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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is the shape ABCD a rectangle?
2. How many sides does ABCD have?
3. Are angles ABC and CDA equal?
| 1. Yes
2. 4
3. Yes
|
|
The diagram consists of a triangle ABC with vertices A, B, and C. Points D and E are located on sides AB and AC, respectively. There are two angles, labeled 1 and 2, which have equal measures. Angle BAC is measured at 80.0 degrees. Additionally, AD is equal to AE, and BE is equal to CD. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is there a triangle ABC in the diagram?
2. How many angles are labeled?
| 1. Yes
2. 2
|
|
The diagram consists of a right triangle ABC. Three squares are constructed outside the triangle using the sides of the triangle as their edges. These squares are labeled as S1, S2, and S3. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Are there three squares in the diagram?
2. Is square S1 constructed on a side of the triangle?
3. Is the square S2 constructed on a side of the triangle?
| 1. Yes
2. Yes
3. Yes
|
|
The diagram consists of two parallel lines, AB and CD. Point E is the intersection of line AD and line BC, with line AD being perpendicular to line BC at point E. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Do lines AD and BC intersect?
2. Is line AD perpendicular to line BC?
3. Does line AD intersect line BC at point E?
| 1. Yes
2. Yes
3. Yes
|
|
The diagram consists of a quadrilateral ABCD. Points A, B, C, and D represent the vertices of the quadrilateral. Point E is the midpoint of side AB, point F is the midpoint of side CD, and point G is the midpoint of side AC. Additionally, line segment FG is parallel to line segment AD. Line segment GE is parallel to line segment BC. There are specific measures for the angles DAC and ACB. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABCD a quadrilateral?
| 1. Yes
|
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The diagram consists of a tree, a bamboo pole, and a point on the ground where the shadow of the bamboo pole and the top of the tree meet. The bamboo pole is labeled as AD and has a length of 2.0 (units). The distance between the bamboo pole and the meeting point on the ground is labeled as 6.0 (units). The distance between the tree and the meeting point on the ground is labeled as 15.0 (units). There is a line segment labeled as BC, which is parallel to the line segment DE. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is BC parallel to DE?
2. Is the length of AD 2.0?
3. Is the distance from the bamboo pole to the meeting point 6.0?
4. Is the distance from the tree to the meeting point 15.0?
| 1. Yes
2. 2
3. 6
4. 15
|
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is BCDE a quadrilateral?
2. Is A a vertex of the trapezoid?
| 1. Yes
2. No
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Are points D, B, and C corners of a square?
2. Is point A inside the square?
3. Is BC a side of the square?
| 1. Yes
2. No
3. Yes
|
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is triangle ABC equilateral?
2. Is triangle DEF isosceles?
3. What is the measure of angle EDF?
| 1. Yes
2. Yes
3. 90
|
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABCD a rectangle?
2. Is A a vertex of the quadrilateral?
| 1. No
2. Yes
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Are all sides of triangle ABC equal?
2. Is D inside triangle ABC?
3. Is D on the same side of line BC as A?
| 1. Yes
2. Yes
3. No
|
|
The diagram consists of a circle labeled as circle O. Point A and point B are on the circumference of the circle. The line segment AB is a chord. There is another point, labeled as C, which is also on the circumference of the circle. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is A on the circumference?
2. Is AB a chord?
3. Is O the center of the circle?
| 1. Yes
2. Yes
3. Yes
|
|
The diagram consists of a circle labeled as circle O. Point P is located outside the circle, and two tangents are drawn from point P to the circle. Points A and B are the points of tangency on the circle. Point C is also located on the circle. Lines OA and OB are drawn from the center of the circle to points A and B, respectively. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is point P outside the circle?
2. Are there two tangents drawn from P?
3. Is C located on the circle?
4. Is OA a radius?
| 1. Yes
2. Yes
3. Yes
4. Yes
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The diagram consists of three intersecting lines labeled as l1, l2, and l3. Line l1 is parallel to line l2, and they intersect line l3 at points A and C. From point A, a perpendicular line AD is drawn to line AC, intersecting line l2 at point D. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Do l1 and l3 intersect?
2. Does line AD intersect line l2?
3. Does line l3 intersect line l2 at point C?
4. What is the measure in degrees of angle DAC?
| 1. Yes
2. Yes
3. Yes
4. 90
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is angle DAB a right angle?
2. Is side AB perpendicular to side AD?
3. Does point E lie on the circumcircle of triangle DBA?
4. Is ABCD a rectangle?
| 1. Yes
2. Yes
3. Yes
4. No
|
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The diagram consists of a quadrilateral ABCD. Line MN is a fold line that passes through the quadrilateral. There are angles 1 and 2 formed by the fold line and the sides of the quadrilateral. There are also angles B and C formed by the remaining sides of the quadrilateral. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABCD a quadrilateral?
2. Does the line MN pass through the quadrilateral?
3. Are there more than 2 angles labelled in the diagram?
| 1. Yes
2. Yes
3. Yes
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is there a line segment labeled AB?
2. Is triangle CDE isosceles?
3. Is angle DCE a right angle?
| 1. Yes
2. Yes
3. Yes
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABCD a square?
2. Does the incircle of triangle CBD touch side CB?
3. Does the incircle touch BD at E?
4. How many points of tangency are explicitly mentioned for the incircle?
| 1. No
2. Yes
3. Yes
4. 3
|
|
The diagram consists of a triangle ABC with vertices A, B, and C. There is an additional line segment MN, which is the perpendicular bisector of the line segment BC. Point D is located on line segment AC. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is there a triangle ABC?
2. Is MN a perpendicular bisector of BC?
3. Is point D located on the line segment AC?
4. Does MN intersect BC at a 90-degree angle?
| 1. Yes
2. Yes
3. Yes
4. Yes
|
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Are DA and BC equal in length?
2. Is ABCD a trapezoid?
3. Are angles CAE and EAB equal?
4. Is ABCD an isosceles trapezoid?
| 1. Yes
2. Yes
3. Yes
4. Yes
|
|
The diagram consists of a quadrilateral ABCD inscribed within a circle, where the circle is denoted as circle O. Point A and point D are the endpoints of the diameter AD. Point B and point C are the remaining two vertices of the quadrilateral. There is an angle CBE. The central angle, angle AOC, can be determined based on the properties of inscribed angles and the relationship between inscribed angles and central angles. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABCD a quadrilateral?
2. Is angle CBE an exterior angle of the quadrilateral?
| 1. Yes
2. Yes
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABCD a quadrilateral?
2. Are sides AB and BC equal in length?
3. Is E on the line through B?
4. Is line BE parallel to AC?
| 1. Yes
2. Yes
3. Yes
4. Yes
|
|
The diagram consists of a quadrilateral with four vertices labeled as A, B, C, and D. The quadrilateral has four sides and four angles. The angles of the quadrilateral are not specified. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is there a vertex labeled 'A'?
2. Is there a vertex labeled 'E'?
3. Does the diagram contain four sides?
4. Is the shape a quadrilateral?
5. Is the number of vertices greater than three?
| 1. Yes
2. No
3. Yes
4. Yes
5. Yes
|
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The diagram consists of two parallel lines, labeled as AB and CD. Line EF intersects AB and CD at points E and F, respectively. Point E is the vertical foot of the perpendicular line EC, which intersects EF. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Does line EF intersect line AB?
2. Is EC perpendicular to AB?
3. How many degrees is angle ECB?
| 1. Yes
2. Yes
3. 90
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is angle BAD a right angle?
2. Is side AB perpendicular to side AD?
3. Is point E on a tangent line passing through A?
4. Is the circle centered at B?
5. Do the tangents through A intersect at C?
| 1. Yes
2. Yes
3. Yes
4. Yes
5. Yes
|
|
The diagram consists of two parallel lines labeled as AB and CD. Line l intersects AB at point E and CD at point F. Angle 1 is labeled. The angles formed by the intersection of line l and the parallel lines are labeled as angle 2. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Does line l intersect AB at point E?
2. Is angle 2 formed by the intersection of line l and CD?
| 1. Yes
2. Yes
|
|
The diagram consists of a quadrilateral ABCD with vertices A, B, C, and D. Diagonal AC intersects diagonal BD at point O. Point E lies on line AD. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABCD a quadrilateral?
2. Do diagonals AC and BD intersect?
3. Is point E on line AD?
4. Is point O inside the quadrilateral ABCD?
5. Does point C lie on line segment AC?
6. Are there 4 vertices in ABCD?
7. Is A, O, and C collinear?
| 1. Yes
2. Yes
3. Yes
4. Yes
5. Yes
6. Yes
7. Yes
|
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The diagram consists of a quadrilateral ABCD with vertices A, B, C, and D. The diagonals AC and BD intersect at point O. Points E and F are the midpoints of segments AO and BO, respectively. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABCD a quadrilateral?
2. Do diagonals AC and BD intersect?
3. Is point E the midpoint of AO?
4. Are the vertices of the quadrilateral labeled A, B, C, and D?
| 1. Yes
2. Yes
3. Yes
4. Yes
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABCD a rectangle?
2. Are sides EF and EG equal in length?
3. Is FG a side of triangle EFG?
4. Is ABCD a triangle?
| 1. Yes
2. Yes
3. Yes
4. No
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is EFGH a rectangle?
2. How many sides does ABCD have?
| 1. Yes
2. 4
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is angle BAC a right angle?
2. Is the shape ABCD a parallelogram?
3. How many vertices does triangle ABC have?
| 1. Yes
2. Yes
3. 3
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Are the diagonals of quadrilateral ABCD equal in length?
2. Is triangle EFG equilateral?
3. Is G a vertex of the quadrilateral?
| 1. Yes
2. Yes
3. No
|
|
The diagram consists of a quadrilateral ABCD inscribed within a circle, denoted as circle O. Points A, B, C, and D are the vertices of the quadrilateral, and they all lie on the circumference of the circle. Point E lies on the extension line of side CD. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABCD a quadrilateral?
2. Is quadrilateral ABCD inscribed in circle O?
3. Does point A lie on the circumference of the circle?
4. Is point E inside the circle?
| 1. Yes
2. Yes
3. Yes
4. No
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. How many vertices does triangle BCD have?
2. Is point A a vertex of triangle BCD?
3. Is the shape formed by B, C, and D a triangle?
| 1. 3
2. No
3. Yes
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is side AB equal in length to side AC?
2. Is ABC an equilateral triangle?
3. Is point D located inside triangle ABC?
| 1. Yes
2. No
3. No
|
|
The diagram consists of a circle with points A and B on its circumference. Chords AB and CD intersect inside the circle. AB is perpendicular to CD. There is an angle CDB. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Are points A and B on the circumference?
2. Do chords AB and CD intersect inside the circle?
3. Is chord AB perpendicular to chord CD?
4. Is there an angle CDB?
5. Is the measure of angle formed by AB and CD 90 degrees?
| 1. Yes
2. Yes
3. Yes
4. Yes
5. Yes
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Are all sides of triangle ABC equal?
2. Is D the mirror image of A?
3. Does B lie on the line segment AD?
4. Is the length of AB equal to BD?
| 1. Yes
2. Yes
3. Yes
4. Yes
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABCD a parallelogram?
2. Is DBAE a square?
3. Do ABCD and DBAE share a side?
4. How many vertices does the square ABCD have?
| 1. Yes
2. No
3. Yes
4. 4
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is angle BAC a right angle?
2. Is DEFG a triangle?
3. Are DG and EF equal?
| 1. Yes
2. No
3. Yes
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is the shape ABCDE a pentagon?
2. Does point F lie on segment DC?
3. How many vertices does the shape have?
4. Is point F on the perpendicular bisector of DC?
| 1. Yes
2. No
3. 5
4. Yes
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Are sides DA and BC equal?
2. Is the shape ABCD a trapezoid?
3. Is the trapezoid isosceles?
4. Does the circle's center lie on vertex B?
5. Does the circle pass through vertex D?
| 1. Yes
2. Yes
3. Yes
4. Yes
5. Yes
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The diagram consists of two right-angled triangles, labeled as ABC and CDE. Triangle ABC has angles measuring 30.0 degrees and 60.0 degrees, while triangle CDE has angles measuring 45.0 degrees and 45.0 degrees. The vertices of the right angles of both triangles coincide at point C. Additionally, line DE is parallel to line BC. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. How many degrees is angle DCE?
| 1. 90
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The diagram consists of a trapezoid ABCD. Point E is the midpoint of the diagonal AD, and point B is connected to point E. There is also a line segment EF that passes through point F. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is point B connected to point E?
| 1. Yes
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is angle DAB a right angle?
2. Are lines AB and AD perpendicular?
3. Is ABCD a trapezoid?
4. Are lines EA and CB parallel?
| 1. Yes
2. Yes
3. Yes
4. Yes
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Are DA and BC of equal length?
2. Is ABCD a trapezoid?
3. Are points C, A, F, G, and D collinear?
4. Is CA equal in length to EG?
| 1. Yes
2. Yes
3. No
4. Yes
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The diagram consists of a triangle ABC inscribed within a circle. Points A, B, and C are the vertices of the triangle, and they all lie on the circumference of the circle. The center of the circle is marked as point O. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABC a triangle?
2. Is point A on the circumference of the circle?
3. Is O the center of the circle?
4. Are all the vertices of the triangle on the circle?
| 1. Yes
2. Yes
3. Yes
4. Yes
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is the figure AB a line segment?
2. Is CDEF a rectangle?
3. How many vertices does rectangle CDEF have?
| 1. Yes
2. Yes
3. 4
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The diagram consists of a circle labeled as circle O. Two tangents, PA and PB, are drawn from an external point P to the circle, intersecting the circle at points A and B respectively. Point C is located on the minor arc AB. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is P outside the circle?
2. Is C on the major arc AB?
| 1. Yes
2. No
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is the shape EFGH a quadrilateral?
2. Is EFGH described as a square?
3. Does the shape ABCD have four sides?
| 1. Yes
2. Yes
3. Yes
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The diagram consists of a circle labeled as circle O. Points A and B are located on the circumference of the circle, with lines PA and PB tangent to the circle at these points respectively. Point C is also on the circumference of the circle. Lines AC and BC are drawn, connecting point C to points A and B respectively. Additionally, lines OA and OB are drawn, connecting point O (the center of the circle) to points A and B respectively. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is point A on the circumference?
2. Is OA a radius of the circle?
3. Is AC a chord of the circle?
| 1. Yes
2. Yes
3. Yes
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABCD a pentagon?
2. How many sides does the pentagon EFGHI have?
3. Is EFGHI a quadrangle?
| 1. No
2. 5
3. No
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABCD a square?
2. Is point E on line BC?
3. How many points are labeled?
4. Is E the midpoint of CD?
| 1. No
2. Yes
3. 5
4. No
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is E located on the line segment CB?
2. Is AE perpendicular to CB?
3. Is ABCD a triangle?
4. Is A a vertex of the quadrilateral?
| 1. Yes
2. Yes
3. No
4. Yes
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The diagram consists of a circle labeled as circle O. The line AB is a diameter of the circle, with point A being the point of tangency between the circle and the line PA. Point P is located outside the circle and is connected to point A. The line PO intersects the circle at point C. There is an angle BCO. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is AB a diameter of circle O?
2. Is point A the point of tangency for line PA?
3. Is point P inside the circle?
| 1. Yes
2. Yes
3. No
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The diagram consists of a circle representing a cake. The cake is divided into equal parts. There are 8 points along the circumference of the circle. Each part is marked with an angle. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Are there any lines outside the circle?
| 1. No
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABCD a triangle?
2. Does E lie on the edge of triangle BDC?
| 1. No
2. No
|
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Are points A, B, and C corners of the square?
| 1. Yes
|
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The diagram consists of a regular pentagon ABCDE. Point A is one of the vertices of the pentagon, and the diagonal AC connects points A and C. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is the polygon ABCDE a pentagon?
2. Is AC a diagonal of the pentagon?
3. Is point A a vertex of the pentagon?
4. How many sides does the polygon have?
| 1. Yes
2. Yes
3. Yes
4. 5
|
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Are sides DA and BC equal in length in trapezoid ABCD?
2. Does trapezoid EFGH have a right angle at vertex F?
3. Is EF perpendicular to EH in trapezoid EFGH?
| 1. Yes
2. No
3. Yes
|
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The diagram consists of a circle labeled as circle O. Points B, C, and D lie on the circumference of the circle. Additionally, there is a point A on the circle. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. How many points are explicitly labelled in the diagram?
| 1. 4
|
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is the shape ABCDE a pentagon?
2. What is the measure of angle CEF?
| 1. Yes
2. 135
|
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The diagram consists of a circle labeled as circle O. There is a diameter AB that passes through the center of the circle. Point C lies on the circumference of the circle, and there is a chord AC that intersects AB. Point P is the intersection of the tangent line passing through C and the extended line of AB. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is there a diameter labeled AB in the circle?
2. Is point O the center of the circle?
3. Is AC a chord?
4. Is point P the intersection of a tangent line and the extended line of AB?
5. Does the tangent line pass through C?
| 1. Yes
2. Yes
3. Yes
4. Yes
5. Yes
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The diagram consists of a rectangle ABCD. Point E is the midpoint of the side AD. Line segment CE is drawn connecting points C and E. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. How many sides does the shape ABCD have?
| 1. 4
|
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The diagram consists of a right triangle ACB, where angle ACB is a right angle. Point C is the vertex of the right angle. Point A is connected to points C and B, forming one side of the triangle. The triangle is then rotated counterclockwise around point C by an angle α, resulting in a new triangle A1B1C. Line A1B1 passes through point B. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is the rotation clockwise?
| 1. No
|
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The diagram consists of a circle denoted as circle O with a radius OA. Point B lies on the radius OA, but it is not coincident with points O or A. A line perpendicular to OA passes through point B and intersects the circle at point C. A rectangle OBCD is formed with OB and BC as sides, and the diagonal BD is connected. The length of CD is given as 6 units and the length of BC is given as 8 units. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is OA a radius of the circle?
2. Does point B lie on the radius OA?
3. Is the line through B perpendicular to OA?
| 1. Yes
2. Yes
3. Yes
|
|
The diagram consists of two lines, labeled as AB and CD, which are parallel to each other. Point E is the intersection point of line AF and line CD. Point B is connected to points E and F. Line BE forms a right angle with line AF. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Do lines AF and CD intersect at point E?
2. Is angle AEF 90 degrees?
| 1. Yes
2. No
|
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The diagram consists of a right triangle ABC. The perpendicular bisector of side AB, labeled as DE, intersects side BC at point D and intersects side AB at point E. Point A is connected to points D and E, forming line AD. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is triangle ABC a right triangle?
2. Does point D lie on side BC?
| 1. Yes
2. Yes
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Are sides AD and BC equal in length?
2. Is triangle EFG equilateral?
3. Does the description mention the relationship between G and the quadrilateral?
| 1. Yes
2. Yes
3. No
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is angle DAB a right angle?
2. Is side AB perpendicular to side AD?
3. Does line AE intersect line BC?
4. Is AE perpendicular to BC?
5. How many right angles does the trapezoid ABCD have?
| 1. Yes
2. Yes
3. Yes
4. Yes
5. 1
|
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. What is the angle at vertex A?
| 1. 90
|
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The diagram consists of a square ABCD, where points A, B, C, and D are the vertices of the square. Point O is the intersection of the diagonals AC and BD. Points E and F are located on the sides AB and BC respectively. Line OE is perpendicular to line OF, and passes through point O. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is O the intersection of diagonals AC and BD?
2. Is point F on side BC?
3. What is the measure of angle EOF?
| 1. Yes
2. Yes
3. 90
|
|
The diagram consists of a triangle ABC inscribed within a circle O. Points A, B, and C are the vertices of the triangle, and they all lie on the circumference of the circle. The center of the circle is marked as point O. Points A and B are connected to point O. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is triangle ABC inscribed in circle O?
2. Is point O the center of the circle?
3. Are points A and B connected to point O?
4. Is angle AOB greater than 0 degrees?
5. Are all three vertices of the triangle on the circle?
| 1. Yes
2. Yes
3. Yes
4. Yes
5. Yes
|
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The diagram consists of a circle labeled as circle O. Points A and B are the intersection points of the circle with lines PA and PB, respectively. Radial line PD intersects the circle at points C and D. Point E is the midpoint of line segment CD. Point P is connected to points A and B. Additionally, lines OP, OA, and OE are drawn in the diagram, with point O as the center of the circle. There is a circle passing through points A, O, E, and P. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is point A on the circle?
2. Is PA a line segment?
| 1. Yes
2. No
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is triangle ABC equilateral?
2. Is angle EDF a right angle?
3. Is triangle DEF isosceles?
4. Are all sides of triangle ABC the same length?
5. Is triangle ABC a right triangle?
| 1. Yes
2. Yes
3. Yes
4. Yes
5. No
|
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABCD a rectangle?
2. Is EFGH a rectangle?
| 1. Yes
2. Yes
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is BCDE a quadrilateral?
2. Are sides EB and CD of the trapezoid equal?
3. Is A a vertex of the trapezoid?
| 1. Yes
2. Yes
3. No
|
|
The diagram consists of two lines, labeled as AB and CD, which are parallel to each other. Point F is located on line AB. Point E is the intersection of lines BE and CD. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is point E on line AB?
| 1. No
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABCD a triangle?
2. Does EFG have four vertices?
3. Is the number of vertices in ABCD greater than the number of vertices in EFG?
| 1. No
2. No
3. Yes
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is triangle ABC equilateral?
2. Is D the midpoint of BC?
3. Is E the midpoint of AC?
4. Is F the midpoint of AB?
5. Is point G inside triangle ABC?
6. Does the circumcircle of DEF pass through A?
| 1. Yes
2. Yes
3. Yes
4. Yes
5. Yes
6. No
|
|
The diagram consists of a triangle ABC inscribed within a circle, where the circle is denoted as circle O. Point A is located on the circumference of the circle, while points B and C are the vertices of the triangle. There is a line segment connecting points B and D, where D is a point on the circumference of the circle. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is A located on the circumference of the circle?
| 1. Yes
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is triangle ABC a right triangle?
2. Is triangle ABC isosceles?
3. Does angle BAC equal 90 degrees?
| 1. Yes
2. Yes
3. Yes
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is DA equal in length to BC?
2. Is ABCD a trapezoid?
| 1. Yes
2. Yes
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Are sides AD and BC equal in length in the quadrilateral?
2. Is EFGH a rectangle?
| 1. Yes
2. Yes
|
|
The diagram consists of a quadrilateral ABCD. Line AC is perpendicular to line BC, and line AD is parallel to line BC. Line BD bisects angle ABC. Points E and F are the midpoints of line BD and line AC, respectively. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is AC perpendicular to BC?
| 1. Yes
|
|
The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is angle A a right angle?
2. Are sides AB and AD perpendicular?
3. Is the shape ABCD a trapezoid?
4. Is the center of the circle point A?
5. Does point E lie on the circle?
| 1. Yes
2. Yes
3. Yes
4. Yes
5. Yes
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is there a line segment present?
2. Is there a point C?
3. Is triangle CDE equilateral?
| 1. Yes
2. Yes
3. Yes
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The diagram consists of a square labeled as ABCD, with each side having the same length. Inside the shaded square, there is a cone whose base is a circle. The cone is formed by enclosing the lateral surface of the cone within a sector of the shaded square. The cone is a three-dimensional object with a pointed top and a curved base. The height of the cone can be determined by calculating the distance from the base of the cone to its pointed top. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is the square labeled ABCD?
2. Is the square shaded?
| 1. Yes
2. Yes
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABCD a rectangle?
2. Does E lie on segment BA?
3. Is E equidistant from A and B?
| 1. No
2. No
3. Yes
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is point D on side CB?
2. How many midpoints are labeled?
3. Is triangle ACB inside the circumcircle of triangle DEF?
4. Is point G the center of a circle?
5. Is point E on side AB?
| 1. Yes
2. 3
3. No
4. Yes
5. Yes
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The diagram consists of a regular hexagon ABCDEF inscribed within a circle, where the circle is denoted as circle O. Points A, B, C, D, E, and F are the vertices of the hexagon. Line BD is drawn, connecting points B and D. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is the polygon ABCDEF a hexagon?
2. Is the hexagon ABCDEF inscribed in the circle?
3. Is the circle's center labeled O?
4. How many sides does the polygon ABCDEF have?
| 1. Yes
2. Yes
3. Yes
4. 6
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The diagram consists of a vertical flagpole and a bamboo pole. The bamboo pole is positioned in such a way that its shadow and the shadow of the flagpole fall on the same point on the ground. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is the flagpole vertical?
2. Is there a bamboo pole in the diagram?
3. Do the shadows of the flagpole and bamboo pole meet at a point?
4. Are the flagpole and bamboo pole shadows separate lines?
| 1. Yes
2. Yes
3. Yes
4. No
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is triangle ABC equilateral?
2. Is DE a line?
3. Is C a point?
| 1. Yes
2. Yes
3. Yes
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The diagram consists of a horizontal line representing the window AB. A beam of sunlight is shown hitting the window at an angle. Point C represents the endpoint of a perpendicular line AC, which is meant to block the sunlight from hitting the window. Point D is the intersection of the perpendicular line and the window AB. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is AC a perpendicular line?
| 1. Yes
|
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The diagram consists of a circle labeled as circle O and a point labeled as P outside the circle. Two tangents are drawn from point P to the circle, intersecting the circle at points A and B respectively. Point O is the center of the circle. Line AB is drawn connecting points A and B, and line OP is drawn connecting points O and P. Point D is the intersection of line OP and the circle. Line BD is drawn connecting points B and D. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is point P outside the circle?
2. Are PA and PB tangents to the circle?
3. Is O the center of the circle?
4. Does line AB connect points A and B?
5. Does the line segment BD exist?
| 1. Yes
2. Yes
3. Yes
4. Yes
5. Yes
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is ABCD a trapezoid?
2. Are any sides of EFGH specified as parallel?
3. Is EH equal to FG?
| 1. Yes
2. No
3. Yes
|
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is there a point A?
2. Is there a line segment BC?
| 1. Yes
2. Yes
|
|
The diagram consists of a circle labeled as circle O. Points A, B, and C are located on the circumference of the circle. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is point A on the circumference?
2. Is point B on the circumference?
| 1. Yes
2. Yes
|
|
The diagram consists of two parallel lines, labeled as line a and line b. Angle 1 is formed between line a and a transversal line. Angle 2 is formed between line b and the same transversal line. Angle 3 is formed by the intersection of line a and line b. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is angle 1 formed by line a and the transversal?
2. Is angle 2 formed by line b and the transversal?
| 1. Yes
2. Yes
|
|
The diagram consists of a square grid, with each small square having a side length. Points A, B, and C are located on the grid points. Point D is the intersection of the perpendicular lines AD and BC. | real | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is the background a square grid?
2. Is point A on a grid point?
3. Is AD perpendicular to BC?
4. Is the intersection point D shown in the diagram?
| 1. Yes
2. Yes
3. Yes
4. Yes
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The diagram consists of a circle labeled as circle O. Inside the circle, there is a chord AB, which intersects the circle at two points. One of the points of intersection is labeled as A. Point C is outside the circle and is connected to point A by a tangent line AC. Point B is on the chord AB and is also connected to the center of the circle. There is an angle formed by points A, O (the center of the circle), and C. | synthetic | <image>Analyze the provided image and answer the following question(s). The answer for each question must be "Yes"/"No", a number, or a simple answer like "AB" (no spaces).
1. Is triangle ABC equilateral?
2. Are the lengths of CB and CD equal?
3. Is DCAB a square?
4. Are the lengths of AB and AD equal?
| 1. Yes
2. Yes
3. No
4. Yes
|
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