A) 8
(B) 10
(C) 15
(D) 18
(E) 20 | |
55 | 如图，一块直角三角板60°的角的顶点A与直角顶点C分别在两平行线FG，DE上，斜边AB平分∠CAG，交直线DE于点H，则∠BCH的大小为（） | images/55.jpg | [
"60°",
"45°",
"30°",
"25°"
] | null | null | 30° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 125,
"img_width": 175,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，一块直角三角板60°的角的顶点A与直角顶点C分别在两平行线FG，DE上，斜边AB平分∠CAG，交直线DE于点H，则∠BCH的大小为（）
Choices:
(A) 60°
(B) 45°
(C) 30°
(D) 25° | |
59 | As shown in the figure, AB is the diameter of ⊙O, CD is the chord of ⊙O, ∠ADC = 26.0, then the degree of ∠CAB is () | images/59.jpg | [
"26°",
"74°",
"64°",
"54°"
] | null | null | 64° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 146,
"img_width": 157,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, AB is the diameter of ⊙O, CD is the chord of ⊙O, ∠ADC = 26.0, then the degree of ∠CAB is ()
Choices:
(A) 26°
(B) 74°
(C) 64°
(D) 54° | |
62 | 如图，E，F分别是菱形ABCD的边AB，AD的中点，且AB＝5，AC＝6．则EF的长为（） | images/62.jpg | [
"4",
"5",
"5.5",
"6"
] | null | null | 4 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 138,
"img_width": 160,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，E，F分别是菱形ABCD的边AB，AD的中点，且AB＝5，AC＝6．则EF的长为（）
Choices:
(A) 4
(B) 5
(C) 5.5
(D) 6 | |
68 | 将一根长度为16cm自然伸直的弹性皮筋AB两端固定在水平的桌面上，然后把中点C竖直向上拉升6cm至D点（如图），则该弹性皮筋被拉长了（） | images/68.jpg | [
"2cm",
"4cm",
"6cm",
"8cm"
] | null | null | 4cm | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 84,
"img_width": 252,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 将一根长度为16cm自然伸直的弹性皮筋AB两端固定在水平的桌面上，然后把中点C竖直向上拉升6cm至D点（如图），则该弹性皮筋被拉长了（）
Choices:
(A) 2cm
(B) 4cm
(C) 6cm
(D) 8cm | |
79 | 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 ∠ABC = 60.0, then the degree of ∠CDE is () | images/79.jpg | [
"30°",
"45°",
"60°",
"70°"
] | null | null | 60° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 104,
"img_width": 123,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
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 ∠ABC = 60.0, then the degree of ∠CDE is ()
Choices:
(A) 30°
(B) 45°
(C) 60°
(D) 70° | |
82 | A square is inscribed in a circle of area 18$\pi$ square units. Find the length of a side of the square. | images/82.jpg | [
"3",
"3 \\sqrt 2",
"6",
"6 \\sqrt 2"
] | null | null | 6 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 202,
"img_width": 200,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: A square is inscribed in a circle of area 18$\pi$ square units. Find the length of a side of the square.
Choices:
(A) 3
(B) 3 \sqrt 2
(C) 6
(D) 6 \sqrt 2 | |
88 | A square is tangent to a line at point P in the figure above. What is the value of x? | images/88.jpg | null | null | null | 30 | free_form | integer | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 277,
"img_width": 442,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question requiring an integer answer and provide the final value, e.g., 1, 2, 3, at the end.
Question: A square is tangent to a line at point P in the figure above. What is the value of x? | |
94 | 如图，D为△ABC内一点，CD平分∠ACB，BD⊥CD，∠A＝∠ABD，若∠DBC＝54°，则∠A的度数为（） | images/94.jpg | [
"36°",
"44°",
"27°",
"54°"
] | null | null | 27° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 74,
"img_width": 160,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，D为△ABC内一点，CD平分∠ACB，BD⊥CD，∠A＝∠ABD，若∠DBC＝54°，则∠A的度数为（）
Choices:
(A) 36°
(B) 44°
(C) 27°
(D) 54° | |
95 | As shown in the figure, the straight lines AB and CD intersect at point O, OD bisects ∠AOE, ∠BOC = 50.0, then ∠EOB = () | images/95.jpg | [
"50°",
"60°",
"70°",
"80°"
] | null | null | 80° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 118,
"img_width": 162,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, the straight lines AB and CD intersect at point O, OD bisects ∠AOE, ∠BOC = 50.0, then ∠EOB = ()
Choices:
(A) 50°
(B) 60°
(C) 70°
(D) 80° | |
114 | In the figure, KL is tangent to $\odot M$ at K. Find the value of x. | images/114.jpg | [
"6.00",
"9.45",
"18.9",
"37.8"
] | null | null | 9.45 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 273,
"img_width": 347,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In the figure, KL is tangent to $\odot M$ at K. Find the value of x.
Choices:
(A) 6.00
(B) 9.45
(C) 18.9
(D) 37.8 | |
119 | As shown in the figure, P is a point outside ⊙O, PA and PB intersect ⊙O at two points C and D respectively. It is known that the central angles of ⁀AB and ⁀CD are 90.0 and 50.0 respectively, then ∠P = () | images/119.jpg | [
"45°",
"40°",
"25°",
"20°"
] | null | null | 20° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 165,
"img_width": 103,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, P is a point outside ⊙O, PA and PB intersect ⊙O at two points C and D respectively. It is known that the central angles of ⁀AB and ⁀CD are 90.0 and 50.0 respectively, then ∠P = ()
Choices:
(A) 45°
(B) 40°
(C) 25°
(D) 20° | |
132 | 如图，在4×4的正方形网格中，每个小正方形的边长均为1，点A，B，C都在格点上，AD⊥BC于D，则AD的长为（） | images/132.jpg | [
"1",
"1.5",
"2",
"\\frac{7}{3}"
] | null | null | 2 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 160,
"img_width": 155,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在4×4的正方形网格中，每个小正方形的边长均为1，点A，B，C都在格点上，AD⊥BC于D，则AD的长为（）
Choices:
(A) 1
(B) 1.5
(C) 2
(D) \frac{7}{3} | |
141 | 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 () | images/141.jpg | [
"3.85米",
"4.00米",
"4.40米",
"4.50米"
] | null | null | 4.40米 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 128,
"img_width": 78,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
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 ()
Choices:
(A) 3.85米
(B) 4.00米
(C) 4.40米
(D) 4.50米 | |
143 | As shown in the figure, in the parallelogram ABCD, CE bisects ∠BCD and it intersects the AD edge at point E, and DE = 3.0, then the length of AB is () | images/143.jpg | [
"1",
"2",
"3",
"6"
] | null | null | 3 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 85,
"img_width": 204,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, in the parallelogram ABCD, CE bisects ∠BCD and it intersects the AD edge at point E, and DE = 3.0, then the length of AB is ()
Choices:
(A) 1
(B) 2
(C) 3
(D) 6 | |
149 | 如图，直线l1∥l2，∠1＝50°，∠2＝75°，则∠3＝（） | images/149.jpg | [
"55°",
"60°",
"65°",
"70°"
] | null | null | 55° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 93,
"img_width": 156,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，直线l1∥l2，∠1＝50°，∠2＝75°，则∠3＝（）
Choices:
(A) 55°
(B) 60°
(C) 65°
(D) 70° | |
150 | As shown in the figure, points A, B, and C are three points on ⊙O, and the straight line CD and ⊙O are tangent to point C. If ∠DCB = 40.0, then the degree of ∠CAB is () | images/150.jpg | [
"40°",
"50°",
"80°",
"100°"
] | null | null | 40° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 144,
"img_width": 110,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, points A, B, and C are three points on ⊙O, and the straight line CD and ⊙O are tangent to point C. If ∠DCB = 40.0, then the degree of ∠CAB is ()
Choices:
(A) 40°
(B) 50°
(C) 80°
(D) 100° | |
152 | 如图，直线l1∥l2，将含30°角的直角三角板按如图方式放置，直角顶点在l2上，若∠1＝76°，则∠2＝（） | images/152.jpg | [
"36°",
"45°",
"44°",
"64°"
] | null | null | 44° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 208,
"img_width": 229,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，直线l1∥l2，将含30°角的直角三角板按如图方式放置，直角顶点在l2上，若∠1＝76°，则∠2＝（）
Choices:
(A) 36°
(B) 45°
(C) 44°
(D) 64° | |
160 | Find x. | images/160.jpg | [
"10",
"11",
"12",
"13"
] | null | null | 12 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 227,
"img_width": 270,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find x.
Choices:
(A) 10
(B) 11
(C) 12
(D) 13 | |
164 | As shown in the figure, in ▱ABCD, CE ⊥ AB, point E is the foot of perpendicular, if ∠D = 55.0, then ∠BCE = () | images/164.jpg | [
"55°",
"35°",
"25°",
"30°"
] | null | null | 35° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 84,
"img_width": 161,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, in ▱ABCD, CE ⊥ AB, point E is the foot of perpendicular, if ∠D = 55.0, then ∠BCE = ()
Choices:
(A) 55°
(B) 35°
(C) 25°
(D) 30° | |
176 | Find $RS$ if $\triangle QRS$ is an equilateral triangle. | images/176.jpg | [
"0.5",
"1",
"1.5",
"2"
] | null | null | 2 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 292,
"img_width": 305,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find $RS$ if $\triangle QRS$ is an equilateral triangle.
Choices:
(A) 0.5
(B) 1
(C) 1.5
(D) 2 | |
178 | 如图，点A、C在∠FBD的两条边BF、BD上，BE平分∠FBD，CE平分∠ACD，连接AE，若∠BEC＝35°，则∠FAE的度数为（） | images/178.jpg | [
"35°",
"45°",
"55°",
"65°"
] | null | null | 55° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 99,
"img_width": 129,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，点A、C在∠FBD的两条边BF、BD上，BE平分∠FBD，CE平分∠ACD，连接AE，若∠BEC＝35°，则∠FAE的度数为（）
Choices:
(A) 35°
(B) 45°
(C) 55°
(D) 65° | |
179 | 如图，在ABCD中，已知AC＝4cm，若△ACD的周长为14cm，则ABCD的周长为（） | images/179.jpg | [
"14cm",
"28cm",
"10cm",
"20cm"
] | null | null | 20cm | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 94,
"img_width": 157,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在ABCD中，已知AC＝4cm，若△ACD的周长为14cm，则ABCD的周长为（）
Choices:
(A) 14cm
(B) 28cm
(C) 10cm
(D) 20cm | |
186 | 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 α, AC ⊥ CD, BD ⊥ 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 () | images/186.jpg | [
"\\frac{20}{3}",
"\\frac{10}{3}",
"7",
"\\frac{14}{3}"
] | null | null | \frac{20}{3} | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 112,
"img_width": 183,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
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 α, AC ⊥ CD, BD ⊥ 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 ()
Choices:
(A) \frac{20}{3}
(B) \frac{10}{3}
(C) 7
(D) \frac{14}{3} | |
192 | As shown in the figure, the diameter CD of ⊙O crosses the midpoint G of chord EF, ∠DCF = 20.0, then ∠EOD is equal to () | images/192.jpg | [
"10°",
"20°",
"40°",
"80°"
] | null | null | 40° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 127,
"img_width": 101,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, the diameter CD of ⊙O crosses the midpoint G of chord EF, ∠DCF = 20.0, then ∠EOD is equal to ()
Choices:
(A) 10°
(B) 20°
(C) 40°
(D) 80° | |
195 | 如图，AB是⊙O的直径，C，D两点在⊙O上，∠BCD＝25°，则∠AOD的度数为（） | images/195.jpg | [
"120°",
"125°",
"130°",
"135°"
] | null | null | 130° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 95,
"img_width": 110,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，AB是⊙O的直径，C，D两点在⊙O上，∠BCD＝25°，则∠AOD的度数为（）
Choices:
(A) 120°
(B) 125°
(C) 130°
(D) 135° | |
196 | 如图所示，在△ABC中，已知点D，E，F分别为边BC，AD，CE的中点，且S△ABC＝4cm2，则S△DEF等于（） | images/196.jpg | [
"2cm2",
"1cm2",
"0.5cm2",
"0.25cm2"
] | null | null | 0.5cm2 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 81,
"img_width": 110,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图所示，在△ABC中，已知点D，E，F分别为边BC，AD，CE的中点，且S△ABC＝4cm2，则S△DEF等于（）
Choices:
(A) 2cm2
(B) 1cm2
(C) 0.5cm2
(D) 0.25cm2 | |
203 | 如图，在5×4的正方形网格中，每个小正方形的边长都是1，△ABC的顶点都在这些小正方形的顶点上，则tan∠BAC的值为（） | images/203.jpg | [
"\\frac{4}{3}",
"0.75",
"0.6",
"0.8"
] | null | null | \frac{4}{3} | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 151,
"img_width": 172,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在5×4的正方形网格中，每个小正方形的边长都是1，△ABC的顶点都在这些小正方形的顶点上，则tan∠BAC的值为（）
Choices:
(A) \frac{4}{3}
(B) 0.75
(C) 0.6
(D) 0.8 | |
206 | Find the scale factor from $Q$ to $Q'$. | images/206.jpg | [
"2",
"3",
"4",
"5"
] | null | null | 3 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 611,
"img_width": 731,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find the scale factor from $Q$ to $Q'$.
Choices:
(A) 2
(B) 3
(C) 4
(D) 5 | |
220 | As shown in the figure, ⊙O is the circumscribed circle of the quadrilateral ABCD, if ∠O = 110.0, then the degree of ∠C is () | images/220.jpg | [
"125°",
"120°",
"105°",
"90°"
] | null | null | 125° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 128,
"img_width": 124,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, ⊙O is the circumscribed circle of the quadrilateral ABCD, if ∠O = 110.0, then the degree of ∠C is ()
Choices:
(A) 125°
(B) 120°
(C) 105°
(D) 90° | |
221 | As shown in the figure, A, B, C are three points on ⊙O, ∠ACB = 25.0, then the degree of ∠BAO is () | images/221.jpg | [
"50°",
"55°",
"60°",
"65°"
] | null | null | 65° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 108,
"img_width": 102,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, A, B, C are three points on ⊙O, ∠ACB = 25.0, then the degree of ∠BAO is ()
Choices:
(A) 50°
(B) 55°
(C) 60°
(D) 65° | |
228 | 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 ∠ACE = 25.0, then the degree of ∠D is () | images/228.jpg | [
"50°",
"55°",
"60°",
"65°"
] | null | null | 50° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 97,
"img_width": 137,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
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 ∠ACE = 25.0, then the degree of ∠D is ()
Choices:
(A) 50°
(B) 55°
(C) 60°
(D) 65° | |
234 | In the figure shown above, AC = 6. What is the length of segment AB? | images/234.jpg | [
"3",
"5",
"6",
"7",
"It cannot be determined from the information given"
] | null | null | 6 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 378,
"img_width": 434,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In the figure shown above, AC = 6. What is the length of segment AB?
Choices:
(A) 3
(B) 5
(C) 6
(D) 7
(E) It cannot be determined from the information given | |
236 | Find $z$. | images/236.jpg | [
"7",
"9",
"12",
"15"
] | null | null | 12 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 423,
"img_width": 447,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find $z$.
Choices:
(A) 7
(B) 9
(C) 12
(D) 15 | |
238 | Find PT | images/238.jpg | [
"6",
"\\frac { 20 } { 3 }",
"7",
"22 / 3"
] | null | null | \frac { 20 } { 3 } | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 250,
"img_width": 238,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find PT
Choices:
(A) 6
(B) \frac { 20 } { 3 }
(C) 7
(D) 22 / 3 | |
242 | Find $m \angle A$ of quadrilateral ABCD | images/242.jpg | [
"45",
"90",
"135",
"180"
] | null | null | 135 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 381,
"img_width": 621,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find $m \angle A$ of quadrilateral ABCD
Choices:
(A) 45
(B) 90
(C) 135
(D) 180 | |
250 | The area $A$ of the shaded region is given. Find $x$. $A = 66$ cm$^2$ . | images/250.jpg | [
"4.6",
"6.5",
"13.0",
"26.0"
] | null | null | 13.0 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 286,
"img_width": 303,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: The area $A$ of the shaded region is given. Find $x$. $A = 66$ cm$^2$ .
Choices:
(A) 4.6
(B) 6.5
(C) 13.0
(D) 26.0 | |
255 | As shown in the figure, ∠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 ∠PAQ is () | images/255.jpg | [
"70°",
"55°",
"40°",
"30°"
] | null | null | 40° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 92,
"img_width": 188,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, ∠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 ∠PAQ is ()
Choices:
(A) 70°
(B) 55°
(C) 40°
(D) 30° | |
256 | 如图，△ABC中，AD平分∠BAC，AD交BC于点D，DE⊥AB，垂足为E，若DE＝3，AC＝4，则△ADC的面积为（） | images/256.jpg | [
"3",
"4",
"5",
"6"
] | null | null | 6 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 75,
"img_width": 148,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，△ABC中，AD平分∠BAC，AD交BC于点D，DE⊥AB，垂足为E，若DE＝3，AC＝4，则△ADC的面积为（）
Choices:
(A) 3
(B) 4
(C) 5
(D) 6 | |
257 | 以直角三角形的三边为边向外作正方形，其中两个正方形的面积如图所示，则正方形A的面积为（） | images/257.jpg | [
"6",
"36",
"64",
"8"
] | null | null | 6 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 119,
"img_width": 109,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 以直角三角形的三边为边向外作正方形，其中两个正方形的面积如图所示，则正方形A的面积为（）
Choices:
(A) 6
(B) 36
(C) 64
(D) 8 | |
269 | 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 () | images/269.jpg | [
"160m",
"160√{3}m",
"(160-160√{3})m",
"360m"
] | null | null | 160√{3}m | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 159,
"img_width": 133,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
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 ()
Choices:
(A) 160m
(B) 160√{3}m
(C) (160-160√{3})m
(D) 360m | |
270 | As shown in the figure, points A and B are three points on ⊙O and AB = AC. Connect BO and CO, if ∠ABC = 65.0, then the degree of ∠BOC is () | images/270.jpg | [
"50°",
"65°",
"100°",
"130°"
] | null | null | 100° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 114,
"img_width": 102,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, points A and B are three points on ⊙O and AB = AC. Connect BO and CO, if ∠ABC = 65.0, then the degree of ∠BOC is ()
Choices:
(A) 50°
(B) 65°
(C) 100°
(D) 130° | |
271 | Find y | images/271.jpg | [
"3",
"4.5",
"5",
"6"
] | null | null | 5 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 287,
"img_width": 448,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find y
Choices:
(A) 3
(B) 4.5
(C) 5
(D) 6 | |
273 | One diagonal of a rhombus is twice as long as the other diagonal. If the area of the rhombus is 169 square millimeters, what are the lengths of the diagonals? | images/273.jpg | [
"6.5",
"13",
"26",
"52"
] | null | null | 26 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 237,
"img_width": 347,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: One diagonal of a rhombus is twice as long as the other diagonal. If the area of the rhombus is 169 square millimeters, what are the lengths of the diagonals?
Choices:
(A) 6.5
(B) 13
(C) 26
(D) 52 | |
274 | 如图，AB、BC、CD、DA都是⊙O的切线，已知AD＝2，BC＝5，则AB+CD的值是（） | images/274.jpg | [
"14",
"12",
"9",
"7"
] | null | null | 7 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 119,
"img_width": 151,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，AB、BC、CD、DA都是⊙O的切线，已知AD＝2，BC＝5，则AB+CD的值是（）
Choices:
(A) 14
(B) 12
(C) 9
(D) 7 | |
275 | As shown in the figure, in Rt△ABC, ∠BAC = 90.0, AD ⊥ BC at D, DE ⊥ AB at E, AD = 3.0, DE = 2.0, then the length of CD is () | images/275.jpg | [
"\\frac{21}{2}",
"\\frac{√{15}}{2}",
"\\frac{9}{2}",
"\\frac{3√{5}}{2}"
] | null | null | \frac{3√{5}}{2} | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 107,
"img_width": 185,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, in Rt△ABC, ∠BAC = 90.0, AD ⊥ BC at D, DE ⊥ AB at E, AD = 3.0, DE = 2.0, then the length of CD is ()
Choices:
(A) \frac{21}{2}
(B) \frac{√{15}}{2}
(C) \frac{9}{2}
(D) \frac{3√{5}}{2} | |
276 | As shown in the figure, it is known that the radius of ⊙O is 5.0 and the chord AB = 8.0, then the distance from the center O to AB is () | images/276.jpg | [
"1mm",
"2mm",
"3mm",
"4mm"
] | null | null | 3mm | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 102,
"img_width": 102,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, it is known that the radius of ⊙O is 5.0 and the chord AB = 8.0, then the distance from the center O to AB is ()
Choices:
(A) 1mm
(B) 2mm
(C) 3mm
(D) 4mm | |
280 | In the figure above, ABCDEF is a regular hexagon, and its center is point O. What is the value of x? | images/280.jpg | [
"80",
"60",
"40",
"30",
"20"
] | null | null | 60 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 123,
"img_width": 130,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In the figure above, ABCDEF is a regular hexagon, and its center is point O. What is the value of x?
Choices:
(A) 80
(B) 60
(C) 40
(D) 30
(E) 20 | |
283 | $\overline{WTY} \cong \overline{TWY}$. Find $x$. | images/283.jpg | [
"2",
"4",
"5",
"10"
] | null | null | 5 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 416,
"img_width": 559,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: $\overline{WTY} \cong \overline{TWY}$. Find $x$.
Choices:
(A) 2
(B) 4
(C) 5
(D) 10 | |
285 | As shown in the figure, it is known that AB is the diameter of ⊙O, if the degree of ∠BOC is 50.0, then the degree of ∠A is () | images/285.jpg | [
"50°",
"40°",
"30°",
"25°"
] | null | null | 25° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 110,
"img_width": 100,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, it is known that AB is the diameter of ⊙O, if the degree of ∠BOC is 50.0, then the degree of ∠A is ()
Choices:
(A) 50°
(B) 40°
(C) 30°
(D) 25° | |
286 | 如图，将一根长度为8cm，自然伸直的弹性皮筋AB两端固定在水平的桌面上，然后把皮筋中点C竖直向上拉升3cm到点D，则此时该弹性皮筋被拉长了（） | images/286.jpg | [
"6cm",
"5cm",
"4cm",
"2cm"
] | null | null | 2cm | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 82,
"img_width": 250,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，将一根长度为8cm，自然伸直的弹性皮筋AB两端固定在水平的桌面上，然后把皮筋中点C竖直向上拉升3cm到点D，则此时该弹性皮筋被拉长了（）
Choices:
(A) 6cm
(B) 5cm
(C) 4cm
(D) 2cm | |
290 | 如图，平行线AB，CD被直线AE所截．若∠1＝105°，则∠2的度数为（） | images/290.jpg | [
"75°",
"85°",
"95°",
"105°"
] | null | null | 75° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 119,
"img_width": 132,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，平行线AB，CD被直线AE所截．若∠1＝105°，则∠2的度数为（）
Choices:
(A) 75°
(B) 85°
(C) 95°
(D) 105° | |
300 | $\overline{HK}$ and $\overline{IG}$ are diameters of $\odot L$. Find $m \widehat {IHJ}$. | images/300.jpg | [
"59",
"135",
"270",
"301"
] | null | null | 270 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 492,
"img_width": 510,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: $\overline{HK}$ and $\overline{IG}$ are diameters of $\odot L$. Find $m \widehat {IHJ}$.
Choices:
(A) 59
(B) 135
(C) 270
(D) 301 | |
304 | In the figure above, two line segments meet at a point on line l. If the value of y is equal to the square of the value of x, what is the value of y? | images/304.jpg | null | null | null | 100 | free_form | integer | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 247,
"img_width": 431,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question requiring an integer answer and provide the final value, e.g., 1, 2, 3, at the end.
Question: In the figure above, two line segments meet at a point on line l. If the value of y is equal to the square of the value of x, what is the value of y? | |
310 | Find z | images/310.jpg | [
"10",
"\\frac { 32 } { 3 }",
"\\frac { 40 } { 3 }",
"\\frac { 50 } { 3 }"
] | null | null | \frac { 40 } { 3 } | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 218,
"img_width": 350,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find z
Choices:
(A) 10
(B) \frac { 32 } { 3 }
(C) \frac { 40 } { 3 }
(D) \frac { 50 } { 3 } | |
315 | In the diagram above, angle A is congruent to angle BED, and angle C is congruent to angle D. If the ratio of the length of AB to the length of EB is 5:1, and the area of the triangle BED is 5*a^2 + 10, what is the area of triangle ABC? | images/315.jpg | [
"5*a^2 + 10",
"25*a^2 + 50",
"25*a^2 + 100",
"125*a^2 + 250",
"cannot be determined"
] | null | null | 125*a^2 + 250 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 463,
"img_width": 749,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In the diagram above, angle A is congruent to angle BED, and angle C is congruent to angle D. If the ratio of the length of AB to the length of EB is 5:1, and the area of the triangle BED is 5*a^2 + 10, what is the area of triangle ABC?
Choices:
(A) 5*a^2 + 10
(B) 25*a^2 + 50
(C) 25*a^2 + 100
(D) 125*a^2 + 250
(E) cannot be determined | |
316 | As shown in the figure, given that points A, B, and C are on ⊙O, ∠AOB = 100.0, then the degree of ∠ACB is () | images/316.jpg | [
"50°",
"80°",
"100°",
"200°"
] | null | null | 50° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 118,
"img_width": 105,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, given that points A, B, and C are on ⊙O, ∠AOB = 100.0, then the degree of ∠ACB is ()
Choices:
(A) 50°
(B) 80°
(C) 100°
(D) 200° | |
318 | Find the area of the figure. Round to the nearest tenth if necessary. | images/318.jpg | [
"191.5",
"1128",
"2256",
"4512"
] | null | null | 2256 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 175,
"img_width": 239,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find the area of the figure. Round to the nearest tenth if necessary.
Choices:
(A) 191.5
(B) 1128
(C) 2256
(D) 4512 | |
320 | 如图，在△ABC中，∠C＝90°，AB＝13，AC＝5，D、E分别是AC、AB的中点，则DE的长是（） | images/320.jpg | [
"6.5",
"6",
"5.5",
"\\frac{√{119}}{2}"
] | null | null | 6 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 90,
"img_width": 170,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在△ABC中，∠C＝90°，AB＝13，AC＝5，D、E分别是AC、AB的中点，则DE的长是（）
Choices:
(A) 6.5
(B) 6
(C) 5.5
(D) \frac{√{119}}{2} | |
322 | 如图，A，B两点被池塘隔开，在AB外选一点C，使点C能直接到达点A和点B，连接AC和BC，并分别找出AC和BC的中点M，N．如果测得MN＝20m，那么A，B两点的距离是（） | images/322.jpg | [
"10m",
"20m",
"35m",
"40m"
] | null | null | 40m | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 107,
"img_width": 148,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，A，B两点被池塘隔开，在AB外选一点C，使点C能直接到达点A和点B，连接AC和BC，并分别找出AC和BC的中点M，N．如果测得MN＝20m，那么A，B两点的距离是（）
Choices:
(A) 10m
(B) 20m
(C) 35m
(D) 40m | |
333 | Find tan X | images/333.jpg | [
"\\frac { 5 } { 12 }",
"\\frac { 12 } { 13 }",
"\\frac { 17 } { 12 }",
"\\frac { 12 } { 5 }"
] | null | null | \frac { 5 } { 12 } | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 149,
"img_width": 297,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find tan X
Choices:
(A) \frac { 5 } { 12 }
(B) \frac { 12 } { 13 }
(C) \frac { 17 } { 12 }
(D) \frac { 12 } { 5 } | |
338 | In triangle ABC above, AB = AC, E is the midpoint of line AB, and D is the midpoint of line AC. If AE = x and ED = 4, what is length BC? | images/338.jpg | [
"6",
"8",
"2*x",
"4*x",
"4*x^2"
] | null | null | 8 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 167,
"img_width": 121,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In triangle ABC above, AB = AC, E is the midpoint of line AB, and D is the midpoint of line AC. If AE = x and ED = 4, what is length BC?
Choices:
(A) 6
(B) 8
(C) 2*x
(D) 4*x
(E) 4*x^2 | |
339 | 如图，在⊙O中，AB=AC，∠BAC＝70°，则∠AEC的度数是（） | images/339.jpg | [
"65°",
"75°",
"50°",
"55°"
] | null | null | 55° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 112,
"img_width": 115,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在⊙O中，AB=AC，∠BAC＝70°，则∠AEC的度数是（）
Choices:
(A) 65°
(B) 75°
(C) 50°
(D) 55° | |
342 | In the figure above, which of the following is the greatest? | images/342.jpg | [
"a",
"b",
"c",
"d",
"e"
] | null | null | d | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 299,
"img_width": 405,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In the figure above, which of the following is the greatest?
Choices:
(A) a
(B) b
(C) c
(D) d
(E) e | |
355 | As shown in the figure, the parallel lines a and b are intercepted by the straight line c. If ∠1 = 50.0, then the degree of ∠2 is () | images/355.jpg | [
"150°",
"130°",
"110°",
"100°"
] | null | null | 130° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 110,
"img_width": 157,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, the parallel lines a and b are intercepted by the straight line c. If ∠1 = 50.0, then the degree of ∠2 is ()
Choices:
(A) 150°
(B) 130°
(C) 110°
(D) 100° | |
360 | If $\frac{I J}{X J}=\frac{HJ}{YJ}, m \angle W X J=130$
and $m \angle WZG=20,$ find $m \angle YIZ$ | images/360.jpg | [
"40",
"50",
"65",
"110"
] | null | null | 50 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 370,
"img_width": 721,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: If $\frac{I J}{X J}=\frac{HJ}{YJ}, m \angle W X J=130$
and $m \angle WZG=20,$ find $m \angle YIZ$
Choices:
(A) 40
(B) 50
(C) 65
(D) 110 | |
364 | As shown in the figure, AB is the diameter of ⊙O, and points C and D are on ⊙O. If ∠ABD = 50.0, then the degree of ∠BCD is () | images/364.jpg | [
"30°",
"35°",
"40°",
"45°"
] | null | null | 40° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 114,
"img_width": 127,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, AB is the diameter of ⊙O, and points C and D are on ⊙O. If ∠ABD = 50.0, then the degree of ∠BCD is ()
Choices:
(A) 30°
(B) 35°
(C) 40°
(D) 45° | |
371 | 如图，在Rt△ABC中，∠ABC＝90°，点D、E、F分别是边AB、BC、CA的中点，若DE+BF＝8，则BF的值为（） | images/371.jpg | [
"3",
"4",
"5",
"6"
] | null | null | 4 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 146,
"img_width": 109,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在Rt△ABC中，∠ABC＝90°，点D、E、F分别是边AB、BC、CA的中点，若DE+BF＝8，则BF的值为（）
Choices:
(A) 3
(B) 4
(C) 5
(D) 6 | |
373 | As shown in the figure, in the quadrilateral ABCD, ∠BAD = 120.0, ∠B = ∠D = 90.0, if you find a point M on BC and CD respectively, so that the perimeter of △AMN is the smallest, then the degree of ∠AMN + ∠ANM is () | images/373.jpg | [
"110°",
"120°",
"140°",
"150°"
] | null | null | 120° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 161,
"img_width": 122,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, in the quadrilateral ABCD, ∠BAD = 120.0, ∠B = ∠D = 90.0, if you find a point M on BC and CD respectively, so that the perimeter of △AMN is the smallest, then the degree of ∠AMN + ∠ANM is ()
Choices:
(A) 110°
(B) 120°
(C) 140°
(D) 150° | |
375 | Find the length of $AC$ in the isosceles triangle ABC. | images/375.jpg | [
"1.5",
"7",
"11",
"12.5"
] | null | null | 7 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 293,
"img_width": 703,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find the length of $AC$ in the isosceles triangle ABC.
Choices:
(A) 1.5
(B) 7
(C) 11
(D) 12.5 | |
378 | 如图，AD是△ABC的中线，E为AD的中点，△ABE的面积为2，则△ABC的面积为（） | images/378.jpg | [
"5",
"6",
"7",
"8"
] | null | null | 8 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 111,
"img_width": 118,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，AD是△ABC的中线，E为AD的中点，△ABE的面积为2，则△ABC的面积为（）
Choices:
(A) 5
(B) 6
(C) 7
(D) 8 | |
386 | Find x | images/386.jpg | [
"5",
"10",
"10 \\sqrt { 3 }",
"20"
] | null | null | 10 \sqrt { 3 } | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 247,
"img_width": 164,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find x
Choices:
(A) 5
(B) 10
(C) 10 \sqrt { 3 }
(D) 20 | |
388 | Express the ratio of $\tan M$ as a decimal to the nearest hundredth. | images/388.jpg | [
"0.38",
"0.42",
"0.92",
"2.40"
] | null | null | 0.42 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 209,
"img_width": 342,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Express the ratio of $\tan M$ as a decimal to the nearest hundredth.
Choices:
(A) 0.38
(B) 0.42
(C) 0.92
(D) 2.40 | |
391 | As shown in the figure, point O is the center of ⊙O, points A, B, and C are on ⊙O, AO ∥ BC, ∠AOB = 40.0, then the degree of ∠OAC is equal to () | images/391.jpg | [
"40°",
"60°",
"50°",
"20°"
] | null | null | 20° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 96,
"img_width": 96,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, point O is the center of ⊙O, points A, B, and C are on ⊙O, AO ∥ BC, ∠AOB = 40.0, then the degree of ∠OAC is equal to ()
Choices:
(A) 40°
(B) 60°
(C) 50°
(D) 20° | |
397 | 如图，点A、B、C都在半径为2的⊙O上，∠C＝30°，则弦AB长为（） | images/397.jpg | [
"1",
"2",
"2.2",
"2.5"
] | null | null | 2 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 70,
"img_width": 73,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，点A、B、C都在半径为2的⊙O上，∠C＝30°，则弦AB长为（）
Choices:
(A) 1
(B) 2
(C) 2.2
(D) 2.5 | |
403 | Find TX if $E X=24$ and $D E=7$ | images/403.jpg | [
"7",
"24",
"25",
"32"
] | null | null | 32 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 221,
"img_width": 564,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find TX if $E X=24$ and $D E=7$
Choices:
(A) 7
(B) 24
(C) 25
(D) 32 | |
407 | 如图，点B，D，E，C在同一条直线上，若△ABD≌△ACE，∠AEC＝110°，则∠DAE的度数为（） | images/407.jpg | [
"30°",
"40°",
"50°",
"60°"
] | null | null | 40° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 67,
"img_width": 76,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，点B，D，E，C在同一条直线上，若△ABD≌△ACE，∠AEC＝110°，则∠DAE的度数为（）
Choices:
(A) 30°
(B) 40°
(C) 50°
(D) 60° | |
408 | Find z. | images/408.jpg | [
"6",
"6 \\sqrt { 2 }",
"6 \\sqrt { 3 }",
"6 \\sqrt { 5 }"
] | null | null | 6 \sqrt { 5 } | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 238,
"img_width": 362,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find z.
Choices:
(A) 6
(B) 6 \sqrt { 2 }
(C) 6 \sqrt { 3 }
(D) 6 \sqrt { 5 } | |
410 | Find the perimeter of $\triangle D E F,$ if $\triangle D E F \sim \triangle C B F,$ perimeter of $\triangle C B F=27, D F=6,$ and $F C=8$ | images/410.jpg | [
"20.25",
"21",
"27",
"36"
] | null | null | 20.25 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 226,
"img_width": 405,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: Find the perimeter of $\triangle D E F,$ if $\triangle D E F \sim \triangle C B F,$ perimeter of $\triangle C B F=27, D F=6,$ and $F C=8$
Choices:
(A) 20.25
(B) 21
(C) 27
(D) 36 | |
413 | 已知：如图，△ABC中，AB＝AC，BD为∠ABC的平分线，∠BDC＝75°，则∠A的度数为（） | images/413.jpg | [
"25°",
"35°",
"40°",
"45°"
] | null | null | 40° | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 132,
"img_width": 123,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 已知：如图，△ABC中，AB＝AC，BD为∠ABC的平分线，∠BDC＝75°，则∠A的度数为（）
Choices:
(A) 25°
(B) 35°
(C) 40°
(D) 45° | |
414 | If $ST=8, TR=4$, and $PT=6$, find $QR$. | images/414.jpg | [
"6",
"8",
"9",
"10"
] | null | null | 9 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 386,
"img_width": 509,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: If $ST=8, TR=4$, and $PT=6$, find $QR$.
Choices:
(A) 6
(B) 8
(C) 9
(D) 10 | |
425 | 在Rt△ABC中，∠C＝90°，若AC＝6，BC＝8，则cosA的值为（） | images/425.jpg | [
"0.6",
"0.8",
"0.75",
"\\frac{4}{3}"
] | null | null | 0.6 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 120,
"img_width": 171,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 在Rt△ABC中，∠C＝90°，若AC＝6，BC＝8，则cosA的值为（）
Choices:
(A) 0.6
(B) 0.8
(C) 0.75
(D) \frac{4}{3} | |
426 | 如图，若DE是△ABC的中位线，△ADE的周长为1，则△ABC的周长为（） | images/426.jpg | [
"1",
"2",
"3",
"4"
] | null | null | 2 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 111,
"img_width": 154,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，若DE是△ABC的中位线，△ADE的周长为1，则△ABC的周长为（）
Choices:
(A) 1
(B) 2
(C) 3
(D) 4 | |
434 | In the figure above, side AC of triangle ABC is on line l. What is x in terms of k? | images/434.jpg | [
"60-k",
"k",
"60+k",
"120-k",
"120-2*k"
] | null | null | 60-k | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 157,
"img_width": 215,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In the figure above, side AC of triangle ABC is on line l. What is x in terms of k?
Choices:
(A) 60-k
(B) k
(C) 60+k
(D) 120-k
(E) 120-2*k | |
443 | As shown in the figure: In Rt△ABC, ∠C = 90.0, AC = 8.0, AB = 10.0, then the value of sinB is equal to () | images/443.jpg | [
"\\frac{3}{5}",
"\\frac{4}{5}",
"\\frac{3}{4}",
"\\frac{4}{3}"
] | null | null | \frac{4}{5} | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 80,
"img_width": 169,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure: In Rt△ABC, ∠C = 90.0, AC = 8.0, AB = 10.0, then the value of sinB is equal to ()
Choices:
(A) \frac{3}{5}
(B) \frac{4}{5}
(C) \frac{3}{4}
(D) \frac{4}{3} | |
446 | 如图，在△ABC中，点D是△ABC的内心，连接DB，DC，过点D作EF∥BC分别交AB、AC于点E、F，若BE+CF＝8，则EF的长度为（） | images/446.jpg | [
"4",
"5",
"8",
"16"
] | null | null | 8 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 105,
"img_width": 144,
"language": "chinese",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GeoQA+",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: 如图，在△ABC中，点D是△ABC的内心，连接DB，DC，过点D作EF∥BC分别交AB、AC于点E、F，若BE+CF＝8，则EF的长度为（）
Choices:
(A) 4
(B) 5
(C) 8
(D) 16 | |
455 | If x = 32 and r = 18, what is the length of the arc shown in the figure above? | images/455.jpg | [
"16*\\pi/5",
"32*\\pi/5",
"36*\\pi",
"288*\\pi/5",
"576*\\pi"
] | null | null | 16*\pi/5 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 353,
"img_width": 575,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "GEOS",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: If x = 32 and r = 18, what is the length of the arc shown in the figure above?
Choices:
(A) 16*\pi/5
(B) 32*\pi/5
(C) 36*\pi
(D) 288*\pi/5
(E) 576*\pi | |
467 | The degree measures of minor arc $\widehat{A C}$ and major arc $\widehat{A D C}$ are $x$ and $y$ respectively. If $m∠ABC = 70°$, find $x$. | images/467.jpg | [
"90",
"100",
"110",
"120"
] | null | null | 110 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 235,
"img_width": 499,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "Geometry3K",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: The degree measures of minor arc $\widehat{A C}$ and major arc $\widehat{A D C}$ are $x$ and $y$ respectively. If $m∠ABC = 70°$, find $x$.
Choices:
(A) 90
(B) 100
(C) 110
(D) 120 | |
478 | 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 () | images/478.jpg | [
"10",
"8",
"6",
"5"
] | null | null | 10 | multi_choice | text | {
"category": "math-targeted-vqa",
"context": "geometry diagram",
"grade": "high school",
"img_height": 97,
"img_width": 125,
"language": "english",
"skills": [
"geometry reasoning",
"algebraic reasoning"
],
"source": "UniGeo",
"split": "testmini",
"task": "geometry problem solving"
} | Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
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 ()
Choices:
(A) 10
(B) 8
(C) 6
(D) 5 |
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