unique_id stringlengths 24 24 | difficulty stringclasses 3
values | nl_description stringlengths 177 973 | pygeox_code stringlengths 322 1.43k | Objs unknown | Rels listlengths 1 6 | Points listlengths 3 15 | extra_rel listlengths 0 3 | possible_solution dict |
|---|---|---|---|---|---|---|---|---|
2obj_3rel_1extra_gen0004 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a major arc with center B, start point C, end point D. There is a line segment BC. There is a line segment CD. There is a line segment AD. Point B lies on the circle. Point C lies on the circle. Line segment BC is a d... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
semicircle1 = scene.add.major_arc(B, C, D)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.add.line_segment(C, D)
line_AD = scene.add.line_segment(A, D)
### relationsh... | {
"circle1": "circle(A)",
"semicircle1": "major_arc(B, C, D)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_AD": "line_segment(A, D)"
} | [
"point_lies_on(B, circle1)",
"point_lies_on(C, circle1)",
"is_diameter(line_BC, circle1)"
] | [
"A",
"B",
"C",
"D"
] | [
"scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BC').length)"
] | {
"points": {
"A": [
-0.5420028623,
-1.0820747743
],
"B": [
0.0515416506,
-2.0125052447
],
"C": [
-1.1355473702,
-0.1516443033
],
"D": [
-2.0470014768,
-2.6966839836
]
},
"circles": {
"A": 1.103628538
}
} |
2obj_3rel_1extra_gen0011 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a minor arc with center A from B to C. There is a quadrilateral with vertices D, E, F, G. There is a line segment DF. There is a line segment DE. The line DF is perpendicular to line DE. G is the midpoint of line DF. G lies on the minor arc ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G = scene.add.points(["A", "B", "C", "D", "E", "F", "G"])
arc1 = scene.add.minor_arc(A, B, C)
quad1 = scene.add.quadrilateral(D, E, F, G)
line_DF = scene.add.line_segment(D, F)
line_DE = scene.add.line_segment(D, E)
### relationships
sce... | {
"arc1": "minor_arc(A, B, C)",
"quad1": "quadrilateral(D, E, F, G)",
"line_DF": "line_segment(D, F)",
"line_DE": "line_segment(D, E)"
} | [
"perpendicular(line_DF, line_DE)",
"is_midpoint(G, line_DF)",
"point_lies_on(G, arc1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [] | {
"points": {
"A": [
1.8533623685,
1.3674870481
],
"B": [
2.9973398477,
1.1538461
],
"C": [
0.8679357972,
1.986568142
],
"D": [
0.3937091058,
2.8362300285
],
"E": [
1.9276867462,
4.1807447819
],
"F": [
1.5935... |
2obj_3rel_1extra_gen0013 | medium | Diagram description: The diagram contains points A, B, C, D, E. There is a rhomboid ABCD. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment AB. There is a line segment CD. Points A, E, and C are collinear. Line segment AC is a diameter of the circle. Line s... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
rhomboid1 = scene.add.rhomboid(A, B, C, D)
circle1 = scene.add.circle(E)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_segment(B, D)
line_AB = scene.add.line_segment(A, B)
line_CD... | {
"rhomboid1": "rhomboid(A, B, C, D)",
"circle1": "circle(E)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_AB": "line_segment(A, B)",
"line_CD": "line_segment(C, D)"
} | [
"collinear(A, E, C)",
"is_diameter(line_AC, circle1)",
"perpendicular(line_AC, line_BD)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [
"scene.constraint.eq(scene.get_object('line_AB').length, scene.get_object('line_CD').length)",
"scene.constraint.eq(scene.get_object('line_AC').length, 2 * scene.get_object('circle1').radius)"
] | {
"points": {
"A": [
-2.2209282911,
-0.5006934325
],
"B": [
-2.4477881921,
1.2498692996
],
"C": [
-0.704213952,
1.5221177192000002
],
"D": [
-0.4776727054,
-0.2272786116
],
"E": [
-1.4622540383,
0.5099838721000001
]
... |
2obj_3rel_1extra_gen0017 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a regular hexagon with vertices A, B, C, D, E, F. There is a circle with center G. There is a line segment AD. There is a line segment BE. Line AD and line BE intersect at point G. Line AD is a diameter of the circle. The circle is the circu... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G = scene.add.points(["A", "B", "C", "D", "E", "F", "G"])
hexagon1 = scene.add.regular_hexagon(A, B, C, D, E, F)
circle1 = scene.add.circle(G)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_segment(B, E)
### relationships... | {
"hexagon1": "regular_hexagon(A, B, C, D, E, F)",
"circle1": "circle(G)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)"
} | [
"lines_intersect_at(line_AD, line_BE, G)",
"is_diameter(line_AD, circle1)",
"is_circumcircle(circle1, hexagon1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [
"scene.constraint.eq(scene.get_object('line_BE').length, scene.get_object('hexagon1').diagonal)"
] | {
"points": {
"A": [
-20,
10
],
"B": [
-15,
1.3397459622
],
"C": [
-5,
1.3397459622
],
"D": [
0,
10
],
"E": [
-5,
18.6602540378
],
"F": [
-15,
18.6602540378
],
"G": [
-10,
10
]
... |
2obj_3rel_1extra_gen0018 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, M, N, K. There is a triangle with vertices A, B, C. There is a parallelogram with vertices D, E, F, G. There is a line segment AM. There is a line segment BN. There is a line segment CK. Line AM is an altitude of triangle ABC from vertex A. Line BN i... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, M, N, K = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "M", "N", "K"])
triangle_ABC = scene.add.triangle(A, B, C)
parallelogram_DEFG = scene.add.parallelogram(D, E, F, G)
line_AM = scene.add.line_segment(A, M)
line_BN = scene.ad... | {
"triangle_ABC": "Triangle(A, B, C)",
"parallelogram_DEFG": "Parallelogram(D, E, F, G)",
"line_AM": "line_segment(A, M)",
"line_BN": "line_segment(B, N)",
"line_CK": "line_segment(C, K)"
} | [
"is_altitude(line_AM, triangle_ABC, A)",
"is_median(line_BN, triangle_ABC, B)",
"parallel(line_AM, line_BN)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"M",
"N",
"K"
] | [] | {
"points": {
"A": [
-3.8020446644,
6.0736721763
],
"B": [
-0.1263204384,
1.20753697
],
"C": [
2.8032157379,
1.6215383468
],
"D": [
-6.8106738406,
7.6917764622
],
"E": [
-8.8835282427,
8.660266438
],
"F": [
7... |
2obj_3rel_1extra_gen0031 | medium | Diagram description: The diagram contains points A, B, C, D, E, F. There is an equilateral triangle ABC. There is a circle with center D. There is a line segment AD. There is a line segment BE. There is a line segment CF. Angle ADB is a right angle. Line AD is a radius of the circle. Line BE is an altitude of the trian... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F = scene.add.points(["A", "B", "C", "D", "E", "F"])
triangle1 = scene.add.equilateral_triangle(A, B, C)
circle1 = scene.add.circle(D)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_segment(B, E)
line_CF = scene.add.line_segm... | {
"triangle1": "equilateral_triangle(A, B, C)",
"circle1": "circle(D)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)"
} | [
"right_angle(A, D, B)",
"is_radius(line_AD, circle1)",
"is_altitude(line_BE, triangle1, B)"
] | [
"A",
"B",
"C",
"D",
"E",
"F"
] | [
"scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BE').length)",
"scene.constraint.leq(scene.get_object('line_CF').length, scene.get_object('circle1').diameter)"
] | {
"points": {
"A": [
2.691923156,
-2.8293262201
],
"B": [
3.7980238123000003,
-2.8384999198000003
],
"C": [
3.2529182378,
-1.8760018952
],
"D": [
3.5175260021,
-3.3151623733
],
"E": [
2.9724209231,
-2.3526639492
],
... |
2obj_3rel_1extra_gen0033 | medium | Diagram description: The diagram contains points A, B, C, D, E, F. There is a right trapezoid ABCD. There is a circle with center E. There is a line segment AD. There is a line segment DC. There is a line segment AC. There is a line segment DE. Line AD is perpendicular to line DC. Line DE is a radius of the circle. Lin... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F = scene.add.points(["A", "B", "C", "D", "E", "F"])
trapezoid1 = scene.add.right_trapezoid(A, B, C, D)
circle1 = scene.add.circle(E)
line_AD = scene.add.line_segment(A, D)
line_DC = scene.add.line_segment(D, C)
line_AC = scene.add.line_segme... | {
"trapezoid1": "right_trapezoid(A, B, C, D)",
"circle1": "circle(E)",
"line_AD": "line_segment(A, D)",
"line_DC": "line_segment(D, C)",
"line_AC": "line_segment(A, C)",
"line_DE": "line_segment(D, E)"
} | [
"line_extension_intersects_circle_at(line_AD, circle1, D, F)",
"is_radius(line_DE, circle1)",
"perpendicular(line_AD, line_DC)"
] | [
"A",
"B",
"C",
"D",
"E",
"F"
] | [
"scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_DC').length)"
] | {
"points": {
"A": [
2.6586649356,
0.5729539843
],
"B": [
0.9782591083000001,
0.246490797
],
"C": [
2.8182871629,
0.8095525079
],
"D": [
2.6201768334,
0.7710643558
],
"E": [
1.7621814161,
1.8581464665
],
"F": [
... |
2obj_3rel_1extra_gen0036 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is an isosceles trapezoid ABCD. There is a major arc FG with center E. There is a line segment AB. There is a line segment CD. There is a line segment AC. There is a line segment BD. There is a line segment EF. Line AC intersects line BD at ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H"])
trapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)
arc1 = scene.add.major_arc(E, F, G)
line_AB = scene.add.line_segment(A, B)
line_CD = scene.add.line_segment(C, D)
line... | {
"trapezoid1": "isosceles_trapezoid(A, B, C, D)",
"arc1": "major_arc(E, F, G)",
"line_AB": "line_segment(A, B)",
"line_CD": "line_segment(C, D)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EF": "line_segment(E, F)"
} | [
"lines_intersect_at(line_AC, line_BD, H)",
"mirror_across_line(trapezoid1, trapezoid1, line_EF)",
"point_lies_on(H, line_AC)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"scene.constraint.eq(scene.get_object('line_AB').length, scene.get_object('line_CD').length)"
] | {
"points": {
"A": [
-9.4704175579,
9.7191307328
],
"B": [
6.6987553793,
-4.7302293336
],
"C": [
6.5474066623,
-4.5974711273
],
"D": [
-9.6217561217,
9.851899819
],
"E": [
4.2998512438,
-2.58771824
],
"F": [
... |
2obj_3rel_1extra_gen0039 | medium | Diagram description: The diagram contains points A, B, C, O, D, E, F, G. There is a triangle ABC with vertices A, B, C. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD intersects line BE at point G. Line AD is an altitude of triangle ABC from ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O, D, E, F, G = scene.add.points(["A", "B", "C", "O", "D", "E", "F", "G"])
triangleABC = scene.add.triangle(A, B, C)
circleO = scene.add.circle(O)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_segment(B, E)
line_CF = scene.add.lin... | {
"triangleABC": "Triangle(A, B, C)",
"circleO": "Circle(O)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)"
} | [
"lines_intersect_at(line_AD, line_BE, G)",
"is_altitude(line_AD, triangleABC, A)",
"is_circumcircle(circleO, triangleABC)"
] | [
"A",
"B",
"C",
"O",
"D",
"E",
"F",
"G"
] | [
"scene.constraint.eq(scene.get_object('triangleABC').area, scene.get_object('circleO').area / 4)"
] | {
"points": {
"A": [
2.245347139,
0.8629813191
],
"B": [
-1.039971974,
-1.6614864147000001
],
"C": [
2.3509706212,
-7.4512803995
],
"O": [
2.8220376315999998,
-3.2874945012
],
"D": [
-1.3017721874000001,
-1.2144808711
... |
2obj_3rel_1extra_gen0040 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a right isosceles triangle with vertices B, C, D. There is a line segment BC. There is a line segment CD. There is a line segment BD. There is a line segment AD. There is a line segment AC. Line segment BC is rotated ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
triangle1 = scene.add.right_isosceles_triangle(B, C, D)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.add.line_segment(C, D)
line BD = scene.add.line_segment(B, D)
li... | {
"circle1": "circle(A)",
"triangle1": "right_isosceles_triangle(B, C, D)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line BD": "line_segment(B, D)",
"line_AD": "line_segment(A, D)",
"line_AC": "line_segment(A, C)"
} | [
"rotation_around_point(line_BC, line_CD, C, 90)",
"is_chord(line_BC, circle1)",
"is_radius(line_AC, circle1)"
] | [
"A",
"B",
"C",
"D"
] | [
"scene.constraint.eq(scene.get_object('line_BC').length, scene.get_object('line_CD').length)",
"scene.constraint.eq(scene.get_object('line_BC').length, 2 * scene.get_object('circle1').area / (3.14159 * 2))"
] | {
"points": {
"A": [
-1.4206359284,
-1.8922063161
],
"B": [
-0.6236852259,
-2.2156407348
],
"C": [
-0.6673103158,
-1.4771872961999999
],
"D": [
-1.4057637273,
-1.5208123683
]
},
"circles": {
"A": 0.8600815562
}
} |
2obj_3rel_1extra_gen0041 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a rhombus with vertices A, B, C, D. There is a major arc with center E, start point F, and end point G. There is a line segment AC. There is a line segment BD. There is a line segment EF. Line segment AC is parallel to line segment EF. Line ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G = scene.add.points(["A", "B", "C", "D", "E", "F", "G"])
rhombus1 = scene.add.rhombus(A, B, C, D)
semicircle1 = scene.add.major_arc(E, F, G)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_segment(B, D)
line_EF = scene.add... | {
"rhombus1": "rhombus(A, B, C, D)",
"semicircle1": "major_arc(E, F, G)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EF": "line_segment(E, F)"
} | [
"parallel(line_AC, line_EF)",
"perpendicular(line_BD, line_EF)",
"point_lies_on(F, semicircle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [] | {
"points": {
"A": [
0.2295455247,
-3.1601850453
],
"B": [
-2.4915705514,
-0.9417461508
],
"C": [
1.007401177,
-0.6534049578000001
],
"D": [
3.7285172465,
-2.871843853
],
"E": [
-1.2864949216000001,
-2.0065524398
],
... |
2obj_3rel_1extra_gen0055 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a rectangle with A, B, C, D. There is a right triangle with E, F, G. There is a line segment AC. There is a line segment EF. There is a line segment FG. There is a line segment EG. Points A, C, E are collinear. Line AC is perpendicular to li... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G = scene.add.points(["A", "B", "C", "D", "E", "F", "G"])
rectangle1 = scene.add.rectangle(A, B, C, D)
right_triangle1 = scene.add.right_triangle(E, F, G)
line_AC = scene.add.line_segment(A, C)
line_EF = scene.add.line_segment(E, F)
line_F... | {
"rectangle1": "rectangle(A, B, C, D)",
"right_triangle1": "right_triangle(E, F, G)",
"line_AC": "line_segment(A, C)",
"line_EF": "line_segment(E, F)",
"line_FG": "line_segment(F, G)",
"lineEG": "line_segment(E, G)"
} | [
"collinear(A, C, E)",
"perpendicular(line_AC, line_EF)",
"is_altitude(line_FG, right_triangle1, F)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [] | {
"points": {
"A": [
-6.3408461274,
-3.4351850959
],
"B": [
-0.7815613938,
-6.3658739175
],
"C": [
-0.6028117252,
-6.0268005412
],
"D": [
-6.1620967193,
-3.096111465
],
"E": [
-0.37503339080000003,
-6.1296777503
],
... |
2obj_3rel_1extra_gen0061 | medium | Diagram description: The diagram contains points A, B, C, O, D, E, F.
There is a triangle with vertices A, B, C.
There is a circle with center O.
There is a line segment AD.
There is a line segment BE.
There is a line segment CF.
Line AD is a median of triangle ABC.
The circle with center O is the circumcircle of trian... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O, D, E, F = scene.add.points(["A", "B", "C", "O", "D", "E", "F"])
triangleABC = scene.add.triangle(A, B, C)
circleO = scene.add.circle(O)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_segment(B, E)
line_CF = scene.add.line_segmen... | {
"triangleABC": "triangle(A, B, C)",
"circleO": "circle(O)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)"
} | [
"is_median(line_AD, triangleABC, A)",
"is_circumcircle(circleO, triangleABC)",
"perpendicular(line_AD, line_BE)"
] | [
"A",
"B",
"C",
"O",
"D",
"E",
"F"
] | [
"scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BE').length)",
"scene.constraint.eq(scene.get_object('triangleABC').area, 12.0)"
] | {
"points": {
"A": [
3.1794244416,
-0.9544728764
],
"B": [
-0.3467874366,
3.2577669251
],
"C": [
1.3356422007,
-5.5581516826
],
"O": [
-1.8730564084,
-1.6020030536
],
"D": [
0.49442739830000004,
-1.1501922169
],
"E... |
2obj_3rel_1extra_gen0063 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a major arc with center A, start point B, and end point C. There is a scalene triangle with vertices D, E, F. There is a line segment DE. There is a line segment EF. There is a line segment FD. There is a line segment FG. Point G lies on the... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G = scene.add.points(["A", "B", "C", "D", "E", "F", "G"])
semicircle1 = scene.add.major_arc(A, B, C)
triangle1 = scene.add.scalene_triangle(D, E, F)
line_DE = scene.add.line_segment(D, E)
line_EF = scene.add.line_segment(E, F)
line_FD = sc... | {
"semicircle1": "major_arc(A, B, C)",
"triangle1": "scalene_triangle(D, E, F)",
"line_DE": "line_segment(D, E)",
"line_EF": "line_segment(E, F)",
"line_FD": "line_segment(F, D)",
"line_perp": "line_segment(F, G)"
} | [
"point_lies_on(G, semicircle1)",
"perpendicular(line_perp, line_FD)",
"is_altitude(line_perp, triangle1, F)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [] | {
"points": {
"A": [
7.6428054032,
8.700965558
],
"B": [
9.3974956923,
-8.3219166124
],
"C": [
-9.4702449893,
8.669933243
],
"D": [
-9.8465461416,
8.8347624404
],
"E": [
8.521389282,
-9.7256758484
],
"F": [
7... |
2obj_3rel_1extra_gen0065 | medium | Diagram description: The diagram contains points A, B, C, D, E, F. There is a triangle ABC. There is a quadrilateral ABCD. There is a line segment AC. There is a line segment BD. E is the midpoint of line AC. Line AC is perpendicular to line BD. Line AC intersects line BD at point F. Further, the length of line AC is e... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F = scene.add.points(["A", "B", "C", "D", "E", "F"])
triangleABC = scene.add.triangle(A, B, C)
quadrilateralABCD = scene.add.quadrilateral(A, B, C, D)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_segment(B, D)
### relation... | {
"triangleABC": "triangle(A, B, C)",
"quadrilateralABCD": "quadrilateral(A, B, C, D)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)"
} | [
"is_midpoint(E, line_AC)",
"perpendicular(line_AC, line_BD)",
"lines_intersect_at(line_AC, line_BD, F)"
] | [
"A",
"B",
"C",
"D",
"E",
"F"
] | [
"scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)"
] | {
"points": {
"A": [
2.0033461468,
-4.6482728201
],
"B": [
1.4642335769,
-4.7280157607
],
"C": [
-0.0730247192,
-2.2462581729
],
"D": [
3.8662482208,
-2.6516448876
],
"E": [
0.9651607626,
-3.4472654817
],
"F": [
... |
2obj_3rel_1extra_gen0075 | medium | Diagram description: The diagram contains points A, B, C, D, E. There is a quadrilateral with vertices A, B, C, D. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment AB. There is a line segment CD. Points A, E, and C are collinear. The line segment AC is a d... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
quadrilateral1 = scene.add.quadrilateral(A, B, C, D)
circle1 = scene.add.circle(E)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_segment(B, D)
line_AB = scene.add.line_segment(A, ... | {
"quadrilateral1": "quadrilateral(A, B, C, D)",
"circle1": "circle(E)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_AB": "line_segment(A, B)",
"line_CD": "line_segment(C, D)"
} | [
"collinear(A, E, C)",
"is_diameter(line_AC, circle1)",
"perpendicular(line_AB, line_CD)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [
"scene.constraint.eq(scene.get_object('line_AB').length, scene.get_object('line_CD').length)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)"
] | {
"points": {
"A": [
-2.6298567850000003,
-1.3936997533
],
"B": [
0.4223762814,
2.7065481751
],
"C": [
-2.4752967251,
4.863581977
],
"D": [
1.6249511767,
1.8113489531
],
"E": [
-2.5525767572999998,
1.7349411143
]
},
... |
2obj_3rel_1extra_gen0080 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a right triangle BCD. There is a line segment BC. There is a line segment CD. There is a line segment BD. Line BC intersects the circle at points B and C. Line BC is a chord of the circle. Right angle at C between lin... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
triangle1 = scene.add.right_triangle(B, C, D)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.add.line_segment(C, D)
line_BD = scene.add.line_segment(B, D)
### relatio... | {
"circle1": "circle(A)",
"triangle1": "right_triangle(B, C, D)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_BD": "line_segment(B, D)"
} | [
"line_intersects_circle_at(line_BC, circle1, B, C)",
"is_chord(line_BC, circle1)",
"right_angle(D, C, B)"
] | [
"A",
"B",
"C",
"D"
] | [
"scene.constraint.eq(scene.get_object('triangle1').area, scene.get_object('circle1').area / 4)"
] | {
"points": {
"A": [
2.9052768854,
-1.9956817924
],
"B": [
2.495744713,
-2.6117476644
],
"C": [
2.257386174,
-2.3527411583
],
"D": [
0.4603743038,
-4.0064954254
]
},
"circles": {
"A": 0.7397660198
}
} |
2obj_3rel_1extra_gen0082 | medium | Diagram description: The diagram contains points A, B, C, D, E. There is a rectangle with points A, B, C, D. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment AB. There is a line segment BC. Line AC intersects the circle at points A and C. Line AC is a diam... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
rectangle1 = scene.add.rectangle(A, B, C, D)
circle1 = scene.add.circle(E)
line_AC = scene.add.line_segment(A, C)
line BD = scene.add.line_segment(B, D)
line_AB = scene.add.line_segment(A, B)
line_... | {
"rectangle1": "rectangle(A, B, C, D)",
"circle1": "circle(E)",
"line_AC": "line_segment(A, C)",
"line BD": "line_segment(B, D)",
"line_AB": "line_segment(A, B)",
"line_BC": "line_segment(B, C)"
} | [
"line_intersects_circle_at(line_AC, circle1, A, C)",
"is_diameter(line_AC, circle1)",
"perpendicular(line_AB, line_BC)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [
"scene.constraint.eq(scene.get_object('rectangle1').area, scene.get_object('circle1').area)"
] | {
"points": {
"A": [
-3.5626201266,
0.4894087244
],
"B": [
-3.8277828202,
0.41171634760000003
],
"C": [
-3.7361094385999998,
0.1510600773
],
"D": [
-3.477589746,
0.2321580242
],
"E": [
-3.6513860608,
0.321270763
]
},... |
2obj_3rel_1extra_gen0086 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is an equilateral triangle with vertices B, C, D. There is a line segment BC. There is a line segment CD. There is a line segment DB. There is a line segment AD. There is a line segment AC. There is a line segment AB. Th... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
triangle1 = scene.add.equilateral_triangle(B, C, D)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.add.line_segment(C, D)
line_DB = scene.add.line_segment(D, B)
line_A... | {
"circle1": "circle(A)",
"triangle1": "equilateral_triangle(B, C, D)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_DB": "line_segment(D, B)",
"line_AD": "line_segment(A, D)",
"line_AC": "line_segment(A, C)",
"line_AB": "line_segment(A, B)"
} | [
"is_circumcircle(circle1, triangle1)",
"is_radius(line_AB, circle1)",
"point_lies_on(B, circle1)"
] | [
"A",
"B",
"C",
"D"
] | [] | {
"points": {
"A": [
-1.1331025232,
-0.9896005392
],
"B": [
-0.8505928367000001,
0.38355169720000004
],
"C": [
-0.0851726386,
-1.9208371874
],
"D": [
-2.4635420613,
-1.4315160287
]
},
"circles": {
"A": 1.4019125474
}
} |
2obj_3rel_1extra_gen0096 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a right triangle BCD. There is a line segment BC. There is a line segment CD. There is a line segment BD. There is a line segment AD. Line BC is perpendicular to line CD. Line BD is a chord of the circle. Point D lies... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
triangle1 = scene.add.right_triangle(B, C, D)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.add.line_segment(C, D)
line_BD = scene.add.line_segment(B, D)
line_AD = sc... | {
"circle1": "circle(A)",
"triangle1": "right_triangle(B, C, D)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_BD": "line_segment(B, D)",
"line_AD": "line_segment(A, D)"
} | [
"perpendicular(line_BC, line_CD)",
"is_chord(line_BD, circle1)",
"point_lies_on(D, circle1)"
] | [
"A",
"B",
"C",
"D"
] | [
"scene.constraint.eq(scene.get_object('triangle1').inradius, 1.0)",
"scene.constraint.leq(scene.get_object('line_BD').length, 6.0)"
] | {
"points": {
"A": [
9.1187686791,
-0.2117659241
],
"B": [
0.6667395205000001,
-2.0910014522
],
"C": [
3.227708695,
0.1290021955
],
"D": [
0.9747010149,
2.728044434
]
},
"circles": {
"A": 8.658424976100001
}
} |
2obj_3rel_1extra_gen0100 | medium | Diagram description: The diagram contains points A, B, C, D, H, M, N. There is a triangle ABC. There is a major arc ADB. There is a line segment AH. There is a line segment MN. H is the orthocenter of triangle ABC. line segment AH is perpendicular to line segment MN. point H lies on line segment MN. | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, H, M, N = scene.add.points(["A", "B", "C", "D", "H", "M", "N"])
triangle_ABC = scene.add.triangle(A, B, C)
semicircle_ADB = scene.add.major_arc(A, D, B)
line_altitude = scene.add.line_segment(A, H)
line_perp_bisector = scene.add.line_segment(M, ... | {
"triangle_ABC": "triangle(A, B, C)",
"semicircle_ADB": "major_arc(A, D, B)",
"line_altitude": "line_segment(A, H)",
"line_perp_bisector": "line_segment(M, N)"
} | [
"is_orthocenter(H, triangle_ABC)",
"perpendicular(line_altitude, line_perp_bisector)",
"point_lies_on(H, line_perp_bisector)"
] | [
"A",
"B",
"C",
"D",
"H",
"M",
"N"
] | [] | {
"points": {
"A": [
0.8024069259000001,
-1.1006515635
],
"B": [
1.0025055073,
2.5092542614999997
],
"C": [
-0.9254212817,
0.16950071830000002
],
"D": [
-0.9334149167,
2.0708436708
],
"H": [
-0.7256235234,
0.1584258135
... |
2obj_3rel_1extra_gen0107 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is an isosceles trapezoid ABCD. There is a minor arc FG with center E. There is a line segment AB. There is a line segment CD. There is a line segment EF. There is a line segment EG. There is an obtuse angle at D formed by points A, D, and C. T... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G = scene.add.points(["A", "B", "C", "D", "E", "F", "G"])
trapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)
arc1 = scene.add.minor_arc(E, F, G)
line_AB = scene.add.line_segment(A, B)
line_CD = scene.add.line_segment(C, D)
line EF = sc... | {
"trapezoid1": "isosceles_trapezoid(A, B, C, D)",
"arc1": "minor_arc(E, F, G)",
"line_AB": "line_segment(A, B)",
"line_CD": "line_segment(C, D)",
"line EF": "line_segment(E, F)",
"line EG": "line_segment(E, G)"
} | [
"obtuse_angle(A, D, C)",
"mirror_across_line(trapezoid1, trapezoid1, line_AB)",
"point_lies_on(F, arc1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [
"scene.constraint.eq(scene.get_object('line_AB').length, scene.get_object('line_CD').length)",
"scene.constraint.leq(scene.get_object('trapezoid1').area, 20)"
] | {
"points": {
"A": [
9.3281191154,
-2.8210619344000003
],
"B": [
-9.3728434293,
8.3935478158
],
"C": [
-9.9281068166,
8.7243991231
],
"D": [
8.7728565816,
-2.4902116974
],
"E": [
0.4536042462,
2.8505895179
],
"F": ... |
2obj_3rel_1extra_gen0125 | medium | Diagram description: The diagram contains points A, B, C, D, E. There is a rhomboid with vertices A, B, C, D. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment AB. There is a line segment BC. Points A, E, and C are collinear. Line segment AC is a diameter o... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
rhomboid1 = scene.add.rhomboid(A, B, C, D)
circle1 = scene.add.circle(E)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_segment(B, D)
line_AB = scene.add.line_segment(A, B)
line_BC... | {
"rhomboid1": "rhomboid(A, B, C, D)",
"circle1": "circle(E)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_AB": "line_segment(A, B)",
"line_BC": "line_segment(B, C)"
} | [
"collinear(A, E, C)",
"is_diameter(line_AC, circle1)",
"perpendicular(line_AC, line_BD)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [] | {
"points": {
"A": [
3.2443171093,
-2.1007472442
],
"B": [
3.2300771508,
-1.6682070392
],
"C": [
2.8834695486,
-1.9274038016000001
],
"D": [
2.8977438229,
-2.3599182459
],
"E": [
3.0638928135,
-2.0140681877
]
},
"c... |
2obj_3rel_1extra_gen0129 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, M, N. There is an isosceles triangle ABC. There is a minor arc with center D and endpoints E and F. There is a line segment AM. There is a line segment BC. N is the orthocenter of triangle ABC. line AM is an altitude of triangle ABC from vertex A. M lie... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, M, N = scene.add.points(["A", "B", "C", "D", "E", "F", "M", "N"])
triangleABC = scene.add.isosceles_triangle(A, B, C)
arcDEF = scene.add.minor_arc(D, E, F)
line_AM = scene.add.line_segment(A, M)
line_BC = scene.add.line_segment(B, C)
### ... | {
"triangleABC": "isosceles_triangle(A, B, C)",
"arcDEF": "minor_arc(D, E, F)",
"line_AM": "line_segment(A, M)",
"line_BC": "line_segment(B, C)"
} | [
"is_orthocenter(N, triangleABC)",
"is_altitude(line_AM, triangleABC, A)",
"point_lies_on(M, line_BC)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"M",
"N"
] | [
"scene.constraint.eq(scene.get_object('triangleABC').inradius, scene.get_object('arcDEF').radius)"
] | {
"points": {
"A": [
-1.8205594228000002,
-0.34314676990000004
],
"B": [
1.1880729985,
-1.1231737836
],
"C": [
-0.6065623143000001,
-3.6608095658
],
"D": [
2.2220557665,
-2.3258101057
],
"E": [
1.3323229682,
-2.0665805274
... |
2obj_3rel_1extra_gen0133 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a trapezoid ABCD. There is a minor arc FG with center E. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment EG. Points A, E, and G are collinear. Point F lies on the minor arc FG. Line... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G = scene.add.points(["A", "B", "C", "D", "E", "F", "G"])
trapezoid1 = scene.add.trapezoid(A, B, C, D)
minor_arc1 = scene.add.minor_arc(E, F, G)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_segment(B, D)
line EF = scene.... | {
"trapezoid1": "trapezoid(A, B, C, D)",
"minor_arc1": "minor_arc(E, F, G)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line EF": "line_segment(E, F)",
"line EG": "line_segment(E, G)"
} | [
"collinear(A, E, G)",
"perpendicular(line_AC, line_BD)",
"point_lies_on(F, minor_arc1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [
"scene.constraint.eq(scene.get_object('trapezoid1').area, scene.get_object('minor_arc1').area)",
"scene.constraint.eq(scene.angle(scene.get_object('F'), scene.get_object('E'), scene.get_object('G')), 60)"
] | {
"points": {
"A": [
-0.7500963155,
3.3024813783
],
"B": [
-2.0228890782,
-1.5716774332
],
"C": [
-3.1794420184,
-0.22986912920000002
],
"D": [
-3.3004004239,
-0.6930792572000001
],
"E": [
-1.4372496366,
-0.2071140571
... |
2obj_3rel_1extra_gen0145 | medium | Diagram description: The diagram contains points A, B, C, D, E. There is a circle with center E. There is a quadrilateral ABCD. There is a line segment AC. There is a line segment BD. There is a line segment AB. Line AC is a chord of the circle. Line AC is perpendicular to line BD. Line AB is a diameter of the circle. ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
quadrilateral1 = scene.add.quadrilateral(A, B, C, D)
circle1 = scene.add.circle(E)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_segment(B, D)
line_AB = scene.add.line_segment(A, ... | {
"quadrilateral1": "quadrilateral(A, B, C, D)",
"circle1": "circle(E)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_AB": "line_segment(A, B)"
} | [
"is_chord(line_AC, circle1)",
"perpendicular(line_AC, line_BD)",
"is_diameter(line_AB, circle1)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [
"scene.constraint.eq(scene.get_object('quadrilateral1').area, scene.get_object('circle1').area)"
] | {
"points": {
"A": [
1.8565625218,
0.2743022304
],
"B": [
0.45347360280000004,
0.8399289088
],
"C": [
0.4059010033,
0.4523691328
],
"D": [
0.7531444358,
3.2812637628
],
"E": [
1.1550180254,
0.5571155487
]
},
"circl... |
2obj_3rel_1extra_gen0146 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a major arc BC. There are line segments BD, CD, and AD. Line BD is a chord of the circle. Angle BDC is a right angle. The circle is congruent to the circle. | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
major_arc1 = scene.add.major_arc(A, B, C)
line_BD = scene.add.line_segment(B, D)
line_CD = scene.add.line_segment(C, D)
line_AD = scene.add.line_segment(A, D)
### relationshi... | {
"circle1": "circle(A)",
"major_arc1": "major_arc(A, B, C)",
"line_BD": "line_segment(B, D)",
"line_CD": "line_segment(C, D)",
"line_AD": "line_segment(A, D)"
} | [
"congruent(circle1, circle1)",
"is_chord(line_BD, circle1)",
"right_angle(B, D, C)"
] | [
"A",
"B",
"C",
"D"
] | [] | {
"points": {
"A": [
0.078879154,
-2.0770927546
],
"B": [
-1.7684913014,
-2.3527898749
],
"C": [
1.9262496100000002,
-1.8013956062
],
"D": [
1.2595198078,
-3.5244607551
]
},
"circles": {
"A": 1.8678293517000002
}
} |
2obj_3rel_1extra_gen0147 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a minor arc BC on that circle. There are line segments BC, AD, and CD. The circle is congruent to itself. Line BC is a chord of the circle. Line AD is perpendicular to line CD. Further, the length of line BC is equal ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
minor_arc1 = scene.add.minor_arc(A, B, C)
line_BC = scene.add.line_segment(B, C)
line_AD = scene.add.line_segment(A, D)
line_CD = scene.add.line_segment(C, D)
### relationshi... | {
"circle1": "circle(A)",
"minor_arc1": "minor_arc(A, B, C)",
"line_BC": "line_segment(B, C)",
"line_AD": "line_segment(A, D)",
"line_CD": "line_segment(C, D)"
} | [
"congruent(circle1, circle1)",
"is_chord(line_BC, circle1)",
"perpendicular(line_AD, line_CD)"
] | [
"A",
"B",
"C",
"D"
] | [
"scene.constraint.eq(scene.get_object('line_BC').length, scene.get_object('line_AD').length)",
"scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('D')), 90)"
] | {
"points": {
"A": [
-2.8687514989,
-1.0257283892
],
"B": [
2.8415239642000003,
1.4836837856
],
"C": [
2.7351414394,
1.7130271396999999
],
"D": [
-2.9704642015,
-0.7942767517
]
},
"circles": {
"A": 6.2373386399
}
} |
2obj_3rel_1extra_gen0159 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a circle with center A. There is a circle with center B. There is a line segment CD. There is a line segment AB. There is a line segment EF. Line segment CD intersects line segment AB at point G. Line segment CD is a chord of the circle with... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G = scene.add.points(["A", "B", "C", "D", "E", "F", "G"])
circle1 = scene.add.circle(A)
circle2 = scene.add.circle(B)
line_CD = scene.add.line_segment(C, D)
line_AB = scene.add.line_segment(A, B)
line EF = scene.add.line_segment(E, F)
###... | {
"circle1": "circle(A)",
"circle2": "circle(B)",
"line_CD": "line_segment(C, D)",
"line_AB": "line_segment(A, B)",
"line EF": "line_segment(E, F)"
} | [
"lines_intersect_at(line_CD, line_AB, G)",
"is_chord(line_CD, circle1)",
"tangent_to_circle(line EF, circle2, F)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [
"scene.constraint.eq(scene.get_object('circle1').area, scene.get_object('circle2').area)"
] | {
"points": {
"A": [
-0.3199577335,
1.332225134
],
"B": [
1.7985067268,
-1.3234025783
],
"C": [
-0.3060577906,
0.9915591444
],
"D": [
0.0202728653,
1.3543538988
],
"E": [
-1.2798732183000001,
0.07401011090000001
],
... |
2obj_3rel_1extra_gen0160 | medium | Diagram description: The diagram contains points A, B, C, D, E. There is a trapezoid ABCD. There is a circle with center E. There is a line segment AB. There is a line segment CD. There is a line segment AC. There is a line segment AD. Line AC intersects the circle at points A and C. Line AB is perpendicular to line AD... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
trapezoid1 = scene.add.trapezoid(A, B, C, D)
circle1 = scene.add.circle(E)
line_AB = scene.add.line_segment(A, B)
line_CD = scene.add.line_segment(C, D)
line_AC = scene.add.line_segment(A, C)
line_... | {
"trapezoid1": "trapezoid(A, B, C, D)",
"circle1": "circle(E)",
"line_AB": "line_segment(A, B)",
"line_CD": "line_segment(C, D)",
"line_AC": "line_segment(A, C)",
"line_AD": "line_segment(A, D)"
} | [
"line_intersects_circle_at(line_AC, circle1, A, C)",
"perpendicular(line_AB, line_AD)",
"is_diameter(line_AC, circle1)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [
"scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_AB').length)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)"
] | {
"points": {
"A": [
-0.3286992795,
0.2599884111
],
"B": [
-4.4260995109,
1.115054346
],
"C": [
-3.5710335777999997,
5.2124545639
],
"D": [
0.5263666411,
4.3573886076
],
"E": [
-1.9498664520000002,
2.7362214805000002
]... |
2obj_3rel_1extra_gen0165 | medium | Diagram description: The diagram contains points A, B, C, D, E. There is a rectangle with points A, B, C, D. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment AB. There is a line segment BC. Points A, E, and C are collinear. Line segment AC is a diameter of... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
rectangle1 = scene.add.rectangle(A, B, C, D)
circle1 = scene.add.circle(E)
line_AC = scene.add.line_segment(A, C)
line BD = scene.add.line_segment(B, D)
line_AB = scene.add.line_segment(A, B)
line_... | {
"rectangle1": "rectangle(A, B, C, D)",
"circle1": "circle(E)",
"line_AC": "line_segment(A, C)",
"line BD": "line_segment(B, D)",
"line_AB": "line_segment(A, B)",
"line_BC": "line_segment(B, C)"
} | [
"collinear(A, E, C)",
"is_diameter(line_AC, circle1)",
"perpendicular(line_AB, line_BC)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [
"scene.constraint.eq(scene.get_object('circle1').diameter, scene.get_object('line_BC').length)"
] | {
"points": {
"A": [
-4.5254097784,
-9.4208446293
],
"B": [
-4.6638554837,
-9.2748452312
],
"C": [
8.7268147849,
3.4228976269
],
"D": [
8.8652598737,
3.2768975212
],
"E": [
2.100702627,
-2.9989734754
]
},
"circles"... |
2obj_3rel_1extra_gen0172 | medium | Diagram description: The diagram contains points A, B, C, D, E, G. There is a right triangle ABC with vertices A, B, C. There is a minor arc with center D, starting at E and ending at G. There is a line segment AB. There is a line segment BC. There is a line segment AC. There is a line segment DG. Line AB is parallel t... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, G = scene.add.points(["A", "B", "C", "D", "E", "G"])
triangleABC = scene.add.right_triangle(A, B, C)
arcDEG = scene.add.minor_arc(D, E, G)
lineAB = scene.add.line_segment(A, B)
lineBC = scene.add.line_segment(B, C)
lineAC = scene.add.line_seg... | {
"triangleABC": "right_triangle(A, B, C)",
"arcDEG": "minor_arc(D, E, G)",
"lineAB": "line_segment(A, B)",
"lineBC": "line_segment(B, C)",
"lineAC": "line_segment(A, C)",
"lineDG": "line_segment(D, G)"
} | [
"parallel(lineAB, lineDG)",
"is_altitude(lineBC, triangleABC, B)",
"point_lies_on(E, arcDEG)"
] | [
"A",
"B",
"C",
"D",
"E",
"G"
] | [
"scene.constraint.eq(scene.get_object('lineAB').length, scene.get_object('lineDG').length)",
"scene.constraint.leq(scene.get_object('arcDEG').central_angle, 90)"
] | {
"points": {
"A": [
-7.5627272844,
9.1663954926
],
"B": [
7.9548730532,
-3.3881150132
],
"C": [
8.0812944848,
-3.2318480947
],
"D": [
9.5537916639,
-7.0709734353
],
"E": [
-8.9134017821,
0.5036189076
],
"G": [
... |
2obj_3rel_1extra_gen0174 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a major arc BC. There is a line segment BC. There is a line segment AD. The angle DAC is obtuse. Line BC is a chord of the circle. Point D lies on the circle. Further, the central angle of the major arc equals twice t... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
major_arc1 = scene.add.major_arc(A, B, C)
line_BC = scene.add.line_segment(B, C)
line_AD = scene.add.line_segment(A, D)
### relationships
scene.relate.obtuse_angle(D, A, C)
... | {
"circle1": "circle(A)",
"major_arc1": "major_arc(A, B, C)",
"line_BC": "line_segment(B, C)",
"line_AD": "line_segment(A, D)"
} | [
"obtuse_angle(D, A, C)",
"is_chord(line_BC, circle1)",
"point_lies_on(D, circle1)"
] | [
"A",
"B",
"C",
"D"
] | [
"scene.constraint.eq(scene.get_object('major_arc1').central_angle, 2 * scene.get_object('major_arc1').inscribed_angle)"
] | {
"points": {
"A": [
2.7886142477,
2.2207901379
],
"B": [
2.5004376199,
3.4385976438
],
"C": [
4.0043666753,
2.517517149
],
"D": [
2.3077924615,
3.3761737489
]
},
"circles": {
"A": 1.2514395233
}
} |
2obj_3rel_1extra_gen0176 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is an isosceles triangle BCD. There is a line segment BC. There is a line segment CD. There is a line segment BD. Point B lies on the circle. Point C lies on the circle. Line BC is a chord of the circle. Further, the are... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
triangle1 = scene.add.isosceles_triangle(B, C, D)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.add.line_segment(C, D)
line_BD = scene.add.line_segment(B, D)
### rel... | {
"circle1": "circle(A)",
"triangle1": "isosceles_triangle(B, C, D)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_BD": "line_segment(B, D)"
} | [
"point_lies_on(B, circle1)",
"point_lies_on(C, circle1)",
"is_chord(line_BC, circle1)"
] | [
"A",
"B",
"C",
"D"
] | [
"scene.constraint.eq(scene.get_object('triangle1').area, scene.get_object('circle1').area / 4)"
] | {
"points": {
"A": [
0.3563510003,
-2.9608178378
],
"B": [
0.7228540182000001,
-1.2823734211
],
"C": [
-1.2502836419,
-2.3523564488
],
"D": [
-1.4626281292,
-0.11784403710000001
]
},
"circles": {
"A": 1.7179930527
}
} |
2obj_3rel_1extra_gen0177 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a rectangle with points A, B, C, D. There is a minor arc with center E, start point F, and end point G. There is a line segment AB. There is a line segment BC. There is a line segment CD. There is a line segment DA. There is a line segment E... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G = scene.add.points(["A", "B", "C", "D", "E", "F", "G"])
rectangle1 = scene.add.rectangle(A, B, C, D)
arc1 = scene.add.minor_arc(E, F, G)
line_AB = scene.add.line_segment(A, B)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.add.li... | {
"rectangle1": "rectangle(A, B, C, D)",
"arc1": "minor_arc(E, F, G)",
"line_AB": "line_segment(A, B)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_DA": "line_segment(D, A)",
"line_EF": "line_segment(E, F)",
"line_EG": "line_segment(E, G)"
} | [
"parallel(line_AB, line_CD)",
"perpendicular(line_AB, line_BC)",
"point_lies_on(F, arc1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [
"scene.constraint.eq(scene.get_object('line_EF').length, scene.get_object('line_AB').length)",
"scene.constraint.eq(scene.angle(scene.get_object('E'), scene.get_object('F'), scene.get_object('G')), 60)"
] | {
"points": {
"A": [
0.5422684601000001,
-5.310222587
],
"B": [
-0.7394702214000001,
1.3324002928
],
"C": [
2.6969506597,
1.9954807719
],
"D": [
3.9786893385,
-4.6471421039
],
"E": [
-0.653797639,
-2.7633888501
],
... |
2obj_3rel_1extra_gen0179 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is an equilateral triangle with vertices B, C, D. There are line segments BC, CD, DB, AD, AC, AB. The circle with center A is the circumcircle of triangle BCD. Line AB is a radius of the circle with center A. Line AC is ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
triangle1 = scene.add.equilateral_triangle(B, C, D)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.add.line_segment(C, D)
line_DB = scene.add.line_segment(D, B)
line_A... | {
"circle1": "circle(A)",
"triangle1": "equilateral_triangle(B, C, D)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_DB": "line_segment(D, B)",
"line_AD": "line_segment(A, D)",
"line_AC": "line_segment(A, C)",
"line_AB": "line_segment(A, B)"
} | [
"is_circumcircle(circle1, triangle1)",
"is_radius(line_AB, circle1)",
"is_radius(line_AC, circle1)"
] | [
"A",
"B",
"C",
"D"
] | [] | {
"points": {
"A": [
-1.2544281272,
-0.7957544587000001
],
"B": [
-1.727439184,
-0.682965869
],
"C": [
-0.9202448080000001,
-0.4425091868
],
"D": [
-1.1156003802,
-1.2617883577
]
},
"circles": {
"A": 0.4862722608
}
} |
2obj_3rel_1extra_gen0182 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a scalene triangle BCD. There are line segments BC, CD, DB, AD, AC, AB. Point A is the centroid of triangle BCD. The circle is the circumcircle of triangle BCD. Line AB is a radius of the circle. Further, the area of ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
triangle1 = scene.add.scalene_triangle(B, C, D)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.add.line_segment(C, D)
line_DB = scene.add.line_segment(D, B)
line_AD = ... | {
"circle1": "circle(A)",
"triangle1": "scalene_triangle(B, C, D)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_DB": "line_segment(D, B)",
"line_AD": "line_segment(A, D)",
"line_AC": "line_segment(A, C)",
"line_AB": "line_segment(A, B)"
} | [
"is_centroid(A, triangle1)",
"is_circumcircle(circle1, triangle1)",
"is_radius(line_AB, circle1)"
] | [
"A",
"B",
"C",
"D"
] | [
"scene.constraint.eq(scene.get_object('triangle1').area, scene.get_object('circle1').area / 4)"
] | {
"points": {
"A": [
0.4909462412,
-2.7802351963
],
"B": [
0.5309000716,
-2.5899772058
],
"C": [
0.3072122493,
-2.8407331779
],
"D": [
0.6343919364,
-2.9101980814
]
},
"circles": {
"A": 0.1987022755
}
} |
2obj_3rel_1extra_gen0198 | medium | Diagram description: The diagram contains points A, B, C, D. There is a semicircle with center A, start point B, and end point C. There is a circle with center D. There is a line segment AB. There is a line segment AC. There is a line segment BC. There is a line segment AD. There is a line segment BD. Point A lies on t... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
semicircle1 = scene.add.major_arc(A, B, C)
circle1 = scene.add.circle(D)
line_AB = scene.add.line_segment(A, B)
line_AC = scene.add.line_segment(A, C)
line_BC = scene.add.line_segment(B, C)
line_AD = scene... | {
"semicircle1": "major_arc(A, B, C)",
"circle1": "circle(D)",
"line_AB": "line_segment(A, B)",
"line_AC": "line_segment(A, C)",
"line_BC": "line_segment(B, C)",
"line_AD": "line_segment(A, D)",
"line_BD": "line_segment(B, D)"
} | [
"point_lies_on(A, circle1)",
"point_lies_on(B, circle1)",
"is_diameter(line_AB, circle1)"
] | [
"A",
"B",
"C",
"D"
] | [
"scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BD').length)"
] | {
"points": {
"A": [
0.10300697760000001,
-0.7122115696
],
"B": [
-0.895637007,
-1.4479136369
],
"C": [
-0.7625641214000001,
-1.6006562865
],
"D": [
-0.3963150163,
-1.0800626062
]
},
"circles": {
"D": 0.6201909622
}
} |
2obj_3rel_1extra_gen0202 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a rectangle with corners A, B, C, D. There is a minor arc with center E, start point F, and end point G. There is a line segment AB. There is a line segment BC. There is a line segment CD. There is a line segment DA. There is a line segment ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G = scene.add.points(["A", "B", "C", "D", "E", "F", "G"])
rectangle1 = scene.add.rectangle(A, B, C, D)
minor_arc1 = scene.add.minor_arc(E, F, G)
line_AB = scene.add.line_segment(A, B)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.... | {
"rectangle1": "rectangle(A, B, C, D)",
"minor_arc1": "minor_arc(E, F, G)",
"line_AB": "line_segment(A, B)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_DA": "line_segment(D, A)",
"line_EF": "line_segment(E, F)",
"line_EG": "line_segment(E, G)"
} | [
"rotation_around_point(line_AB, line_BC, B, 90)",
"perpendicular(line_AB, line_BC)",
"point_lies_on(F, minor_arc1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [
"scene.constraint.eq(scene.get_object('minor_arc1').central_angle, 90)",
"scene.constraint.leq(scene.get_object('line_AB').length, scene.get_object('line_BC').length)"
] | {
"points": {
"A": [
2.1382395146,
3.7599598181
],
"B": [
1.8186946220000002,
3.1664805624
],
"C": [
2.4121739601,
2.8469356886
],
"D": [
2.7317187542,
3.4404149856
],
"E": [
-1.5552294468999999,
-0.6099314999000001
],... |
2obj_3rel_1extra_gen0221 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a major arc with center A and endpoints B and C. There is a semicircle with center D and endpoints E and F. There is a line segment BE. There is a line segment CF. There is a line segment AD. Line segment BE intersects line segment CF at G. ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G = scene.add.points(["A", "B", "C", "D", "E", "F", "G"])
major_arc1 = scene.add.major_arc(A, B, C)
semicircle1 = scene.add.semicircle(D, E, F)
line_BE = scene.add.line_segment(B, E)
line_CF = scene.add.line_segment(C, F)
line_AD = scene.a... | {
"major_arc1": "major_arc(A, B, C)",
"semicircle1": "semicircle(D, E, F)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)",
"line_AD": "line_segment(A, D)"
} | [
"lines_intersect_at(line_BE, line_CF, G)",
"point_lies_on(G, major_arc1)",
"perpendicular(line_AD, line_BE)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [] | {
"points": {
"A": [
0.743848618,
2.3349107443
],
"B": [
0.8705829962,
1.6610366431
],
"C": [
0.4626316972,
1.7095422391000001
],
"D": [
0.7837426165,
1.2447352767
],
"E": [
-1.757351096,
1.5648698416
],
"F": [
... |
2obj_3rel_1extra_gen0224 | medium | Diagram description: The diagram contains points A, B, C, O, D, E, F. There is a triangle with vertices A, B, C. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD is a median of triangle ABC from vertex A. The circle with center O is the circumc... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O, D, E, F = scene.add.points(["A", "B", "C", "O", "D", "E", "F"])
triangle_ABC = scene.add.triangle(A, B, C)
circle_O = scene.add.circle(O)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_segment(B, E)
line_CF = scene.add.line_segm... | {
"triangle_ABC": "triangle(A, B, C)",
"circle_O": "circle(O)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)"
} | [
"is_median(line_AD, triangle_ABC, A)",
"is_circumcircle(circle_O, triangle_ABC)",
"perpendicular(line_AD, line_BE)"
] | [
"A",
"B",
"C",
"O",
"D",
"E",
"F"
] | [] | {
"points": {
"A": [
6.8088525230000005,
8.8145794019
],
"B": [
-6.0799088923,
2.6261188111
],
"C": [
0.37119867570000004,
-6.3970328499
],
"O": [
2.260522828,
1.7714276814
],
"D": [
-2.8543555387,
-1.8854568946999999
... |
2obj_3rel_1extra_gen0225 | medium | Diagram description: The diagram contains points A, B, C, D, E, F. There is a equilateral triangle with vertices A, B, C. There is a right triangle with vertices D, E, F. There is a line segment AC. There is a line segment DF. There is a line segment BE. The line AC is parallel to line DF. The line BE is perpendicular ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F = scene.add.points(["A", "B", "C", "D", "E", "F"])
triangle1 = scene.add.equilateral_triangle(A, B, C)
triangle2 = scene.add.right_triangle(D, E, F)
line_AC = scene.add.line_segment(A, C)
line_DF = scene.add.line_segment(D, F)
line_BE = sce... | {
"triangle1": "equilateral_triangle(A, B, C)",
"triangle2": "right_triangle(D, E, F)",
"line_AC": "line_segment(A, C)",
"line_DF": "line_segment(D, F)",
"line_BE": "line_segment(B, E)"
} | [
"parallel(line_AC, line_DF)",
"perpendicular(line_BE, line_AC)",
"is_altitude(line_BE, triangle1, B)"
] | [
"A",
"B",
"C",
"D",
"E",
"F"
] | [] | {
"points": {
"A": [
-0.2989274905,
4.9082142622
],
"B": [
4.7218528472,
4.6109833206
],
"C": [
1.9540531227,
0.4114755694
],
"D": [
1.5073409711,
3.9354969549
],
"E": [
0.8275628386,
2.6598448416
],
"F": [
2... |
2obj_3rel_1extra_gen0231 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is an isosceles trapezoid ABCD. There is a major arc FG with center E. There is a line segment AD. There is a line segment BC. There is a line segment EF. There is a line segment EG. Point F lies on the major arc FG. Point G lies on the major a... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G = scene.add.points(["A", "B", "C", "D", "E", "F", "G"])
trapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)
arc1 = scene.add.major_arc(E, F, G)
line_AD = scene.add.line_segment(A, D)
line_BC = scene.add.line_segment(B, C)
line_EF = sc... | {
"trapezoid1": "isosceles_trapezoid(A, B, C, D)",
"arc1": "major_arc(E, F, G)",
"line_AD": "line_segment(A, D)",
"line_BC": "line_segment(B, C)",
"line_EF": "line_segment(E, F)",
"line_EG": "line_segment(E, G)"
} | [
"point_lies_on(F, arc1)",
"point_lies_on(G, arc1)",
"mirror_across_line(trapezoid1, trapezoid1, line_EF)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [] | {
"points": {
"A": [
-9.7230016993,
-9.1706144183
],
"B": [
4.4611837504,
9.6335385013
],
"C": [
4.581724622,
9.7961196726
],
"D": [
-9.846219287,
-9.3311873777
],
"E": [
-8.778803655699999,
-7.9174865738
],
"F": [... |
2obj_3rel_1extra_gen0233 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a major arc with center A and endpoints B and C. There is a parallelogram with vertices D, E, F, G. There is a line segment DH. There is a line segment GI. There is a line segment EF. The angle BAC is a right angle. Line DH is perpendi... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I"])
major_arc1 = scene.add.major_arc(A, B, C)
parallelogram1 = scene.add.parallelogram(D, E, F, G)
line_DH = scene.add.line_segment(D, H)
line_GI = scene.add.line_segmen... | {
"major_arc1": "major_arc(A, B, C)",
"parallelogram1": "parallelogram(D, E, F, G)",
"line_DH": "line_segment(D, H)",
"line_GI": "line_segment(G, I)",
"line_EF": "line_segment(E, F)"
} | [
"right_angle(B, A, C)",
"perpendicular(line_DH, line_EF)",
"point_lies_on(H, major_arc1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [
"scene.constraint.eq(scene.get_object('major_arc1').central_angle, 2 * scene.get_object('major_arc1').inscribed_angle)",
"scene.constraint.leq(scene.get_object('line_DH').length, scene.get_object('major_arc1').radius)"
] | {
"points": {
"A": [
1.3882454062,
2.0131632522
],
"B": [
0.6635299401,
2.1346484362
],
"C": [
1.2667602116,
1.2884477578
],
"D": [
1.3705773095,
2.6618504021
],
"E": [
3.9368109782,
0.5500006156
],
"F": [
2.... |
2obj_3rel_1extra_gen0242 | medium | Diagram description: The diagram contains points A, B, C, O, D, E, F. There is an acute triangle ABC. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. O is the orthocenter of triangle ABC. line AD is an altitude of triangle ABC from vertex A. line BE i... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O, D, E, F = scene.add.points(["A", "B", "C", "O", "D", "E", "F"])
triangle_ABC = scene.add.acute_triangle(A, B, C)
circle_O = scene.add.circle(O)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_segment(B, E)
line_CF = scene.add.lin... | {
"triangle_ABC": "acute_triangle(A, B, C)",
"circle_O": "circle(O)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)"
} | [
"is_orthocenter(O, triangle_ABC)",
"is_altitude(line_AD, triangle_ABC, A)",
"is_altitude(line_BE, triangle_ABC, B)"
] | [
"A",
"B",
"C",
"O",
"D",
"E",
"F"
] | [
"scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BE').length)",
"scene.constraint.leq(scene.get_object('triangle_ABC').area, 10)"
] | {
"points": {
"A": [
0.2215098674,
-3.9062264439
],
"B": [
0.9096302929000001,
-0.4137316753
],
"C": [
5.8546012572,
-3.2020681505
],
"O": [
1.1421179320000001,
-2.2735753799
],
"D": [
1.8817466842,
-0.9618820640000001
... |
2obj_3rel_1extra_gen0248 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a parallelogram ABCD. There is a rectangle EFGH. There is a line segment AC. There is a line segment EG. There is a line segment AB. There is a line segment EF. Parallelogram ABCD is scaled by a factor of 2 to form rectangle EFGH. Line AC... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H"])
parallelogram1 = scene.add.parallelogram(A, B, C, D)
rectangle1 = scene.add.rectangle(E, F, G, H)
line_AC = scene.add.line_segment(A, C)
line_EG = scene.add.line_segment(E, ... | {
"parallelogram1": "parallelogram(A, B, C, D)",
"rectangle1": "rectangle(E, F, G, H)",
"line_AC": "line_segment(A, C)",
"line_EG": "line_segment(E, G)",
"line_AB": "line_segment(A, B)",
"line_EF": "line_segment(E, F)"
} | [
"scale(parallelogram1, rectangle1, 2)",
"perpendicular(line_AC, line_EG)",
"parallel(line_AB, line_EF)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
4.0457114379,
3.3545360009
],
"B": [
3.3732485225,
-1.2981450451
],
"C": [
0.6853215894,
1.3662165138
],
"D": [
1.3577845233999999,
6.0188975984
],
"E": [
2.0234687319,
-1.4468705107
],
"F": [
... |
2obj_3rel_1extra_gen0251 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is an equilateral triangle BCD. There is a line segment BC. There is a line segment CD. There is a line segment DB. Point B lies on the circle. Point C lies on the circle. The circle is the circumcircle of triangle BCD. ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
triangle1 = scene.add.equilateral_triangle(B, C, D)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.add.line_segment(C, D)
line_DB = scene.add.line_segment(D, B)
### r... | {
"circle1": "circle(A)",
"triangle1": "equilateral_triangle(B, C, D)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_DB": "line_segment(D, B)"
} | [
"point_lies_on(B, circle1)",
"point_lies_on(C, circle1)",
"is_circumcircle(circle1, triangle1)"
] | [
"A",
"B",
"C",
"D"
] | [
"scene.constraint.eq(scene.get_object('triangle1').perimeter, 3 * scene.get_object('line_BC').length)",
"scene.constraint.eq(scene.get_object('line_BC').length, scene.get_object('line_CD').length)",
"scene.constraint.eq(scene.get_object('line_CD').length, scene.get_object('line_DB').length)"
] | {
"points": {
"A": [
2.577400661,
-2.734680191
],
"B": [
1.8100535694,
-3.6091901196
],
"C": [
3.7184220152,
-2.9619672884
],
"D": [
2.2037263835,
-1.6328831475
]
},
"circles": {
"A": 1.1634385079
}
} |
2obj_3rel_1extra_gen0267 | medium | Diagram description: The diagram contains points A, B, C, D, E. There is a circle with center E. There is a rhombus with vertices A, B, C, D. There is a line segment AC. There is a line segment BD. Line AC is perpendicular to line BD. Line AC is a diameter of the circle. Further, the area of rhombus ABCD equals the are... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
rhombus1 = scene.add.rhombus(A, B, C, D)
circle1 = scene.add.circle(E)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_segment(B, D)
### relationships
scene.relate.is_diameter(lin... | {
"rhombus1": "rhombus(A, B, C, D)",
"circle1": "circle(E)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)"
} | [
"is_diameter(line_AC, circle1)",
"perpendicular(line_AC, line_BD)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [
"scene.constraint.eq(scene.get_object('rhombus1').area, scene.get_object('circle1').area)"
] | {
"points": {
"A": [
-0.2352149719,
-1.0913749303
],
"B": [
-1.0197515744,
0.2865609388
],
"C": [
0.5607241199,
0.41423855340000004
],
"D": [
1.345260748,
-0.9636973257
],
"E": [
0.16275466830000002,
-0.3385682198
]
... |
2obj_3rel_1extra_gen0273 | medium | Diagram description: The diagram contains points A, B, C, D, E. There is a minor arc BC with center A. There is a major arc DE with center A. There is a line segment BD. There is a line segment CE. There is a line segment DE. Point B lies on minor arc BC. Point D lies on major arc DE. Line BD is perpendicular to line C... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
minor_arc1 = scene.add.minor_arc(A, B, C)
major_arc2 = scene.add.major_arc(A, D, E)
line_BD = scene.add.line_segment(B, D)
line_CE = scene.add.line_segment(C, E)
line_DE = scene.add.line_segment(D,... | {
"minor_arc1": "minor_arc(A, B, C)",
"major_arc2": "major_arc(A, D, E)",
"line_BD": "line_segment(B, D)",
"line_CE": "line_segment(C, E)",
"line_DE": "line_segment(D, E)"
} | [
"point_lies_on(B, minor_arc1)",
"point_lies_on(D, major_arc2)",
"perpendicular(line_BD, line_CE)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [] | {
"points": {
"A": [
0.29361295870000004,
0.14922646920000002
],
"B": [
-0.8949923043,
-4.0466864816
],
"C": [
4.3480454294,
-1.4570254723
],
"D": [
0.4061738413,
-2.3982811393
],
"E": [
-0.6751550552000001,
2.5080298749
... |
2obj_3rel_1extra_gen0284 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a minor arc with center A, start point B, and end point C. There is a regular octagon with vertices D, E, F, G, H, I, J, K. There is a line segment AB. There is a line segment AC. There is a line segment DE. There is a line segme... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I, J, K = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K"])
minor_arc1 = scene.add.minor_arc(A, B, C)
regular_octagon1 = scene.add.regular_octagon(D, E, F, G, H, I, J, K)
line_AB = scene.add.line_segment(A, B)... | {
"minor_arc1": "minor_arc(A, B, C)",
"regular_octagon1": "regular_octagon(D, E, F, G, H, I, J, K)",
"line_AB": "line_segment(A, B)",
"line_AC": "line_segment(A, C)",
"line_DE": "line_segment(D, E)",
"line_EF": "line_segment(E, F)"
} | [
"point_lies_on(B, minor_arc1)",
"point_lies_on(C, minor_arc1)",
"perpendicular(line_AB, line_AC)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [
"scene.constraint.eq(scene.get_object('minor_arc1').inscribed_angle, 45)",
"scene.constraint.leq(scene.get_object('regular_octagon1').area, 20)"
] | {
"points": {
"A": [
-10,
-10
],
"B": [
-10,
10
],
"C": [
10,
-10
],
"D": [
4.9202872723,
0.1008215933
],
"E": [
4.7213411095,
0.20939363
],
"F": [
4.5038929054,
0.1454894727
],
"G": [
4.3... |
2obj_4rel_2extra_gen0005 | medium | Diagram description: The diagram contains points A, B, C, D. There is a major arc with center A, start point B, end point C. There is a circle with center D. There is a line segment AC. There is a line segment BC. There is a line segment AD. There is a line segment BD. There is a line segment CD. Line AC and line BC in... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
semicircle1 = scene.add.major_arc(A, B, C)
circle1 = scene.add.circle(D)
line_AC = scene.add.line_segment(A, C)
line_BC = scene.add.line_segment(B, C)
line_AD = scene.add.line_segment(A, D)
line_BD = scene... | {
"semicircle1": "major_arc(A, B, C)",
"circle1": "circle(D)",
"line_AC": "line_segment(A, C)",
"line_BC": "line_segment(B, C)",
"line_AD": "line_segment(A, D)",
"line_BD": "line_segment(B, D)",
"line_CD": "line_segment(C, D)"
} | [
"lines_intersect_at(line_AC, line_BC, C)",
"angle_bisector(A, C, B, line_CD)",
"is_radius(line_AD, circle1)",
"is_radius(line_BD, circle1)"
] | [
"A",
"B",
"C",
"D"
] | [] | {
"points": {
"A": [
-2.5529065904,
-0.1629040937
],
"B": [
3.4496802282,
1.785703601
],
"C": [
1.6921651677,
-4.832752722
],
"D": [
-0.08219874170000001,
2.4458415597
]
},
"circles": {
"D": 3.5930420451
}
} |
2obj_4rel_2extra_gen0009 | medium | Diagram description: The diagram contains points A, B, C, D, E. There is a square with vertices A, B, C, D. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment EA. There is a line segment AB. E is the centroid of the square. Points A, E, and C are collinear. ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
square1 = scene.add.square(A, B, C, D)
circle1 = scene.add.circle(E)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_segment(B, D)
line_EA = scene.add.line_segment(E, A)
line_AB = s... | {
"square1": "square(A, B, C, D)",
"circle1": "circle(E)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EA": "line_segment(E, A)",
"line_AB": "line_segment(A, B)"
} | [
"is_centroid(E, square1)",
"collinear(A, E, C)",
"is_diameter(line_AC, circle1)",
"is_radius(line_EA, circle1)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [
"scene.constraint.eq(scene.get_object('circle1').area, scene.get_object('square1').area)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('E'), scene.get_object('B')), 90)"
] | {
"points": {
"A": [
-2.1756376402,
1.0465165025
],
"B": [
-2.03079325,
1.2829226854
],
"C": [
-1.8017184858,
1.1285127541
],
"D": [
-1.9468086523,
0.894524168
],
"E": [
-1.9889662755000002,
1.0862080195
]
},
"circ... |
2obj_4rel_2extra_gen0010 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a major arc with center B and endpoints C and D. There are line segments AB, AC, AD, BC, and CD. Point B lies on the circle. Point C lies on the circle. Point D lies on the circle. Line AB intersects line CD at point ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
semicircle1 = scene.add.major_arc(B, C, D)
line_AB = scene.add.line_segment(A, B)
line_AC = scene.add.line_segment(A, C)
line_AD = scene.add.line_segment(A, D)
line_BC = scene... | {
"circle1": "circle(A)",
"semicircle1": "major_arc(B, C, D)",
"line_AB": "line_segment(A, B)",
"line_AC": "line_segment(A, C)",
"line_AD": "line_segment(A, D)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)"
} | [
"point_lies_on(B, circle1)",
"point_lies_on(C, circle1)",
"point_lies_on(D, circle1)",
"lines_intersect_at(line_AB, line_CD, A)"
] | [
"A",
"B",
"C",
"D"
] | [] | {
"points": {
"A": [
-0.374426295,
-0.2800487264
],
"B": [
0.2856272549,
-0.6963409641
],
"C": [
0.0418659377,
0.3800048186
],
"D": [
-0.7907185279000001,
-0.9401022664
]
},
"circles": {
"A": 0.7803652417
}
} |
2obj_4rel_2extra_gen0012 | medium | Diagram description: The diagram contains points A, B, C, D, E. There is a circle with center A. There is a kite BCDE. There is a line segment BC. There is a line segment CD. There is a line segment DE. There is a line segment BE. There is a line segment AC. There is a line segment AD. B, A, and C are collinear. The an... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
circle1 = scene.add.circle(A)
kite1 = scene.add.kite(B, C, D, E)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.add.line_segment(C, D)
line_DE = scene.add.line_segment(D, E)
line_BE = scene... | {
"circle1": "circle(A)",
"kite1": "kite(B, C, D, E)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_DE": "line_segment(D, E)",
"line_BE": "line_segment(B, E)",
"line_AC": "line_segment(A, C)",
"line_AD": "line_segment(A, D)"
} | [
"collinear(B, A, C)",
"right_angle(B, A, D)",
"is_radius(line_AC, circle1)",
"is_radius(line_AD, circle1)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [] | {
"points": {
"A": [
-0.9139620274,
1.2199642091
],
"B": [
-1.2087986442,
1.3534672418
],
"C": [
-0.202163955,
0.8976597049
],
"D": [
-0.5916576843,
1.9317623852999999
],
"E": [
9.9998928678,
-9.9897015185
]
},
"ci... |
2obj_4rel_2extra_gen0024 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a trapezoid ABCD. There is a scalene triangle EFG. There are line segments AC, BD, EF, FG, GE. Line AC and line BD intersect at point H. Line AC is perpendicular to line BD. Point H is the centroid of trapezoid ABCD. Line EF is an altitud... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H"])
trapezoid1 = scene.add.trapezoid(A, B, C, D)
triangle1 = scene.add.scalene_triangle(E, F, G)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_segment(B, D)
li... | {
"trapezoid1": "trapezoid(A, B, C, D)",
"triangle1": "scalene_triangle(E, F, G)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EF": "line_segment(E, F)",
"line_FG": "line_segment(F, G)",
"line_GE": "line_segment(G, E)"
} | [
"lines_intersect_at(line_AC, line_BD, H)",
"perpendicular(line_AC, line_BD)",
"is_centroid(H, trapezoid1)",
"is_altitude(line_EF, triangle1, E)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"scene.constraint.eq(scene.get_object('line_BD').length, scene.get_object('line_AC').length)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('H'), scene.get_object('B')), 90)"
] | {
"points": {
"A": [
4.6539056147,
2.5064071231
],
"B": [
-0.6629254674,
-1.6744266373999999
],
"C": [
3.5179081695,
-6.9912582093
],
"D": [
8.8347397741,
-2.8104240886
],
"E": [
-2.3217306541,
-4.5355663373
],
"F"... |
2obj_4rel_2extra_gen0030 | medium | Diagram description: The diagram contains points A, B, C, O, D, E, F, G. There is an isosceles triangle ABC with AB = BC. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD is parallel to line BE. Line AD intersects line CF at point G. Line AD is... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O, D, E, F, G = scene.add.points(["A", "B", "C", "O", "D", "E", "F", "G"])
triangleABC = scene.add.isosceles_triangle(A, B, C)
circleO = scene.add.circle(O)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_segment(B, E)
line_CF = sce... | {
"triangleABC": "isosceles_triangle(A, B, C)",
"circleO": "circle(O)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)"
} | [
"parallel(line_AD, line_BE)",
"lines_intersect_at(line_AD, line_CF, G)",
"is_altitude(line_AD, triangleABC, A)",
"is_circumcircle(circleO, triangleABC)"
] | [
"A",
"B",
"C",
"O",
"D",
"E",
"F",
"G"
] | [] | {
"points": {
"A": [
0.117322281,
1.3922903470999999
],
"B": [
1.7128001796999999,
-0.4396421627
],
"C": [
-0.6365307646,
0.17855576750000002
],
"O": [
0.6332377427,
0.23087669200000002
],
"D": [
-0.23019294380000002,
0.07... |
2obj_4rel_2extra_gen0036 | medium | Diagram description: The diagram contains points A, B, C, D, E. There is a rhomboid ABCD. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment BC. Line AC intersects the circle at points A and C. Line BC is tangent to the circle at point C. Line AC is perpendi... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
rhomboid1 = scene.add.rhomboid(A, B, C, D)
circle1 = scene.add.circle(E)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_segment(B, D)
line_BC = scene.add.line_segment(B, C)
### re... | {
"rhomboid1": "rhomboid(A, B, C, D)",
"circle1": "circle(E)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_BC": "line_segment(B, C)"
} | [
"line_intersects_circle_at(line_AC, circle1, A, C)",
"tangent_to_circle(line_BC, circle1, C)",
"perpendicular(line_AC, line_BD)",
"is_diameter(line_AC, circle1)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [] | {
"points": {
"A": [
0.2421320275,
-2.3332283951
],
"B": [
-1.3740401788,
-7.2119163503
],
"C": [
0.6218008241,
-2.4758929569
],
"D": [
2.2379833915,
2.4027914705
],
"E": [
0.4342022116,
-2.3969926047
]
},
"circles... |
2obj_4rel_2extra_gen0042 | medium | Diagram description: The diagram contains points A, B, C, D, F. There is a circle with center A. There is a circle with center B. There is a line segment CD. There is a line segment AF. The circles are similar. Line AF is the angle bisector of angle CAD. Line CD is a chord of the circle with center A. Line CD is perpen... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, F = scene.add.points(["A", "B", "C", "D", "F"])
circle1 = scene.add.circle(A)
circle2 = scene.add.circle(B)
line_CD = scene.add.line_segment(C, D)
line_AF = scene.add.line_segment(A, F)
### relationships
scene.relate.similar(circle1, circle2)
... | {
"circle1": "circle(A)",
"circle2": "circle(B)",
"line_CD": "line_segment(C, D)",
"line_AF": "line_segment(A, F)"
} | [
"similar(circle1, circle2)",
"angle_bisector(C, A, D, line_AF)",
"is_chord(line_CD, circle1)",
"perpendicular(line_CD, line_AF)"
] | [
"A",
"B",
"C",
"D",
"F"
] | [
"scene.constraint.eq(scene.get_object('circle1').area, scene.get_object('circle2').area)",
"scene.constraint.eq(scene.angle(scene.get_object('C'), scene.get_object('A'), scene.get_object('F')), 90)"
] | {
"points": {
"A": [
0.6671048148000001,
1.8948808095
],
"B": [
8.3023289883,
-6.1883522764
],
"C": [
2.7589443361,
3.8379269959
],
"D": [
-1.4247346892000001,
-0.0481653753
],
"F": [
6.2118354363,
-4.0744505921
]
},... |
2obj_4rel_2extra_gen0053 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a right isosceles triangle BCD. There is a line segment BC. There is a line segment CD. There is a line segment BD. There is a line segment AD. There is a line segment AC. Line BC is tangent to the circle at point B. ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
triangle1 = scene.add.right_isosceles_triangle(B, C, D)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.add.line_segment(C, D)
line_BD = scene.add.line_segment(B, D)
li... | {
"circle1": "circle(A)",
"triangle1": "right_isosceles_triangle(B, C, D)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_BD": "line_segment(B, D)",
"line_AD": "line_segment(A, D)",
"line_AC": "line_segment(A, C)"
} | [
"tangent_to_circle(line_BC, circle1, B)",
"obtuse_angle(D, C, B)",
"is_chord(line_BD, circle1)",
"point_lies_on(D, circle1)"
] | [
"A",
"B",
"C",
"D"
] | [] | {
"points": {
"A": [
-0.0034949858,
1.4465584897000001
],
"B": [
0.0282300963,
1.7280107779
],
"C": [
0.3096293483,
1.6962915405999999
],
"D": [
0.2779631073,
1.4148862733
]
},
"circles": {
"A": 0.28323454540000004
}
} |
2obj_4rel_2extra_gen0054 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is an isosceles triangle ABC. There is a right triangle DEF. There are line segments AD, BE, CF, DE, AF, and BD. Angle ABC is acute. The extensions of line AD and line BE intersect at point G. Line AD is perpendicular to line BE. Line CF is an ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G = scene.add.points(["A", "B", "C", "D", "E", "F", "G"])
triangle1 = scene.add.isosceles_triangle(A, B, C)
triangle2 = scene.add.right_triangle(D, E, F)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_segment(B, E)
line_CF... | {
"triangle1": "isosceles_triangle(A, B, C)",
"triangle2": "right_triangle(D, E, F)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)",
"line_DE": "line_segment(D, E)",
"line_AF": "line_segment(A, F)",
"line_BD": "line_segment(B, D)"
} | [
"acute_angle(A, B, C)",
"line_extensions_intersect_at(line_AD, line_BE, G)",
"perpendicular(line_AD, line_BE)",
"is_altitude(line_CF, triangle1, C)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [
"scene.constraint.eq(scene.get_object('triangle1').perimeter, scene.get_object('triangle2').perimeter)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 75)"
] | {
"points": {
"A": [
2.5195653250000003,
-3.8260998706000002
],
"B": [
1.2338784742,
-0.2636072685
],
"C": [
-1.8744649646,
-2.4275263805
],
"D": [
-3.3254035365,
1.1342943863000001
],
"E": [
1.794541251,
0.3970371648
... |
2obj_4rel_2extra_gen0073 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a triangle with vertices B, C, D. There is a line segment BC. There is a line segment CD. There is a line segment BD. There is a line segment AD. There is a line segment AC. Line BC is perpendicular to line CD. Angle ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
triangle1 = scene.add.triangle(B, C, D)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.add.line_segment(C, D)
line_BD = scene.add.line_segment(B, D)
line_AD = scene.ad... | {
"circle1": "circle(A)",
"triangle1": "triangle(B, C, D)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_BD": "line_segment(B, D)",
"line_AD": "line_segment(A, D)",
"line_AC": "line_segment(A, C)"
} | [
"perpendicular(line_BC, line_CD)",
"obtuse_angle(B, C, D)",
"is_chord(line_BD, circle1)",
"is_radius(line_AD, circle1)"
] | [
"A",
"B",
"C",
"D"
] | [
"scene.constraint.eq(scene.get_object('line_CD').length, scene.get_object('line_AD').length)",
"scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('C'), scene.get_object('D')), 90)"
] | {
"points": {
"A": [
0.7109213866,
-0.8799265570000001
],
"B": [
9.9429679187,
0.0857258633
],
"C": [
-0.9937981105,
-1.2540667637
],
"D": [
-2.122508206,
7.9594650677
]
},
"circles": {
"A": 9.2824117304
}
} |
2obj_4rel_2extra_gen0075 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is an isosceles trapezoid ABCD. There is a rectangle EFGH. There is a line segment AC. There is a line segment BD. There is a line segment EG. There is a line segment FH. Line AC and line BD intersect at point I. Line EG and line FH in... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I, J = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "J"])
trapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)
rectangle1 = scene.add.rectangle(E, F, G, H)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.ad... | {
"trapezoid1": "isosceles_trapezoid(A, B, C, D)",
"rectangle1": "rectangle(E, F, G, H)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EG": "line_segment(E, G)",
"line_FH": "line_segment(F, H)"
} | [
"line_extensions_intersect_at(line_AC, line_BD, I)",
"line_extensions_intersect_at(line_EG, line_FH, J)",
"perpendicular(line_AC, line_BD)",
"perpendicular(line_EG, line_FH)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J"
] | [
"scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('I'), scene.get_object('B')), 90)"
] | {
"points": {
"A": [
5.4384528126,
1.783127144
],
"B": [
2.4548141921,
-1.5429999278
],
"C": [
0.13849303300000002,
1.4954495799
],
"D": [
2.1671367747,
3.7569588015
],
"E": [
-0.311804519,
0.1578929444
],
"F": [
... |
2obj_4rel_2extra_gen0077 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is an acute triangle BCD. There is a line segment BC. There is a line segment CD. There is a line segment DB. There is a line segment AD. There is a line segment AC. There is a line segment BD. Line AC is a radius of the... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
triangle1 = scene.add.acute_triangle(B, C, D)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.add.line_segment(C, D)
line_DB = scene.add.line_segment(D, B)
line_AD = sc... | {
"circle1": "circle(A)",
"triangle1": "acute_triangle(B, C, D)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_DB": "line_segment(D, B)",
"line_AD": "line_segment(A, D)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)"
} | [
"is_radius(line_AC, circle1)",
"is_radius(line_AD, circle1)",
"perpendicular(line_AC, line_AD)",
"is_midpoint(D, line_BC)"
] | [
"A",
"B",
"C",
"D"
] | [
"scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_AC').length)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('C'), scene.get_object('D')), 45)"
] | {
"points": {
"A": [
5.7611967956,
2.7163533985
],
"B": [
-9.9655741101,
9.2748682333
],
"C": [
6.2864435918,
-4.8866194589
],
"D": [
-1.8417762564,
2.1911082143
]
},
"circles": {
"A": 7.6210942188
}
} |
2obj_4rel_2extra_gen0098 | medium | Diagram description: The diagram contains points A, B, C, D.
There is a circle with center A.
There is a right triangle BCD.
There is a line segment BC.
There is a line segment CD.
There is a line segment BD.
There is a line segment AD.
There is a line segment AC.
Point B lies on the circle.
Point C lies on the circle.... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
triangle1 = scene.add.right_triangle(B, C, D)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.add.line_segment(C, D)
line_BD = scene.add.line_segment(B, D)
line_AD = sc... | {
"circle1": "circle(A)",
"triangle1": "right_triangle(B, C, D)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_BD": "line_segment(B, D)",
"line_AD": "line_segment(A, D)",
"line_AC": "line_segment(A, C)"
} | [
"point_lies_on(B, circle1)",
"point_lies_on(C, circle1)",
"is_chord(line_BC, circle1)",
"similar(triangle1, triangle1)"
] | [
"A",
"B",
"C",
"D"
] | [
"scene.constraint.eq(scene.get_object('triangle1').area, scene.get_object('circle1').area / 4)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('D')), 45)"
] | {
"points": {
"A": [
0.25547185170000003,
-0.8214779268
],
"B": [
0.8398740610000001,
1.8873476435
],
"C": [
1.6170845455,
-3.235038108
],
"D": [
3.918962672,
-2.8857782376000003
]
},
"circles": {
"A": 2.7711481181
}
} |
2obj_4rel_2extra_gen0102 | medium | Diagram description: The diagram contains points A, B, C, O. There is a right isosceles triangle ABC. There is a circle with center O. There is a line segment AB. There is a line segment BC. There is a line segment AC. There is a line segment AO. There is a line segment BO. There is a line segment CO. Line AB intersect... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O = scene.add.points(["A", "B", "C", "O"])
triangleABC = scene.add.right_isosceles_triangle(A, B, C)
circleO = scene.add.circle(O)
lineAB = scene.add.line_segment(A, B)
lineBC = scene.add.line_segment(B, C)
lineAC = scene.add.line_segment(A, C)
lin... | {
"triangleABC": "right_isosceles_triangle(A, B, C)",
"circleO": "circle(O)",
"lineAB": "line_segment(A, B)",
"lineBC": "line_segment(B, C)",
"lineAC": "line_segment(A, C)",
"lineAO": "line_segment(A, O)",
"lineBO": "line_segment(B, O)",
"lineCO": "line_segment(C, O)"
} | [
"line_intersects_circle_at(lineAB, circleO, A, B)",
"line_intersects_circle_at(lineBC, circleO, B, C)",
"congruent(lineAB, lineBC)",
"is_circumcircle(circleO, triangleABC)"
] | [
"A",
"B",
"C",
"O"
] | [
"scene.constraint.eq(scene.get_object('lineAB').length, scene.get_object('lineBC').length)",
"scene.constraint.eq(scene.get_object('lineAC').length, scene.get_object('lineAB').length * 2**0.5)"
] | {
"points": {
"A": [
-2.7728845876,
-0.5200432818
],
"B": [
-2.2765846918,
-1.7230670194000002
],
"C": [
-3.4796084205,
-2.2193669084
],
"O": [
-3.1262465107,
-1.3697051041
]
},
"circles": {
"O": 0.9202118552
}
} |
2obj_4rel_2extra_gen0103 | medium | Diagram description: The diagram contains points A, B, C, O, D, E, F. There is a triangle ABC with points A, B, C. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. The circle is the circumcircle of triangle ABC. Point A lies on the circle. Line AD is a... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O, D, E, F = scene.add.points(["A", "B", "C", "O", "D", "E", "F"])
triangleABC = scene.add.triangle(A, B, C)
circleO = scene.add.circle(O)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_segment(B, E)
line_CF = scene.add.line_segmen... | {
"triangleABC": "triangle(A, B, C)",
"circleO": "circle(O)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)"
} | [
"is_circumcircle(circleO, triangleABC)",
"point_lies_on(A, circleO)",
"is_altitude(line_AD, triangleABC, A)",
"is_altitude(line_BE, triangleABC, B)"
] | [
"A",
"B",
"C",
"O",
"D",
"E",
"F"
] | [] | {
"points": {
"A": [
-1.548728347,
0.40230969200000005
],
"B": [
-1.0873026585,
3.4098728911
],
"C": [
0.8448048104,
0.1978435579
],
"O": [
-0.2290409494,
1.7390188120999999
],
"D": [
0.11854567490000001,
1.4052121994
... |
2obj_4rel_2extra_gen0105 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a minor arc BC with center A. There is a line segment BC. There is a line segment AD. The circle is congruent to itself. Angle BAD is a right angle. Line BC is a chord of the circle. Line AD is a radius of the circle. | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
minor_arc1 = scene.add.minor_arc(A, B, C)
line_BC = scene.add.line_segment(B, C)
line_AD = scene.add.line_segment(A, D)
### relationships
scene.relate.congruent(circle1, cir... | {
"circle1": "circle(A)",
"minor_arc1": "minor_arc(A, B, C)",
"line_BC": "line_segment(B, C)",
"line_AD": "line_segment(A, D)"
} | [
"congruent(circle1, circle1)",
"right_angle(B, A, D)",
"is_chord(line_BC, circle1)",
"is_radius(line_AD, circle1)"
] | [
"A",
"B",
"C",
"D"
] | [] | {
"points": {
"A": [
0.07958341990000001,
-3.4000789401000002
],
"B": [
2.5666820504,
-0.8687989212
],
"C": [
3.4377277373,
-4.5472079121
],
"D": [
-2.4516965943,
-0.9129803068000001
]
},
"circles": {
"A": 3.548667092
}
} |
2obj_4rel_2extra_gen0111 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a rectangle ABCD. There is a square EFGH. There is a line segment AC. There is a line segment BD. There is a line segment EG. There is a line segment FH. Line AC and line BD intersect at I. Point I lies on line AC. Point I lies on line... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I"])
rectangle1 = scene.add.rectangle(A, B, C, D)
square1 = scene.add.square(E, F, G, H)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_segment(B, D)
lin... | {
"rectangle1": "rectangle(A, B, C, D)",
"square1": "square(E, F, G, H)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EG": "line_segment(E, G)",
"line_FH": "line_segment(F, H)"
} | [
"lines_intersect_at(line_AC, line_BD, I)",
"point_lies_on(I, line_AC)",
"point_lies_on(I, line_BD)",
"perpendicular(line_AC, line_BD)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [
"scene.constraint.eq(scene.get_object('rectangle1').area, scene.get_object('square1').area)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('I'), scene.get_object('B')), 90)"
] | {
"points": {
"A": [
0.9441996482,
2.2282673987
],
"B": [
-0.6071954428,
0.14956820140000002
],
"C": [
-2.6858947227,
1.7009631746
],
"D": [
-1.134499956,
3.7796623473
],
"E": [
0.12087398070000001,
-2.5429150135
],
... |
2obj_4rel_2extra_gen0119 | medium | Diagram description: The diagram contains points A, B, C, D, E. There is a square with vertices A, B, C, D. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment EA. There is a line segment ED. Line BD is the perpendicular bisector of line AC. The extensions of... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
square1 = scene.add.square(A, B, C, D)
circle1 = scene.add.circle(E)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_segment(B, D)
line_EA = scene.add.line_segment(E, A)
line_ED = s... | {
"square1": "square(A, B, C, D)",
"circle1": "circle(E)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EA": "line_segment(E, A)",
"line_ED": "line_segment(E, D)"
} | [
"perpendicular_bisector_at(line_AC, line_BD)",
"line_extensions_intersect_at(line_AC, line_BD, E)",
"is_radius(line_EA, circle1)",
"is_radius(line_ED, circle1)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [] | {
"points": {
"A": [
0.3257612454,
2.6012681347
],
"B": [
-0.332628329,
1.9193543367
],
"C": [
-1.0145421156,
2.5777439035
],
"D": [
-0.356152554,
3.2596576972999998
],
"E": [
-0.3443904399,
2.5895059931
]
},
"circ... |
2obj_4rel_2extra_gen0128 | medium | Diagram description: The diagram contains points A, B, C, D, E. There is a square with points A, B, C, D. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment AB. There is a line segment CD. Line AC is a diameter of the circle. Line BD is a diameter of the cir... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
square1 = scene.add.square(A, B, C, D)
circle1 = scene.add.circle(E)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_segment(B, D)
line_AB = scene.add.line_segment(A, B)
line_CD = s... | {
"square1": "square(A, B, C, D)",
"circle1": "circle(E)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_AB": "line_segment(A, B)",
"line_CD": "line_segment(C, D)"
} | [
"is_diameter(line_AC, circle1)",
"is_diameter(line_BD, circle1)",
"parallel(line_AB, line_CD)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [] | {
"points": {
"A": [
-3.3901028315,
-1.6135652082
],
"B": [
-2.4377227483,
1.6170796238
],
"C": [
0.7929220798000001,
0.6646995504000001
],
"D": [
-0.1594580075,
-2.5659452941
],
"E": [
-1.2985903699999999,
-0.4744328384
... |
2obj_4rel_2extra_gen0130 | medium | Diagram description: The diagram contains points A, B, C, O. There is a major arc with center A, start point B, and end point C. There is a circle with center O. There is a line segment AB. There is a line segment OC. There is a line segment AC. There is a line segment BC. Line OC is a radius of the circle. Line AB is ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O = scene.add.points(["A", "B", "C", "O"])
semicircle1 = scene.add.major_arc(A, B, C)
circle1 = scene.add.circle(O)
line_AB = scene.add.line_segment(A, B)
line_OC = scene.add.line_segment(O, C)
line_AC = scene.add.line_segment(A, C)
line_BC = scene... | {
"semicircle1": "major_arc(A, B, C)",
"circle1": "circle(O)",
"line_AB": "line_segment(A, B)",
"line_OC": "line_segment(O, C)",
"line_AC": "line_segment(A, C)",
"line_BC": "line_segment(B, C)"
} | [
"is_radius(line_OC, circle1)",
"is_chord(line_AB, circle1)",
"perpendicular(line_AB, line_AC)",
"point_lies_on(C, semicircle1)"
] | [
"A",
"B",
"C",
"O"
] | [] | {
"points": {
"A": [
0.2934028786,
0.1064350579
],
"B": [
1.7836091612,
0.0319156478
],
"C": [
0.21888347130000002,
-1.383771223
],
"O": [
1.001246309,
-0.6759278029
]
},
"circles": {
"O": 1.0550516368
}
} |
2obj_4rel_2extra_gen0135 | medium | Diagram description: The diagram contains points A, B, C, O, D, E, F. There is an acute triangle ABC. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. The circle is the circumcircle of triangle ABC. Line AD is an altitude of triangle ABC from vertex A.... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O, D, E, F = scene.add.points(["A", "B", "C", "O", "D", "E", "F"])
triangleABC = scene.add.acute_triangle(A, B, C)
circleO = scene.add.circle(O)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_segment(B, E)
line_CF = scene.add.line_... | {
"triangleABC": "acute_triangle(A, B, C)",
"circleO": "circle(O)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)"
} | [
"is_circumcircle(circleO, triangleABC)",
"is_altitude(line_AD, triangleABC, A)",
"is_altitude(line_BE, triangleABC, B)",
"congruent(line_AD, line_BE)"
] | [
"A",
"B",
"C",
"O",
"D",
"E",
"F"
] | [
"scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BE').length)",
"scene.constraint.leq(scene.get_object('triangleABC').area, 10)"
] | {
"points": {
"A": [
1.7609701511,
1.7433499226
],
"B": [
-0.414479749,
0.3614196032
],
"C": [
-2.3678520701,
5.8397180171
],
"O": [
-0.7688075685,
3.3224802289
],
"D": [
-0.6062615451000001,
0.8992769124000001
],
... |
2obj_4rel_2extra_gen0152 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, O. There is an obtuse triangle with vertices A, B, C. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD is an altitude of triangle ABC from vertex A. Line AD intersects the circl... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, O = scene.add.points(["A", "B", "C", "D", "E", "F", "O"])
triangleABC = scene.add.obtuse_triangle(A, B, C)
circleO = scene.add.circle(O)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_segment(B, E)
line_CF = scene.add.line... | {
"triangleABC": "obtuse_triangle(A, B, C)",
"circleO": "circle(O)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)"
} | [
"is_altitude(line_AD, triangleABC, A)",
"line_intersects_circle_at(line_AD, circleO, A, D)",
"is_altitude(line_BE, triangleABC, B)",
"is_altitude(line_CF, triangleABC, C)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"O"
] | [
"scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BE').length)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('O'), scene.get_object('D')), 90)"
] | {
"points": {
"A": [
-3.1079493652,
-0.7009736756
],
"B": [
1.3558415155,
4.8457884107
],
"C": [
2.6410921383,
-0.7580368423
],
"D": [
2.3413582112,
0.5488369721
],
"E": [
1.3003592728,
-0.7447304934000001
],
"F": ... |
2obj_4rel_2extra_gen0154 | medium | Diagram description: The diagram contains points A, B, C, D, E. There is a circle with center A. There is a major arc BC. There is a line segment BD. There is a line segment AC. There is a line segment ED. Line BD is the perpendicular bisector of line AC. Line BD is parallel to line ED. Line BD is a chord of the circle... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
circle1 = scene.add.circle(A)
major_arc1 = scene.add.major_arc(A, B, C)
line_BD = scene.add.line_segment(B, D)
line_AC = scene.add.line_segment(A, C)
line_ED = scene.add.line_segment(E, D)
### rel... | {
"circle1": "circle(A)",
"major_arc1": "major_arc(A, B, C)",
"line_BD": "line_segment(B, D)",
"line_AC": "line_segment(A, C)",
"line_ED": "line_segment(E, D)"
} | [
"perpendicular_bisector_at(line_BD, line_AC)",
"parallel(line_BD, line_ED)",
"is_chord(line_BD, circle1)",
"point_lies_on(D, circle1)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [
"scene.constraint.eq(scene.get_object('line_BD').length, scene.get_object('line_ED').length)",
"scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('D')), 90)"
] | {
"points": {
"A": [
1.5929726319,
-0.6507668513
],
"B": [
1.8281155206,
-0.5724598749
],
"C": [
1.7091660732,
-0.41716132
],
"D": [
1.5172016857,
-0.4232393913
],
"E": [
1.2066169795000001,
-0.2730919456
]
},
"cir... |
2obj_4rel_2extra_gen0159 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a right triangle with vertices B, C, D. There is a line segment BC. There is a line segment CD. There is a line segment BD. There is a line segment AD. There is a line segment AC. Line BC is perpendicular to line CD. ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
triangle1 = scene.add.right_triangle(B, C, D)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.add.line_segment(C, D)
line_BD = scene.add.line_segment(B, D)
line_AD = sc... | {
"circle1": "circle(A)",
"triangle1": "right_triangle(B, C, D)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_BD": "line_segment(B, D)",
"line_AD": "line_segment(A, D)",
"line_AC": "line_segment(A, C)"
} | [
"perpendicular(line_BC, line_CD)",
"right_angle(B, C, D)",
"is_chord(line_BD, circle1)",
"is_radius(line_AD, circle1)"
] | [
"A",
"B",
"C",
"D"
] | [] | {
"points": {
"A": [
0.3757721721,
4.3900183993
],
"B": [
-0.2178468462,
-0.9756908817000001
],
"C": [
-0.8270063953000001,
-1.6787653473000002
],
"D": [
-3.5290814816,
0.6623733562
]
},
"circles": {
"A": 5.3984460379
}
} |
2obj_4rel_2extra_gen0170 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a major arc with center A and endpoints B and C. There is a quadrilateral with vertices D, E, F, G. There is a line segment DF. There is a line segment EG. There is a line segment DE. There is a line segment FG. Point D lies on the major arc... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G = scene.add.points(["A", "B", "C", "D", "E", "F", "G"])
major_arc1 = scene.add.major_arc(A, B, C)
quad1 = scene.add.quadrilateral(D, E, F, G)
line_DF = scene.add.line_segment(D, F)
line_EG = scene.add.line_segment(E, G)
line_DE = scene.a... | {
"major_arc1": "major_arc(A, B, C)",
"quad1": "quadrilateral(D, E, F, G)",
"line_DF": "line_segment(D, F)",
"line_EG": "line_segment(E, G)",
"line_DE": "line_segment(D, E)",
"line_FG": "line_segment(F, G)"
} | [
"point_lies_on(D, major_arc1)",
"point_lies_on(F, major_arc1)",
"collinear(D, F, G)",
"perpendicular(line_DF, line_EG)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [] | {
"points": {
"A": [
-0.3755472965,
3.9044422329
],
"B": [
1.0806748986999999,
2.6963020449
],
"C": [
0.4788210852,
5.5927077387
],
"D": [
-2.2565930568,
4.1090213653
],
"E": [
2.4085816774,
1.6908037479
],
"F": [
... |
2obj_4rel_2extra_gen0173 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a trapezoid with vertices A, B, C, D. There is a parallelogram with vertices E, F, G, H. There is a line segment AB. There is a line segment CD. There is a line segment EF. Line AB is parallel to line CD. Line EF is parallel to line CD. P... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H"])
trapezoid1 = scene.add.trapezoid(A, B, C, D)
parallelogram1 = scene.add.parallelogram(E, F, G, H)
line_AB = scene.add.line_segment(A, B)
line_CD = scene.add.line_segment(C, ... | {
"trapezoid1": "trapezoid(A, B, C, D)",
"parallelogram1": "parallelogram(E, F, G, H)",
"line_AB": "line_segment(A, B)",
"line_CD": "line_segment(C, D)",
"line_EF": "line_segment(E, F)"
} | [
"parallel(line_AB, line_CD)",
"parallel(line_EF, line_CD)",
"point_lies_on(A, line_AB)",
"point_lies_on(B, line_AB)",
"point_lies_on(E, line_EF)",
"point_lies_on(F, line_EF)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"scene.constraint.eq(scene.get_object('line_AB').length, scene.get_object('line_CD').length)",
"scene.constraint.eq(scene.get_object('line_EF').slope, 0)"
] | {
"points": {
"A": [
-1.3409988224,
8.550430824
],
"B": [
-0.9208258414,
8.5504309692
],
"C": [
2.475447003,
-5.7846444957
],
"D": [
2.0552740161,
-5.7846444664
],
"E": [
-0.7242343509,
0.0631130381
],
"F": [
... |
2obj_4rel_2extra_gen0179 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a minor arc with center A, start point B, and end point C. There is an isosceles trapezoid with vertices D, E, F, G. There is a line segment DF. There is a line segment EG. There is a line segment DE. There is a line segment FG. The exten... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H"])
arc1 = scene.add.minor_arc(A, B, C)
trapezoid1 = scene.add.isosceles_trapezoid(D, E, F, G)
line_DF = scene.add.line_segment(D, F)
line_EG = scene.add.line_segment(E, G)
line... | {
"arc1": "minor_arc(A, B, C)",
"trapezoid1": "isosceles_trapezoid(D, E, F, G)",
"line_DF": "line_segment(D, F)",
"line_EG": "line_segment(E, G)",
"line_DE": "line_segment(D, E)",
"line_FG": "line_segment(F, G)"
} | [
"line_extensions_intersect_at(line_DF, line_EG, H)",
"congruent(line_DE, line_FG)",
"perpendicular(line_DF, line_DE)",
"point_lies_on(C, arc1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
0.6520526802000001,
1.5343834986
],
"B": [
0.8859292525,
0.8658308999000001
],
"C": [
-0.0336717325,
1.3570619715
],
"D": [
0.3219091501,
0.47399510040000004
],
"E": [
2.4065224995,
-0.8995539275000001... |
2obj_4rel_2extra_gen0181 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, M, N. There is an equilateral triangle ABC. There is a rhomboid DEFG. There is a line segment AM. There is a line segment BN. There is a line segment CD. There is a line segment EF. Line CD is parallel to line EF. Triangle ABC is similar to triangle ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, M, N = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "M", "N"])
triangle_ABC = scene.add.equilateral_triangle(A, B, C)
rhomboid_DEFG = scene.add.rhomboid(D, E, F, G)
line_AM = scene.add.line_segment(A, M)
line_BN = scene.add.line... | {
"triangle_ABC": "equilateral_triangle(A, B, C)",
"rhomboid_DEFG": "rhomboid(D, E, F, G)",
"line_AM": "line_segment(A, M)",
"line_BN": "line_segment(B, N)",
"line_CD": "line_segment(C, D)",
"line_EF": "line_segment(E, F)"
} | [
"parallel(line_CD, line_EF)",
"similar(triangle_ABC, triangle_ABC)",
"is_altitude(line_AM, triangle_ABC, A)",
"is_median(line_BN, triangle_ABC, B)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"M",
"N"
] | [
"scene.constraint.eq(scene.get_object('line_AM').length, scene.get_object('line_BN').length)",
"scene.constraint.leq(scene.get_object('line_CD').length, scene.get_object('line_EF').length)"
] | {
"points": {
"A": [
2.4887198178,
7.9151456112
],
"B": [
8.9237059115,
3.4936726574
],
"C": [
1.8771051943,
0.1315482219
],
"D": [
0.5348349925,
-0.2049224865
],
"E": [
2.2623824882,
0.06880224010000001
],
"F": [
... |
2obj_4rel_2extra_gen0199 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, O. There is an obtuse triangle ABC. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD is a diameter of the circle. Point A lies on the circle. Line BE is an altitude of triangle ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, O = scene.add.points(["A", "B", "C", "D", "E", "F", "O"])
triangleABC = scene.add.obtuse_triangle(A, B, C)
circleO = scene.add.circle(O)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_segment(B, E)
line_CF = scene.add.line... | {
"triangleABC": "obtuse_triangle(A, B, C)",
"circleO": "circle(O)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)"
} | [
"is_diameter(line_AD, circleO)",
"point_lies_on(A, circleO)",
"is_altitude(line_BE, triangleABC, B)",
"is_altitude(line_CF, triangleABC, C)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"O"
] | [] | {
"points": {
"A": [
-2.8995184591000003,
-4.1040848578
],
"B": [
-4.4280135027,
-5.3621863775
],
"C": [
0.5707269008,
6.0314909874
],
"D": [
-3.748659099,
-1.6779034677
],
"E": [
-3.4454520631,
-5.6985982089
],
"F... |
2obj_4rel_2extra_gen0200 | medium | Diagram description: The diagram contains points A, B, C, O, D, E, F, H. There is a scalene triangle ABC. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD is an altitude of triangle ABC from vertex A. Line BE is an altitude of triangle ABC from... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O, D, E, F, H = scene.add.points(["A", "B", "C", "O", "D", "E", "F", "H"])
triangleABC = scene.add.scalene_triangle(A, B, C)
circleO = scene.add.circle(O)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_segment(B, E)
line_CF = scene... | {
"triangleABC": "scalene_triangle(A, B, C)",
"circleO": "circle(O)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)"
} | [
"is_altitude(line_AD, triangleABC, A)",
"is_altitude(line_BE, triangleABC, B)",
"line_extensions_intersect_at(line_AD, line_BE, H)",
"is_circumcircle(circleO, triangleABC)"
] | [
"A",
"B",
"C",
"O",
"D",
"E",
"F",
"H"
] | [
"scene.constraint.eq(scene.get_object('triangleABC').inradius, 1.5)",
"scene.constraint.leq(scene.get_object('line_BE').length, scene.get_object('line_CF').length)"
] | {
"points": {
"A": [
-2.4467568065,
0.27858177970000003
],
"B": [
1.2197000949,
-0.2613318935
],
"C": [
3.5883759570000002,
9.5932174784
],
"O": [
0.1520090771,
5.2072492099
],
"D": [
1.1421291997,
-0.5840556019
],
... |
2obj_4rel_2extra_gen0204 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is a quadrilateral with vertices A, B, C, D. There is a rectangle with vertices E, F, G, H. There is a line segment AC. There is a line segment BD. There is a line segment EG. There is a line segment FH. The extensions of line AC and l... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I, J = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "J"])
quadrilateral1 = scene.add.quadrilateral(A, B, C, D)
rectangle1 = scene.add.rectangle(E, F, G, H)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.... | {
"quadrilateral1": "quadrilateral(A, B, C, D)",
"rectangle1": "rectangle(E, F, G, H)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EG": "line_segment(E, G)",
"line_FH": "line_segment(F, H)"
} | [
"line_extensions_intersect_at(line_AC, line_BD, I)",
"line_extensions_intersect_at(line_EG, line_FH, J)",
"perpendicular(line_AC, line_BD)",
"perpendicular(line_EG, line_FH)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J"
] | [
"scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('I'), scene.get_object('B')), 90)"
] | {
"points": {
"A": [
-3.5652052889,
-3.9608329915000002
],
"B": [
0.7026513938000001,
-0.7654137964000001
],
"C": [
-3.4770568692,
-2.1176153858
],
"D": [
2.5458698686,
-0.8535619946
],
"E": [
-0.9128348384,
0.909103071900... |
2obj_4rel_2extra_gen0227 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a major arc with center A, start point B, and end point C. There is a minor arc with center D, start point E, and end point F. There is a line segment AB. There is a line segment DF. There is a line segment GH. The line segment GH is the ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H"])
semicircle1 = scene.add.major_arc(A, B, C)
minor_arc1 = scene.add.minor_arc(D, E, F)
line_AB = scene.add.line_segment(A, B)
line_DF = scene.add.line_segment(D, F)
line_perp ... | {
"semicircle1": "major_arc(A, B, C)",
"minor_arc1": "minor_arc(D, E, F)",
"line_AB": "line_segment(A, B)",
"line_DF": "line_segment(D, F)",
"line_perp": "line_segment(G, H)"
} | [
"perpendicular_bisector_at(line_AB, line_perp)",
"perpendicular(line_perp, line_DF)",
"point_lies_on(G, semicircle1)",
"is_midpoint(H, minor_arc1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
1.1479025841000001,
0.3909986087
],
"B": [
2.0058879655,
0.9257825991
],
"C": [
1.4714135931,
-0.5668497178
],
"D": [
0.8794051572,
-1.6748705825
],
"E": [
-1.4111692536,
0.3977584106
],
"F": [... |
2obj_4rel_2extra_gen0244 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, O. There is an isosceles triangle ABC with AB = BC. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD intersects line BE at G. Line BE intersects line CF at H. Line AD is a... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, O = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "O"])
triangleABC = scene.add.isosceles_triangle(A, B, C)
circleO = scene.add.circle(O)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_segment(B, E)
line_... | {
"triangleABC": "isosceles_triangle(A, B, C)",
"circleO": "circle(O)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)"
} | [
"lines_intersect_at(line_AD, line_BE, G)",
"lines_intersect_at(line_BE, line_CF, H)",
"is_altitude(line_AD, triangleABC, A)",
"is_altitude(line_BE, triangleABC, B)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"O"
] | [
"scene.constraint.eq(scene.get_object('triangleABC').inradius, 2.0)",
"scene.constraint.leq(scene.get_object('line_AD').length, scene.get_object('triangleABC').perimeter / 3)"
] | {
"points": {
"A": [
1.2311707258,
0.600717134
],
"B": [
-6.4037866617,
0.0677766938
],
"C": [
-0.8032160942000001,
-5.1485689645
],
"D": [
-2.5812495512,
-3.4925184913000002
],
"E": [
0.2139798731,
-2.2739230335
],
... |
2obj_4rel_2extra_gen0250 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a right triangle ABC with vertices A, B, C. There is a parallelogram DEFG with vertices D, E, F, G. There is a line segment BD. There is a line segment CF. There is a line segment AC. B lies on line segment BD. F lies on line segment CF. Lin... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G = scene.add.points(["A", "B", "C", "D", "E", "F", "G"])
triangleABC = scene.add.right_triangle(A, B, C)
parallelogramDEFG = scene.add.parallelogram(D, E, F, G)
line_BD = scene.add.line_segment(B, D)
line_CF = scene.add.line_segment(C, F)... | {
"triangleABC": "right_triangle(A, B, C)",
"parallelogramDEFG": "parallelogram(D, E, F, G)",
"line_BD": "line_segment(B, D)",
"line_CF": "line_segment(C, F)",
"line_AC": "line_segment(A, C)"
} | [
"point_lies_on(B, line_BD)",
"point_lies_on(F, line_CF)",
"lines_intersect_at(line_BD, line_CF, C)",
"perpendicular(line_BD, line_CF)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [
"scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)",
"scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 45)"
] | {
"points": {
"A": [
1.4570854661000001,
3.9367145135
],
"B": [
6.0022994443,
2.8471798987
],
"C": [
4.9127648497,
-1.6980340628000001
],
"D": [
4.4614649014,
-3.5807233103
],
"E": [
4.2421691048,
-0.20949292320000001
... |
2obj_4rel_2extra_gen0260 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a circle with center B. There is a line segment CD. There is a line segment EF. There is a line segment GH. circle with center B is a scaled version of the circle with center A with a scale factor of 2. li... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H"])
circle1 = scene.add.circle(A)
circle2 = scene.add.circle(B)
line_CD = scene.add.line_segment(C, D)
line_EF = scene.add.line_segment(E, F)
line_GH = scene.add.line_segment(G,... | {
"circle1": "circle(A)",
"circle2": "circle(B)",
"line_CD": "line_segment(C, D)",
"line_EF": "line_segment(E, F)",
"line_GH": "line_segment(G, H)"
} | [
"scale(circle1, circle2, 2)",
"parallel(line_CD, line_EF)",
"is_diameter(line_GH, circle1)",
"point_lies_on(C, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
-2.259102753,
-0.043182204
],
"B": [
-0.3905443262,
1.3182193496
],
"C": [
-2.0025130042,
-0.037522055900000004
],
"D": [
-1.140164953,
-1.1795233635
],
"E": [
3.0093451917,
2.2712942426
],
"F"... |
2obj_4rel_2extra_gen0265 | medium | Diagram description: The diagram contains points A, B, C, D, E, F. There is a major arc with center A and endpoints B and C. There is a semicircle with center D and endpoints E and F. There is a line segment BE. There is a line segment CF. There is a line segment DE. Point B lies on the major arc with center A and endp... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F = scene.add.points(["A", "B", "C", "D", "E", "F"])
major_arc1 = scene.add.major_arc(A, B, C)
semicircle1 = scene.add.semicircle(D, E, F)
line_BE = scene.add.line_segment(B, E)
line_CF = scene.add.line_segment(C, F)
line_DE = scene.add.line_... | {
"major_arc1": "major_arc(A, B, C)",
"semicircle1": "semicircle(D, E, F)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)",
"line_DE": "line_segment(D, E)"
} | [
"point_lies_on(B, major_arc1)",
"point_lies_on(C, major_arc1)",
"point_lies_on(E, semicircle1)",
"point_lies_on(F, semicircle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F"
] | [
"scene.constraint.eq(scene.get_object('major_arc1').radius, scene.get_object('semicircle1').radius)",
"scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 90)"
] | {
"points": {
"A": [
-0.2666773595,
0.967742567
],
"B": [
-0.2116824576,
-2.8468148917000002
],
"C": [
3.5478801033,
1.0227374691
],
"D": [
0.19227944530000002,
1.3414559041
],
"E": [
3.3591308813,
3.4686429448
],
... |
2obj_4rel_2extra_gen0270 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a major arc with center A, start point B, and end point C. There is a trapezoid with vertices D, E, F, G. There is a line segment DF. There is a line segment EG. There is a line segment DE. There is a line segment FG. Angle DFG is a right an... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G = scene.add.points(["A", "B", "C", "D", "E", "F", "G"])
major_arc1 = scene.add.major_arc(A, B, C)
trapezoid1 = scene.add.trapezoid(D, E, F, G)
line_DF = scene.add.line_segment(D, F)
line_EG = scene.add.line_segment(E, G)
line_DE = scene.... | {
"major_arc1": "major_arc(A, B, C)",
"trapezoid1": "trapezoid(D, E, F, G)",
"line_DF": "line_segment(D, F)",
"line_EG": "line_segment(E, G)",
"line_DE": "line_segment(D, E)",
"line_FG": "line_segment(F, G)"
} | [
"right_angle(D, F, G)",
"parallel(line_DE, line_FG)",
"perpendicular(line_DF, line_EG)",
"point_lies_on(D, major_arc1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [] | {
"points": {
"A": [
2.6719953669,
0.0690915423
],
"B": [
0.7743425213,
2.8879975917
],
"C": [
-0.5565470738,
-0.9910150746
],
"D": [
6.0544848173,
-0.25659344500000003
],
"E": [
-2.08473516,
2.2858749189
],
"F": [... |
2obj_4rel_2extra_gen0274 | medium | Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a right isosceles triangle BCD. There is a line segment AC. There is a line segment BC. There is a line segment CD. Line AC and line BC intersect at point C. Angle ACD is acute. Line BC is a chord of the circle. Line ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D = scene.add.points(["A", "B", "C", "D"])
circle1 = scene.add.circle(A)
triangle1 = scene.add.right_isosceles_triangle(B, C, D)
line_AC = scene.add.line_segment(A, C)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.add.line_segment(C, D)
#... | {
"circle1": "circle(A)",
"triangle1": "right_isosceles_triangle(B, C, D)",
"line_AC": "line_segment(A, C)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)"
} | [
"lines_intersect_at(line_AC, line_BC, C)",
"acute_angle(A, C, D)",
"is_chord(line_BC, circle1)",
"is_radius(line_AC, circle1)"
] | [
"A",
"B",
"C",
"D"
] | [
"scene.constraint.eq(scene.get_object('circle1').area, scene.get_object('triangle1').perimeter)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('C'), scene.get_object('D')), 45)"
] | {
"points": {
"A": [
1.0376982347,
1.0508040609
],
"B": [
0.8966285588,
2.5812525347
],
"C": [
2.5681465438,
1.1918737338
],
"D": [
1.1787679199,
-0.47964422770000004
]
},
"circles": {
"A": 1.5369361305
}
} |
2obj_4rel_2extra_gen0279 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is a triangle with vertices A, B, C. There is an acute triangle with vertices D, E, F. There is a line segment AG. There is a line segment BH. There is a line segment IJ. Line AG is an altitude of triangle ABC from vertex A. Line BH is... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I, J = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "J"])
triangleABC = scene.add.triangle(A, B, C)
acute_triangleDEF = scene.add.acute_triangle(D, E, F)
line_altitude = scene.add.line_segment(A, G)
line_median = sc... | {
"triangleABC": "Triangle(A, B, C)",
"acute_triangleDEF": "AcuteTriangle(D, E, F)",
"line_altitude": "line_segment(A, G)",
"line_median": "line_segment(B, H)",
"line_perp_bisector": "line_segment(I, J)"
} | [
"is_altitude(line_altitude, triangleABC, A)",
"is_median(line_median, triangleABC, B)",
"lines_intersect_at(line_altitude, line_median, G)",
"perpendicular_bisector_at(line_median, line_perp_bisector)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J"
] | [] | {
"points": {
"A": [
3.3287456384,
-4.9018030208
],
"B": [
3.3154353474000002,
-5.1877707957
],
"C": [
-9.815539618,
8.873368849
],
"D": [
9.689999518,
-2.7556225636000002
],
"E": [
-4.6842995424,
-2.1566008055
],
... |
2obj_4rel_2extra_gen0287 | medium | Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There is a major arc BC. There are line segments BD and CE. The extensions of line BD and line CE intersect at point F. Line BD is parallel to line CE. Point B lies on the circle. Point C lies on the circle. | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F = scene.add.points(["A", "B", "C", "D", "E", "F"])
circle1 = scene.add.circle(A)
major_arc1 = scene.add.major_arc(A, B, C)
line1 = scene.add.line_segment(B, D)
line2 = scene.add.line_segment(C, E)
### relationships
scene.relate.line_exten... | {
"circle1": "circle(A)",
"major_arc1": "major_arc(A, B, C)",
"line1": "line_segment(B, D)",
"line2": "line_segment(C, E)"
} | [
"line_extensions_intersect_at(line1, line2, F)",
"parallel(line1, line2)",
"point_lies_on(B, circle1)",
"point_lies_on(C, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F"
] | [] | {
"points": {
"A": [
-0.9553726197,
0.9495920691
],
"B": [
-3.3017717772,
-1.0758429798
],
"C": [
1.2898793197,
3.0866039736
],
"D": [
-0.6489934669,
1.3289671427
],
"E": [
-3.8095147198,
-1.5361247208000002
],
"F"... |
2obj_4rel_2extra_gen0291 | medium | Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There is a circle with center B. There is a line segment CD. There is a line segment AB. There is a line segment EF. Point C lies on the circle with center A. Point D lies on the circle with center A. Line CD is a chord ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F = scene.add.points(["A", "B", "C", "D", "E", "F"])
circle1 = scene.add.circle(A)
circle2 = scene.add.circle(B)
line_CD = scene.add.line_segment(C, D)
line_AB = scene.add.line_segment(A, B)
line EF = scene.add.line_segment(E, F)
### relatio... | {
"circle1": "circle(A)",
"circle2": "circle(B)",
"line_CD": "line_segment(C, D)",
"line_AB": "line_segment(A, B)",
"line EF": "line_segment(E, F)"
} | [
"point_lies_on(C, circle1)",
"point_lies_on(D, circle1)",
"is_chord(line_CD, circle1)",
"perpendicular(line_AB, line_CD)"
] | [
"A",
"B",
"C",
"D",
"E",
"F"
] | [] | {
"points": {
"A": [
2.5994998812,
-2.7620221214000003
],
"B": [
2.272234328,
-2.4997267692
],
"C": [
2.134761964,
0.3825362835
],
"D": [
-0.570798427,
-2.9931877299
],
"E": [
6.5119632711,
3.4572983406
],
"F": [
... |
2obj_4rel_2extra_gen0298 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a minor arc with center A from B to C. There is a rhombus with vertices D, E, F, G. There is a line segment DF. There is a line segment GE. There is a line segment AC. Line DF and line GE intersect at H. H is the midpoint of line AC. Line... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H"])
arc1 = scene.add.minor_arc(A, B, C)
rhombus1 = scene.add.rhombus(D, E, F, G)
line_DF = scene.add.line_segment(D, F)
line_GE = scene.add.line_segment(G, E)
line_AC = scene.ad... | {
"arc1": "minor_arc(A, B, C)",
"rhombus1": "rhombus(D, E, F, G)",
"line_DF": "line_segment(D, F)",
"line_GE": "line_segment(G, E)",
"line_AC": "line_segment(A, C)"
} | [
"lines_intersect_at(line_DF, line_GE, H)",
"is_midpoint(H, line_AC)",
"perpendicular(line_DF, line_GE)",
"point_lies_on(B, arc1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"scene.constraint.eq(scene.get_object('rhombus1').perimeter, 4 * scene.get_object('line_DF').length)",
"scene.constraint.eq(scene.get_object('arc1').inscribed_angle, 45)"
] | {
"points": {
"A": [
3.0556971384,
-4.3973328124
],
"B": [
-1.6658795836,
-4.9864120634999995
],
"C": [
2.4666181285,
0.324243661
],
"D": [
2.7219248243000003,
-1.7564363114
],
"E": [
3.2463293567,
-1.9685873172
],
... |
2obj_4rel_2extra_gen0317 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a circle with center B. There is a line segment CD. There is a line segment AB. There is a line segment EF. The extensions of line segment CD and line segment AB intersect at point G. Line segment AB is th... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H"])
circle1 = scene.add.circle(A)
circle2 = scene.add.circle(B)
line_CD = scene.add.line_segment(C, D)
line_AB = scene.add.line_segment(A, B)
line EF = scene.add.line_segment(E,... | {
"circle1": "circle(A)",
"circle2": "circle(B)",
"line_CD": "line_segment(C, D)",
"line_AB": "line_segment(A, B)",
"line EF": "line_segment(E, F)"
} | [
"line_extensions_intersect_at(line_CD, line_AB, G)",
"perpendicular_bisector_at(line_CD, line_AB)",
"is_chord(line_CD, circle1)",
"tangent_to_circle(line EF, circle2, H)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
1.5191431343000001,
1.6168863503000002
],
"B": [
1.066156427,
1.3659925644
],
"C": [
2.1559383621,
-0.06722089740000001
],
"D": [
0.4293611923,
3.0500998576
],
"E": [
-2.7178055909000003,
0.2777535232
... |
2obj_4rel_2extra_gen0322 | medium | Diagram description: The diagram contains points A, B, C, O. There is a right triangle with vertices A, B, C. There is a circle with center O. There is a line segment AB. There is a line segment BC. There is a line segment AC. There is a line segment OA. There is a line segment OC. Line AC is a diameter of the circle. ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O = scene.add.points(["A", "B", "C", "O"])
right_triangle_ABC = scene.add.right_triangle(A, B, C)
circle_O = scene.add.circle(O)
line_AB = scene.add.line_segment(A, B)
line_BC = scene.add.line_segment(B, C)
line_AC = scene.add.line_segment(A, C)
li... | {
"right_triangle_ABC": "right_triangle(A, B, C)",
"circle_O": "circle(O)",
"line_AB": "line_segment(A, B)",
"line_BC": "line_segment(B, C)",
"line_AC": "line_segment(A, C)",
"line_OA": "line_segment(O, A)",
"line_OC": "line_segment(O, C)"
} | [
"is_diameter(line_AC, circle_O)",
"line_extension_intersects_circle_at(line_AB, circle_O, A, B)",
"is_radius(line_OA, circle_O)",
"is_radius(line_OC, circle_O)"
] | [
"A",
"B",
"C",
"O"
] | [
"scene.constraint.eq(scene.get_object('line_AB').length, scene.get_object('line_BC').length)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)"
] | {
"points": {
"A": [
0.1093814238,
-2.7794350007
],
"B": [
-2.0484769898,
0.729595622
],
"C": [
1.4605536392,
2.8874540376
],
"O": [
0.7849675329,
0.0540095182
]
},
"circles": {
"O": 2.9128721927
}
} |
2obj_4rel_2extra_gen0329 | medium | Diagram description: The diagram contains points A, B, C, O. There is a right triangle ABC with vertices A, B, C. There is a circle with center O. There is a line segment AC. There is a line segment BC. There is a line segment AB. There is a line segment OA. There is a line segment OC. Line AC is a diameter of the circ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O = scene.add.points(["A", "B", "C", "O"])
triangleABC = scene.add.right_triangle(A, B, C)
circleO = scene.add.circle(O)
line_AC = scene.add.line_segment(A, C)
line_BC = scene.add.line_segment(B, C)
line_AB = scene.add.line_segment(A, B)
line_OA = ... | {
"triangleABC": "right_triangle(A, B, C)",
"circleO": "circle(O)",
"line_AC": "line_segment(A, C)",
"line_BC": "line_segment(B, C)",
"line_AB": "line_segment(A, B)",
"line_OA": "line_segment(O, A)",
"line_OC": "line_segment(O, C)"
} | [
"is_diameter(line_AC, circleO)",
"point_lies_on(A, circleO)",
"point_lies_on(C, circleO)",
"is_radius(line_OA, circleO)"
] | [
"A",
"B",
"C",
"O"
] | [
"scene.constraint.eq(scene.get_object('triangleABC').area, 6)",
"scene.constraint.eq(scene.get_object('triangleABC').inradius, 1)"
] | {
"points": {
"A": [
-4.391930401,
-2.8066143777
],
"B": [
-0.5535495611,
-1.6810520015
],
"C": [
-1.3977183125,
1.1977232134
],
"O": [
-2.8948243988,
-0.8044455631
]
},
"circles": {
"O": 2.5000012827
}
} |
2obj_4rel_2extra_gen0330 | medium | Diagram description: The diagram contains points A, B, C, D, E. There is a kite ABCD. There is a circle with center E. There are line segments AC, BD, AB, CD. Line AB is tangent to the circle at point A. Line AC and line BD intersect at point E. Line AC is a diameter of the circle. Line AC is perpendicular to line BD. | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
kite1 = scene.add.kite(A, B, C, D)
circle1 = scene.add.circle(E)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_segment(B, D)
line_AB = scene.add.line_segment(A, B)
line_CD = scene... | {
"kite1": "kite(A, B, C, D)",
"circle1": "circle(E)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_AB": "line_segment(A, B)",
"line_CD": "line_segment(C, D)"
} | [
"tangent_to_circle(line_AB, circle1, A)",
"lines_intersect_at(line_AC, line_BD, E)",
"is_diameter(line_AC, circle1)",
"perpendicular(line_AC, line_BD)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [] | {
"points": {
"A": [
1.4514294488,
-4.414802038
],
"B": [
-4.6479287324000005,
8.3204396406
],
"C": [
1.0883836609,
-4.5824031216000005
],
"D": [
2.1838906056,
-6.4783525355
],
"E": [
1.2711218304,
-4.5011527238
]
},... |
2obj_4rel_2extra_gen0338 | medium | Diagram description: The diagram contains points A, B, C, D, E. There is a rectangle with A, B, C, D. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment AB. There is a line segment BC. Line AC intersects the circle at points A and C. Line BD extends to inter... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
rectangle1 = scene.add.rectangle(A, B, C, D)
circle1 = scene.add.circle(E)
line_AC = scene.add.line_segment(A, C)
line BD = scene.add.line_segment(B, D)
line_AB = scene.add.line_segment(A, B)
line_... | {
"rectangle1": "rectangle(A, B, C, D)",
"circle1": "circle(E)",
"line_AC": "line_segment(A, C)",
"line BD": "line_segment(B, D)",
"line_AB": "line_segment(A, B)",
"line_BC": "line_segment(B, C)"
} | [
"line_intersects_circle_at(line_AC, circle1, A, C)",
"line_extension_intersects_circle_at(line BD, circle1, B, D)",
"is_diameter(line_AC, circle1)",
"perpendicular(line_AB, line_BC)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [] | {
"points": {
"A": [
-1.7624933232000002,
1.419627432
],
"B": [
-1.0806107435,
-0.7557666471000001
],
"C": [
-2.5237094083000002,
-1.2081094315
],
"D": [
-3.2055919699,
0.9672846509
],
"E": [
-2.1431013487,
0.1057590038
... |
2obj_4rel_2extra_gen0339 | medium | Diagram description: The diagram contains points A, B, C, D, E, F. There is a major arc with center A, start point B, end point C. There is an isosceles triangle with vertices D, E, F. There is a line segment DE. There is a line segment DF. There is a line segment EF. There is a line segment AD. Point D lies on the maj... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F = scene.add.points(["A", "B", "C", "D", "E", "F"])
major_arc1 = scene.add.major_arc(A, B, C)
isosceles_triangle1 = scene.add.isosceles_triangle(D, E, F)
line_DE = scene.add.line_segment(D, E)
line_DF = scene.add.line_segment(D, F)
line EF =... | {
"major_arc1": "major_arc(A, B, C)",
"isosceles_triangle1": "isosceles_triangle(D, E, F)",
"line_DE": "line_segment(D, E)",
"line_DF": "line_segment(D, F)",
"line EF": "line_segment(E, F)",
"line_AD": "line_segment(A, D)"
} | [
"point_lies_on(D, major_arc1)",
"lines_intersect_at(line_DE, line_AD, D)",
"is_altitude(line_DF, isosceles_triangle1, D)",
"perpendicular(line_DE, line_DF)"
] | [
"A",
"B",
"C",
"D",
"E",
"F"
] | [] | {
"points": {
"A": [
-4.2105987974,
-0.7134239375
],
"B": [
-7.8023543439,
-9.932589956
],
"C": [
5.4904788696,
-2.6583753746000003
],
"D": [
-6.9038203755000005,
8.8070946113
],
"E": [
5.615921607,
-6.1862537631
],
... |
2obj_4rel_2extra_gen0344 | medium | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a circle with center B. There is a line segment CD. There is a line segment EF. There is a line segment AH. The extensions of line CD and line EF intersect at point G. Line AH is a radius of the circle wit... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H"])
circle1 = scene.add.circle(A)
circle2 = scene.add.circle(B)
line_CD = scene.add.line_segment(C, D)
line_EF = scene.add.line_segment(E, F)
line_AH = scene.add.line_segment(A,... | {
"circle1": "circle(A)",
"circle2": "circle(B)",
"line_CD": "line_segment(C, D)",
"line_EF": "line_segment(E, F)",
"line_AH": "line_segment(A, H)"
} | [
"line_extensions_intersect_at(line_CD, line_EF, G)",
"is_radius(line_AH, circle1)",
"perpendicular(line_CD, line_EF)",
"point_lies_on(H, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"scene.constraint.eq(scene.get_object('circle1').diameter, 6)",
"scene.constraint.leq(scene.get_object('line_CD').length, scene.get_object('circle1').diameter)"
] | {
"points": {
"A": [
0.3733957257,
0.9454679823000001
],
"B": [
-2.4430955752,
-8.6015465013
],
"C": [
2.3658653505,
-2.1802576103
],
"D": [
0.3263969189,
2.1579725965
],
"E": [
-6.6356118866,
0.3679378264
],
"F": ... |
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