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 |
|---|---|---|---|---|---|---|---|---|
3obj_4rel_1extra_gen7101 | hard | Diagram description: The diagram contains points A, B, C, O, P, Q, R, S, T, U, V. There is a scalene triangle ABC with vertices A, B, C. There is a circle with center O. There is a regular heptagon PQRSTUV with vertices P, Q, R, S, T, U, V. There is a line segment AB. There is a line segment BC. There is a line segment... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O, P, Q, R, S, T, U, V = scene.add.points(["A", "B", "C", "O", "P", "Q", "R", "S", "T", "U", "V"])
triangleABC = scene.add.scalene_triangle(A, B, C)
circleO = scene.add.circle(O)
heptagonPQRSTUV = scene.add.regular_heptagon(P, Q, R, S, T, U, V)
lin... | {
"triangleABC": "scalene_triangle(A, B, C)",
"circleO": "circle(O)",
"heptagonPQRSTUV": "regular_heptagon(P, Q, R, S, T, U, V)",
"lineAB": "line_segment(A, B)",
"lineBC": "line_segment(B, C)",
"lineAC": "line_segment(A, C)",
"lineOP": "line_segment(O, P)"
} | [
"is_incircle(circleO, triangleABC)",
"parallel(lineAB, lineOP)",
"right_angle(C, B, A)",
"is_centroid(O, heptagonPQRSTUV)"
] | [
"A",
"B",
"C",
"O",
"P",
"Q",
"R",
"S",
"T",
"U",
"V"
] | [
"scene.constraint.eq(scene.get_object('triangleABC').inradius, scene.get_object('heptagonPQRSTUV').side_length)",
"scene.constraint.leq(scene.get_object('lineAC').length, scene.get_object('circleO').area)"
] | {
"points": {
"A": [
4.6934183126,
-3.0689249432
],
"B": [
1.9837670671,
1.7689265041
],
"C": [
-3.9171801075,
-1.5361582105
],
"O": [
1.3001082082,
-0.6556179940000001
],
"P": [
0.2970249848,
1.1353016727
],
"Q": ... |
3obj_4rel_1extra_gen7102 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a right triangle ABC. There is an obtuse triangle DEF. There is a circle with center G. There is a line segment AC. There is a line segment DF. There is a line segment GE. There is a line segment AF. There is a line segment DE. Line DF in... | 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"])
right_tri = scene.add.right_triangle(A, B, C)
obtuse_tri = scene.add.obtuse_triangle(D, E, F)
circle1 = scene.add.circle(G)
line_AC = scene.add.line_segment(A, C)
line_DF = ... | {
"right_tri": "right_triangle(A, B, C)",
"obtuse_tri": "obtuse_triangle(D, E, F)",
"circle1": "circle(G)",
"line_AC": "line_segment(A, C)",
"line_DF": "line_segment(D, F)",
"line_GE": "line_segment(G, E)",
"line_AF": "line_segment(A, F)",
"line_DE": "line_segment(D, E)"
} | [
"lines_intersect_at(line_AC, line_DF, H)",
"similar(right_tri, obtuse_tri)",
"is_circumcircle(circle1, right_tri)",
"perpendicular(line_GE, line_AF)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"scene.constraint.eq(scene.get_object('obtuse_tri').circumradius, scene.get_object('right_tri').circumradius)",
"scene.constraint.leq(scene.get_object('line_DE').length, scene.get_object('line_AC').length)"
] | {
"points": {
"A": [
-0.14877346660000001,
0.46539006050000004
],
"B": [
0.1492654878,
1.7575026248
],
"C": [
2.4191826223,
1.2339328529
],
"D": [
1.6338545456,
0.9280848729000001
],
"E": [
1.21327979,
-0.32947424750000004... |
3obj_4rel_1extra_gen7104 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M, N. There is a regular hexagon with vertices A, B, C, D, E, F. There is a rectangle with vertices G, H, I, J. There is a trapezoid with vertices K, L, M, N. There is a line segment GH. There is a line segment HI. There is a line segm... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I, J, K, L, M, N = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N"])
hexagon1 = scene.add.regular_hexagon(A, B, C, D, E, F)
rectangle1 = scene.add.rectangle(G, H, I, J)
trapezoid1 = scene.add.tr... | {
"hexagon1": "regular_hexagon(A, B, C, D, E, F)",
"rectangle1": "rectangle(G, H, I, J)",
"trapezoid1": "trapezoid(K, L, M, N)",
"line_GH": "line_segment(G, H)",
"line_HI": "line_segment(H, I)",
"line_IJ": "line_segment(I, J)",
"line_JK": "line_segment(J, K)",
"line_KL": "line_segment(K, L)",
"line_LM... | [
"lines_intersect_at(line_AC, line_CE, C)",
"line_extensions_intersect_at(line_GH, line_HI, H)",
"rotation_around_point(line_GH, line_HI, H, 90)",
"perpendicular(line_AC, line_EG)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L",
"M",
"N"
] | [] | {
"points": {
"A": [
3.2617943228,
1.3601467627
],
"B": [
1.2330604933,
2.3548838017
],
"C": [
-0.6427739673,
1.0953172874
],
"D": [
-0.48987459850000004,
-1.158986266
],
"E": [
1.538859231,
-2.153723305
],
"F": [
... |
3obj_4rel_1extra_gen7107 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a square ABCD. There is a right triangle EFG. There is a circle with center H. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment FG. There is a line segment EG. The circle is the i... | 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"])
square1 = scene.add.square(A, B, C, D)
right_triangle1 = scene.add.right_triangle(E, F, G)
circle1 = scene.add.circle(H)
line_AC = scene.add.line_segment(A, C)
line_BD = sce... | {
"square1": "square(A, B, C, D)",
"right_triangle1": "right_triangle(E, F, G)",
"circle1": "circle(H)",
"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_EG": "line_segment(E, G)"
} | [
"is_incircle(circle1, square1)",
"perpendicular(line_AC, line_BD)",
"is_centroid(H, square1)",
"is_altitude(line_EF, right_triangle1, E)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
-0.2961248749,
0.46191747980000003
],
"B": [
-0.5680793548,
-0.4574891673
],
"C": [
-1.4874858952,
-0.1855345769
],
"D": [
-1.2155314416,
0.7338720251
],
"E": [
2.7951669089,
2.6799197218
],
"F... |
3obj_4rel_1extra_gen7108 | hard | Diagram description: The diagram contains points A, B, C, O, D, E, F, G. There is a scalene triangle ABC. There is a major arc AC with center O. There is a square DEFG. There is a line segment BE. There is a line segment AG. There is a right angle at B. Line BE is a median of triangle ABC from vertex B to the midpoint ... | 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.scalene_triangle(A, B, C)
arc1 = scene.add.major_arc(O, A, C)
square1 = scene.add.square(D, E, F, G)
line_BE = scene.add.line_segment(B, E)
line_AG =... | {
"triangleABC": "scalene_triangle(A, B, C)",
"arc1": "major_arc(O, A, C)",
"square1": "square(D, E, F, G)",
"line_BE": "line_segment(B, E)",
"line_AG": "line_segment(A, G)"
} | [
"right_angle(A, B, C)",
"is_median(line_BE, triangleABC, B)",
"point_lies_on(E, line_AG)",
"perpendicular(line_BE, line_AG)"
] | [
"A",
"B",
"C",
"O",
"D",
"E",
"F",
"G"
] | [
"scene.constraint.eq(scene.get_object('triangleABC').area, scene.get_object('square1').area)"
] | {
"points": {
"A": [
1.8965454395,
-0.22076365250000002
],
"B": [
2.1577191416,
0.4270382139
],
"C": [
1.5103994725,
0.6880689526
],
"O": [
2.9573214121999998,
0.7663894895000001
],
"D": [
1.887850361,
0.6916252576
],
... |
3obj_4rel_1extra_gen7109 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a rhombus with vertices A, B, C, D. There is a circle with center E. There is a quadrilateral with vertices F, G, H, I. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment GH. E i... | 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"])
rhombus1 = scene.add.rhombus(A, B, C, D)
circle1 = scene.add.circle(E)
quad1 = scene.add.quadrilateral(F, G, H, I)
line_AC = scene.add.line_segment(A, C)
line_BD = s... | {
"rhombus1": "rhombus(A, B, C, D)",
"circle1": "circle(E)",
"quad1": "quadrilateral(F, G, H, I)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EF": "line_segment(E, F)",
"line_GH": "line_segment(G, H)"
} | [
"is_centroid(E, rhombus1)",
"is_chord(line_GH, circle1)",
"collinear(A, E, C)",
"perpendicular_bisector_at(line_AC, line_BD)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [] | {
"points": {
"A": [
1.6772610349,
1.6865057308
],
"B": [
1.1470888501,
1.8732340712000002
],
"C": [
0.8499406017000001,
1.3961041452
],
"D": [
1.3801127575,
1.2093757857
],
"E": [
1.2636007548000001,
1.5413048509
],
... |
3obj_4rel_1extra_gen7110 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M, N, O. There is a quadrilateral with vertices A, B, C, D. There is a regular pentagon with vertices E, F, G, H, I. There is a quadrilateral with vertices J, K, L, M. There is a line segment AC. There is a line segment BD. There is a ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I, J, K, L, M, N, O = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O"])
quad1 = scene.add.quadrilateral(A, B, C, D)
pentagon1 = scene.add.regular_pentagon(E, F, G, H, I)
quad2 = scene.add.q... | {
"quad1": "quadrilateral(A, B, C, D)",
"pentagon1": "regular_pentagon(E, F, G, H, I)",
"quad2": "quadrilateral(J, K, L, M)",
"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_NO": "line_segment(N, O)"
} | [
"line_extensions_intersect_at(line_AC, line_BD, N)",
"line_extensions_intersect_at(line_EG, line_FH, O)",
"point_lies_on(N, line_AC)",
"point_lies_on(O, line_EG)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L",
"M",
"N",
"O"
] | [
"scene.constraint.eq(scene.get_object('quad1').area, scene.get_object('pentagon1').area)"
] | {
"points": {
"A": [
-1.5023647944,
-3.06850487
],
"B": [
-0.7508670096000001,
2.2185879978
],
"C": [
0.8447731647000001,
0.41362510220000004
],
"D": [
1.9301319732,
-2.2887389691
],
"E": [
3.3701011078,
0.9016298457
]... |
3obj_4rel_1extra_gen7112 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a rhomboid with vertices A, B, C, D. There is a square with vertices E, F, G, H. There is a major arc with center I and endpoints J and K. There is a line segment AC. There is a line segment BD. There is a line segment EF. There ... | 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"])
rhomboid1 = scene.add.rhomboid(A, B, C, D)
square1 = scene.add.square(E, F, G, H)
semicircle1 = scene.add.major_arc(I, J, K)
line_AC = scene.add.line... | {
"rhomboid1": "rhomboid(A, B, C, D)",
"square1": "square(E, F, G, H)",
"semicircle1": "major_arc(I, J, K)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EF": "line_segment(E, F)",
"line_FG": "line_segment(F, G)"
} | [
"perpendicular(line_AC, line_BD)",
"collinear(A, I, J)",
"parallel(line_EF, line_AC)",
"right_angle(F, E, H)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [
"scene.constraint.eq(scene.get_object('rhomboid1').area, scene.get_object('square1').area)"
] | {
"points": {
"A": [
1.0405506316,
0.3751244359
],
"B": [
1.3247350588,
0.5431484535000001
],
"C": [
1.1881878631,
0.2420203843
],
"D": [
0.8912629732,
0.0576244969
],
"E": [
0.7043903224,
-0.3516737918
],
"F": [
... |
3obj_4rel_1extra_gen7115 | hard | Diagram description: In the diagram, two squares ABCD and EFGH are similar to each other. Side AB of the first square intersects side EF of the second square at point M. A parallelogram IJKL is constructed such that side IJ is parallel to side AB. Sides AB and EF of the squares are perpendicular to each other at their ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I, J, K, L, M = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M"])
square1 = scene.add.square(A, B, C, D)
square2 = scene.add.square(E, F, G, H)
parallelogram1 = scene.add.parallelogram(I, J, K, L)
li... | {
"square1": "square(A, B, C, D)",
"square2": "square(E, F, G, H)",
"parallelogram1": "parallelogram(I, J, K, L)",
"line_AB": "line_segment(A, B)",
"line_EF": "line_segment(E, F)",
"line_IJ": "line_segment(I, J)"
} | [
"similar(square1, square2)",
"lines_intersect_at(line_AB, line_EF, M)",
"parallel(line_IJ, line_AB)",
"perpendicular(line_AB, line_EF)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L",
"M"
] | [] | {
"points": {
"A": [
-0.5732317774,
0.7920780580000001
],
"B": [
0.6613706028,
0.1845669128
],
"C": [
1.2689058213,
1.4190025921
],
"D": [
0.0343398351,
2.0265593122
],
"E": [
-0.49154481850000004,
0.4656441886
],
... |
3obj_4rel_1extra_gen7116 | hard | 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 an acute triangle with vertices D, E, F. There is a scalene triangle with vertices G, H, I. There is a line segment DE. There is a line segment DF. There is a line segment EG. T... | 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"])
semicircle1 = scene.add.major_arc(A, B, C)
acute_triangle1 = scene.add.acute_triangle(D, E, F)
scalene_triangle1 = scene.add.scalene_triangle(G, H, I)
line_DE = scen... | {
"semicircle1": "major_arc(A, B, C)",
"acute_triangle1": "acute_triangle(D, E, F)",
"scalene_triangle1": "scalene_triangle(G, H, I)",
"line_DE": "line_segment(D, E)",
"line_FI": "line_segment(F, I)",
"line_HI": "line_segment(H, I)",
"line_DF": "line_segment(D, F)",
"line_EG": "line_segment(E, G)"
} | [
"perpendicular(line_DE, line_DF)",
"parallel(line_FI, line_HI)",
"is_centroid(G, acute_triangle1)",
"is_orthocenter(E, scalene_triangle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [
"scene.constraint.eq(scene.get_object('line_DE').length, scene.get_object('line_DF').length)",
"scene.constraint.leq(scene.get_object('acute_triangle1').area, 10.0)"
] | {
"points": {
"A": [
-0.8113625214,
-0.0365325586
],
"B": [
0.11496427050000001,
-0.5086411981
],
"C": [
-1.1842915318,
-1.0070436163
],
"D": [
0.7859602988000001,
-3.0498934229
],
"E": [
1.0826675821,
-3.4507492637
],... |
3obj_4rel_1extra_gen7117 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, M. There is an acute triangle with vertices A, B, C. There is a square with vertices D, E, F, G. There is a square with vertices H, I, J, K. There is a line segment AD. There is a line segment CF. There is a line segment EG. There is a li... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I, J, K, M = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "M"])
triangleABC = scene.add.acute_triangle(A, B, C)
square1 = scene.add.square(D, E, F, G)
square2 = scene.add.square(H, I, J, K)
line_AD = scene... | {
"triangleABC": "acute_triangle(A, B, C)",
"square1": "square(D, E, F, G)",
"square2": "square(H, I, J, K)",
"line_AD": "line_segment(A, D)",
"line_CF": "line_segment(C, F)",
"line_EG": "line_segment(E, G)",
"line_HI": "line_segment(H, I)"
} | [
"similar(square1, square2)",
"perpendicular(line_AD, line_CF)",
"lines_intersect_at(line_AD, line_CF, M)",
"is_centroid(M, triangleABC)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"M"
] | [
"scene.constraint.eq(scene.get_object('square1').area, scene.get_object('triangleABC').circumradius)",
"scene.constraint.leq(scene.get_object('line_CF').slope, 0)"
] | {
"points": {
"A": [
0.143277352,
-3.0619341886
],
"B": [
3.2767647176,
2.1661198248
],
"C": [
-2.4113847758,
-0.154534153
],
"D": [
0.44156647060000004,
1.1296956892
],
"E": [
0.6040468224000001,
-0.658856392
],
"... |
3obj_4rel_1extra_gen7118 | hard | Diagram description: In the diagram, two circles are present: circle1 with center A and circle2 with center B. A minor arc minor_arc1 is drawn on circle1 with center A, starting at point C and ending at point D. Line segment CD is a chord of circle1, and its midpoint E lies on circle1. Additionally, line segments AC 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)
circle2 = scene.add.circle(B)
minor_arc1 = scene.add.minor_arc(A, C, D)
line_CD = scene.add.line_segment(C, D)
line_AB = scene.add.line_segment(A, B)
line_AC = scene.a... | {
"circle1": "circle(A)",
"circle2": "circle(B)",
"minor_arc1": "minor_arc(A, C, D)",
"line_CD": "line_segment(C, D)",
"line_AB": "line_segment(A, B)",
"line_AC": "line_segment(A, C)"
} | [
"is_chord(line_CD, circle1)",
"is_midpoint(E, line_CD)",
"perpendicular(line_AB, line_AC)",
"point_lies_on(E, circle1)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [] | {
"points": {
"A": [
0.8862150944,
-4.2938807827
],
"B": [
4.18736669,
-2.4503126405
],
"C": [
-3.5499664995,
3.6496868054
],
"D": [
-3.1966939426,
3.8369141248
],
"E": [
-3.3743525843,
3.7452333269
]
},
"circles":... |
3obj_4rel_1extra_gen7119 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is a rhombus with points A, B, C, D. There is a right isosceles triangle with points E, F, G. There is a minor arc with center H, start point I, end point J. There is a line segment AC. There is a line segment BD. There is a line segme... | 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"])
rhombus1 = scene.add.rhombus(A, B, C, D)
triangle1 = scene.add.right_isosceles_triangle(E, F, G)
arc1 = scene.add.minor_arc(H, I, J)
line_AC = scene.add.line... | {
"rhombus1": "rhombus(A, B, C, D)",
"triangle1": "right_isosceles_triangle(E, F, G)",
"arc1": "minor_arc(H, I, J)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EF": "line_segment(E, F)",
"line_FG": "line_segment(F, G)"
} | [
"perpendicular(line_AC, line_BD)",
"parallel(line_EF, line_BD)",
"is_orthocenter(F, triangle1)",
"point_lies_on(I, arc1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J"
] | [
"scene.constraint.eq(scene.get_object('arc1').central_angle, 90)",
"scene.constraint.leq(scene.get_object('triangle1').area, 10)"
] | {
"points": {
"A": [
-2.182765785,
-4.0857007081
],
"B": [
0.5157044859000001,
-0.5373426826000001
],
"C": [
3.6816598941,
2.6010189193
],
"D": [
0.9831896079,
-0.9473391821
],
"E": [
1.2263676118,
0.0207212879
],
... |
3obj_4rel_1extra_gen7120 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is an equilateral triangle ABC. There is a major arc with center D, start point E, end point F. There is a square GHIJ. There is a line segment AD. There is a line segment CF. Line segments AD and CF intersect at point K. The angle ... | 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"])
triangle1 = scene.add.equilateral_triangle(A, B, C)
arc1 = scene.add.major_arc(D, E, F)
square1 = scene.add.square(G, H, I, J)
line_AD = scene.add.li... | {
"triangle1": "equilateral_triangle(A, B, C)",
"arc1": "major_arc(D, E, F)",
"square1": "square(G, H, I, J)",
"line_AD": "line_segment(A, D)",
"line_CF": "line_segment(C, F)"
} | [
"lines_intersect_at(line_AD, line_CF, K)",
"obtuse_angle(A, K, C)",
"is_centroid(K, triangle1)",
"point_lies_on(G, arc1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [
"scene.constraint.eq(scene.get_object('square1').area, 4)",
"scene.constraint.leq(scene.get_object('line_AD').length, scene.get_object('triangle1').area)"
] | {
"points": {
"A": [
-2.3643288419,
1.8116450915
],
"B": [
0.9888378628000001,
-1.4961551116
],
"C": [
2.1768954257,
3.0616727166
],
"D": [
0.9383249681,
0.9507692235
],
"E": [
0.51578594,
1.661567172
],
"F": [
... |
3obj_4rel_1extra_gen7122 | hard | Diagram description: In the diagram, a circle with center A is tangent to line segment BG at point G, where G is the centroid of rectangle BCDE. Right triangle FGH has its right angle at G. The diagonals BD and CF of the rectangle intersect at point G, which is also the vertex of the right angle in triangle FGH. The ad... | 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)
rectangle1 = scene.add.rectangle(B, C, D, E)
right_triangle1 = scene.add.right_triangle(F, G, H)
line_BG = scene.add.line_segment(B, G)
line_GH... | {
"circle1": "circle(A)",
"rectangle1": "rectangle(B, C, D, E)",
"right_triangle1": "right_triangle(F, G, H)",
"line_BG": "line_segment(B, G)",
"line_GH": "line_segment(G, H)",
"line_HF": "line_segment(H, F)",
"line_BD": "line_segment(B, D)",
"line_CF": "line_segment(C, F)"
} | [
"tangent_to_circle(line_BG, circle1, G)",
"is_centroid(G, rectangle1)",
"right_angle(F, G, H)",
"lines_intersect_at(line_BD, line_CF, G)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"scene.constraint.eq(scene.get_object('line_GH').length, scene.get_object('line_HF').length)"
] | {
"points": {
"A": [
2.3031539215,
-1.3021467089
],
"B": [
0.8783671184,
-4.3692135226
],
"C": [
0.8641102900000001,
-4.5716621919
],
"D": [
2.426683866,
-4.6817617956
],
"E": [
2.4409528101,
-4.4793252931
],
"F": ... |
3obj_4rel_1extra_gen7126 | hard | Diagram description: The diagram contains points A, B, C, O, D, E, F, G. There is an isosceles triangle ABC. There is a circle with center O. There is an isosceles trapezoid DEFG. There is a line segment AB. There is a line segment BC. There is a line segment AC. There is a line segment DF. The circle is the circumcirc... | 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"])
triangle_ABC = scene.add.isosceles_triangle(A, B, C)
circle_O = scene.add.circle(O)
trapezoid_DEFG = scene.add.isosceles_trapezoid(D, E, F, G)
line_AB = scene.add.line_segme... | {
"triangle_ABC": "isosceles_triangle(A, B, C)",
"circle_O": "circle(O)",
"trapezoid_DEFG": "isosceles_trapezoid(D, E, F, G)",
"line_AB": "line_segment(A, B)",
"line_BC": "line_segment(B, C)",
"line_AC": "line_segment(A, C)",
"line_DF": "line_segment(D, F)"
} | [
"is_circumcircle(circle_O, triangle_ABC)",
"parallel(line_AB, line_DF)",
"lines_intersect_at(line_AB, line_BC, B)",
"is_orthocenter(B, triangle_ABC)"
] | [
"A",
"B",
"C",
"O",
"D",
"E",
"F",
"G"
] | [
"scene.constraint.leq(scene.get_object('line_DF').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": [
3.094605581,
-2.9952285894
],
"B": [
2.4113845633,
0.2510647381
],
"C": [
5.6576777598,
0.9342857263000001
],
"O": [
4.3761410362,
-1.0304715109
],
"D": [
-1.577987554,
1.7770658474
],
"E": [
... |
3obj_4rel_1extra_gen7127 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M, N. There is a rhombus ABCD. There is a rectangle EFGH. There is a parallelogram IJKL. 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 line... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I, J, K, L, M, N = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N"])
rhombus1 = scene.add.rhombus(A, B, C, D)
rectangle1 = scene.add.rectangle(E, F, G, H)
parallelogram1 = scene.add.parallelogra... | {
"rhombus1": "rhombus(A, B, C, D)",
"rectangle1": "rectangle(E, F, G, H)",
"parallelogram1": "parallelogram(I, J, K, L)",
"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_EG, M)",
"line_extensions_intersect_at(line_BD, line_FH, N)",
"perpendicular(line_AC, line_BD)",
"parallel(line_AC, line_EG)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L",
"M",
"N"
] | [
"scene.constraint.eq(scene.get_object('rhombus1').inradius, 2.0)"
] | {
"points": {
"A": [
-3.4490177172,
0.5243766081
],
"B": [
-0.0692258597,
2.7274513051
],
"C": [
2.5556339619,
-0.3363117586
],
"D": [
-0.8241579802000001,
-2.5393865658
],
"E": [
-2.4892365543,
0.3868035922
],
"F"... |
3obj_4rel_1extra_gen7128 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M. There is a rectangle with A, B, C, D. There is a rectangle with E, F, G, H. There is a trapezoid with I, J, K, L. There is a line segment AC. There is a line segment EG. There is a line segment IK. There is a line segment JL. The re... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I, J, K, L, M = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M"])
rect1 = scene.add.rectangle(A, B, C, D)
rect2 = scene.add.rectangle(E, F, G, H)
trapezoid1 = scene.add.trapezoid(I, J, K, L)
line_AC ... | {
"rect1": "rectangle(A, B, C, D)",
"rect2": "rectangle(E, F, G, H)",
"trapezoid1": "trapezoid(I, J, K, L)",
"line_AC": "line_segment(A, C)",
"line_EG": "line_segment(E, G)",
"line_IK": "line_segment(I, K)",
"line_JL": "line_segment(J, L)"
} | [
"congruent(rect1, rect2)",
"parallel(line_AC, line_EG)",
"lines_intersect_at(line_AC, line_IK, M)",
"right_angle(J, M, L)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L",
"M"
] | [
"scene.constraint.eq(scene.get_object('rect1').area, scene.get_object('trapezoid1').area)"
] | {
"points": {
"A": [
-3.1369765622,
-4.5550535826
],
"B": [
2.4257685679,
-4.8336404551
],
"C": [
2.8325034629,
3.2879246536
],
"D": [
-2.7302417052,
3.5665116347
],
"E": [
2.7671008083,
4.3310081055000005
],
"F": ... |
3obj_4rel_1extra_gen7130 | hard | Diagram description: The diagram contains points A, B, C, D, E, O. There is a triangle with vertices A, B, C. There is a quadrilateral with vertices A, B, C, D. There is a circle with center O. There is a line segment AC. There is a line segment AD. There is a line segment BC. E is the midpoint of line AC. The angle BA... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, O = scene.add.points(["A", "B", "C", "D", "E", "O"])
triangleABC = scene.add.triangle(A, B, C)
quadrilateralABCD = scene.add.quadrilateral(A, B, C, D)
circleO = scene.add.circle(O)
line_AC = scene.add.line_segment(A, C)
line_AD = scene.add.li... | {
"triangleABC": "triangle(A, B, C)",
"quadrilateralABCD": "quadrilateral(A, B, C, D)",
"circleO": "circle(O)",
"line_AC": "line_segment(A, C)",
"line_AD": "line_segment(A, D)",
"line_BC": "line_segment(B, C)"
} | [
"is_midpoint(E, line_AC)",
"obtuse_angle(B, A, D)",
"is_orthocenter(O, triangleABC)",
"is_circumcircle(circleO, triangleABC)"
] | [
"A",
"B",
"C",
"D",
"E",
"O"
] | [
"scene.constraint.eq(scene.get_object('triangleABC').area, 12.0)",
"scene.constraint.leq(scene.get_object('line_AD').length, 6.0)",
"scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('D')), 120)"
] | {
"points": {
"A": [
2.2513839659,
-1.114495913
],
"B": [
-1.3715201297,
-4.9338382221
],
"C": [
-2.8677151599,
0.1133606238
],
"D": [
0.6499452507,
4.2877248851
],
"E": [
-0.3081645926,
-0.5005672626000001
],
"O":... |
3obj_4rel_1extra_gen7131 | hard | Diagram description: The diagram contains points A, B, C, O, H, D, E, F, P, Q, R, S, T, U. There is a triangle ABC. There is a circle with center O. There is a regular hexagon PQRSTU. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment PQ. Line AD is an altitude o... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O, H, D, E, F, P, Q, R, S, T, U = scene.add.points(["A", "B", "C", "O", "H", "D", "E", "F", "P", "Q", "R", "S", "T", "U"])
triangleABC = scene.add.triangle(A, B, C)
circleO = scene.add.circle(O)
hexagonPQRSTU = scene.add.regular_hexagon(P, Q, R, S,... | {
"triangleABC": "Triangle(A, B, C)",
"circleO": "Circle(O)",
"hexagonPQRSTU": "RegularHexagon(P, Q, R, S, T, U)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)",
"line_PQ": "line_segment(P, Q)"
} | [
"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",
"H",
"D",
"E",
"F",
"P",
"Q",
"R",
"S",
"T",
"U"
] | [
"scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BE').length)",
"scene.constraint.eq(scene.get_object('line_AD').slope, scene.get_object('line_CF').slope)"
] | {
"points": {
"A": [
0.15603326480000002,
-0.5715616036
],
"B": [
-1.1424225168,
2.5929062798
],
"C": [
-1.6207273918,
0.548017944
],
"O": [
0.053190038700000004,
1.2348659978
],
"H": [
-2.7134922918,
0.09962809040000001
... |
3obj_4rel_1extra_gen7134 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is an isosceles trapezoid ABCD. There is a circle with center E. There is a regular hexagon FGHIJK. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment EG. E is the centroid of... | 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"])
trapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)
circle1 = scene.add.circle(E)
hexagon1 = scene.add.regular_hexagon(F, G, H, I, J, K)
line_AC =... | {
"trapezoid1": "isosceles_trapezoid(A, B, C, D)",
"circle1": "circle(E)",
"hexagon1": "regular_hexagon(F, G, H, I, J, K)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EF": "line_segment(E, F)",
"line_EG": "line_segment(E, G)"
} | [
"is_centroid(E, trapezoid1)",
"line_intersects_circle_at(line_AC, circle1, A, C)",
"perpendicular(line_AC, line_BD)",
"is_radius(line_EF, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [
"scene.constraint.eq(scene.get_object('hexagon1').inradius, scene.get_object('circle1').diameter)"
] | {
"points": {
"A": [
1.649751321,
-0.7031706819
],
"B": [
1.3707432169,
-1.4477520787
],
"C": [
0.664149917,
-1.0830987448
],
"D": [
0.9431575844000001,
-0.3385182989
],
"E": [
1.1569505222,
-0.8931350504000001
],
... |
3obj_4rel_1extra_gen7135 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a square with points A, B, C, D. There is a circle with center E. There is a rhomboid with points F, G, H, I. There is a line segment AC. There is a line segment EF. There is a line segment GI. The line segment AC and the line segment ... | 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"])
square1 = scene.add.square(A, B, C, D)
circle1 = scene.add.circle(E)
rhomboid1 = scene.add.rhomboid(F, G, H, I)
line_AC = scene.add.line_segment(A, C)
line_EF = scen... | {
"square1": "square(A, B, C, D)",
"circle1": "circle(E)",
"rhomboid1": "rhomboid(F, G, H, I)",
"line_AC": "line_segment(A, C)",
"line_EF": "line_segment(E, F)",
"line_GI": "line_segment(G, I)"
} | [
"lines_intersect_at(line_AC, line_EF, E)",
"line_extension_intersects_circle_at(line_GI, circle1, G, I)",
"is_circumcircle(circle1, square1)",
"perpendicular(line_AC, line_EF)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [] | {
"points": {
"A": [
-0.9219870589,
0.1038967617
],
"B": [
0.7887289015000001,
-0.1239471528
],
"C": [
1.0165735453,
1.5867698995000001
],
"D": [
-0.6941428386,
1.8146140462
],
"E": [
0.047292673,
0.8453335681
],
"... |
3obj_4rel_1extra_gen7136 | hard | Diagram description: The diagram contains points A, B, C, O, P, Q, R, S, T, U. There is an obtuse triangle ABC with vertices A, B, C. There is a circle with center O. There is a regular hexagon PQRSTU with vertices P, Q, R, S, T, U. There is a line segment AP. There is a line segment BQ. There is a line segment CR. The... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O, P, Q, R, S, T, U = scene.add.points(["A", "B", "C", "O", "P", "Q", "R", "S", "T", "U"])
triangleABC = scene.add.obtuse_triangle(A, B, C)
circleO = scene.add.circle(O)
hexagonPQRSTU = scene.add.regular_hexagon(P, Q, R, S, T, U)
line_AP = scene.ad... | {
"triangleABC": "obtuse_triangle(A, B, C)",
"circleO": "circle(O)",
"hexagonPQRSTU": "regular_hexagon(P, Q, R, S, T, U)",
"line_AP": "line_segment(A, P)",
"line_BQ": "line_segment(B, Q)",
"line_CR": "line_segment(C, R)"
} | [
"is_circumcircle(circleO, triangleABC)",
"is_centroid(O, hexagonPQRSTU)",
"perpendicular(line_AP, line_BQ)",
"parallel(line_BQ, line_CR)"
] | [
"A",
"B",
"C",
"O",
"P",
"Q",
"R",
"S",
"T",
"U"
] | [
"scene.constraint.eq(scene.get_object('triangleABC').area, 2 * scene.get_object('hexagonPQRSTU').inradius)",
"scene.constraint.leq(scene.get_object('line_AP').length, scene.get_object('circleO').area)"
] | {
"points": {
"A": [
0.6489474391000001,
-2.606754866
],
"B": [
-1.0156178244,
-1.0186878912
],
"C": [
-0.42528626220000004,
-3.7327742284000003
],
"O": [
-0.7204755063,
-2.3757362089000003
],
"P": [
-1.7396229068,
-2.2038... |
3obj_4rel_1extra_gen7139 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L. There is a minor arc with center A and endpoints B and C. There is a scalene triangle with vertices D, E, and F. There is a triangle with vertices G, H, and I. There is a line segment DE. There is a line segment EF. There is a line seg... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I, J, K, L = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L"])
arc1 = scene.add.minor_arc(A, B, C)
triangle1 = scene.add.scalene_triangle(D, E, F)
triangle2 = scene.add.triangle(G, H, I)
line_DE = scene.a... | {
"arc1": "minor_arc(A, B, C)",
"triangle1": "scalene_triangle(D, E, F)",
"triangle2": "triangle(G, H, I)",
"line_DE": "line_segment(D, E)",
"line_EF": "line_segment(E, F)",
"line_FD": "line_segment(F, D)",
"line_GH": "line_segment(G, H)",
"line_HI": "line_segment(H, I)",
"line_IG": "line_segment(I, G... | [
"is_midpoint(J, line_DE)",
"angle_bisector(D, E, F, line_EK)",
"is_orthocenter(L, triangle1)",
"perpendicular(line_EF, line_GH)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L"
] | [
"scene.constraint.eq(scene.get_object('arc1').central_angle, 90)",
"scene.constraint.leq(scene.get_object('triangle1').area, 10)"
] | {
"points": {
"A": [
2.6006218534,
-0.103118729
],
"B": [
-2.1463413569,
-3.6912975130000003
],
"C": [
-0.9875569492,
4.6438444761
],
"D": [
3.622552735,
-2.9331645201
],
"E": [
-3.0746062404,
-4.8387503121
],
"F":... |
3obj_4rel_1extra_gen7140 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a rhombus ABCD. There is a circle with center E. There is a regular hexagon FGHIJK. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment GH. Line segment AC extended intersec... | 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"])
rhombus1 = scene.add.rhombus(A, B, C, D)
circle1 = scene.add.circle(E)
hexagon1 = scene.add.regular_hexagon(F, G, H, I, J, K)
line_AC = scene.add.lin... | {
"rhombus1": "rhombus(A, B, C, D)",
"circle1": "circle(E)",
"hexagon1": "regular_hexagon(F, G, H, I, J, K)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EF": "line_segment(E, F)",
"line_GH": "line_segment(G, H)"
} | [
"line_extension_intersects_circle_at(line_AC, circle1, A, C)",
"collinear(A, E, C)",
"is_centroid(E, rhombus1)",
"is_circumcircle(circle1, hexagon1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [
"scene.constraint.eq(scene.get_object('rhombus1').area, scene.get_object('circle1').area)",
"scene.constraint.eq(scene.get_object('hexagon1').diagonal, 2 * scene.get_object('circle1').radius)"
] | {
"points": {
"A": [
-1.5853847025999999,
2.0325741675
],
"B": [
-2.3551039874,
2.0730894916000002
],
"C": [
-2.066069063,
1.3585487793
],
"D": [
-1.2963495583,
1.3180336491
],
"E": [
-1.8257269533,
1.6955615991
],
... |
3obj_4rel_1extra_gen7141 | hard | Diagram description: The diagram contains points A, B, C, O, P, Q, R, S. There is a triangle ABC with vertices A, B, C. There is a circle with center O. There is a rhombus PQRS with vertices P, Q, R, S. There is a line segment AP. There is a line segment BQ. There is a line segment CR. There is a line segment OS. O is ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O, P, Q, R, S = scene.add.points(["A", "B", "C", "O", "P", "Q", "R", "S"])
triangleABC = scene.add.triangle(A, B, C)
circleO = scene.add.circle(O)
rhombusPQRS = scene.add.rhombus(P, Q, R, S)
line_AP = scene.add.line_segment(A, P)
line_BQ = scene.ad... | {
"triangleABC": "triangle(A, B, C)",
"circleO": "circle(O)",
"rhombusPQRS": "rhombus(P, Q, R, S)",
"line_AP": "line_segment(A, P)",
"line_BQ": "line_segment(B, Q)",
"line_CR": "line_segment(C, R)",
"line_OS": "line_segment(O, S)"
} | [
"is_orthocenter(O, triangleABC)",
"line_extension_intersects_circle_at(line_AP, circleO, A, P)",
"is_circumcircle(circleO, triangleABC)",
"perpendicular(line_OS, line_AP)"
] | [
"A",
"B",
"C",
"O",
"P",
"Q",
"R",
"S"
] | [
"scene.constraint.eq(scene.get_object('triangleABC').area, scene.get_object('rhombusPQRS').inradius * 2)",
"scene.constraint.leq(scene.get_object('line_AP').slope, scene.get_object('line_BQ').slope + 1)"
] | {
"points": {
"A": [
0.1186358415,
-1.6398583132
],
"B": [
-1.3894200788,
-2.6992316599
],
"C": [
0.2820527392,
-3.4755606903
],
"O": [
-0.3295767946,
-2.6048833855
],
"P": [
0.7140353049,
-2.397416769
],
"Q": [
... |
3obj_4rel_1extra_gen7142 | hard | 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 with center A. There is a minor arc DE with center A. There is a line segment BC. There is a line segment DE. There is a line segment AD. line BC intersects line DE at point F. angle BFD is obtuse... | 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)
semicircle1 = scene.add.major_arc(A, B, C)
minor_arc1 = scene.add.minor_arc(A, D, E)
line_BC = scene.add.line_segment(B, C)
line_DE = scene.add.line_segment(D,... | {
"circle1": "circle(A)",
"semicircle1": "major_arc(A, B, C)",
"minor_arc1": "minor_arc(A, D, E)",
"line_BC": "line_segment(B, C)",
"line_DE": "line_segment(D, E)",
"line_AD": "line_segment(A, D)"
} | [
"lines_intersect_at(line_BC, line_DE, F)",
"obtuse_angle(B, F, D)",
"perpendicular_bisector_at(line_AD, line_BC)",
"point_lies_on(F, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F"
] | [] | {
"points": {
"A": [
-1.7264268923000001,
-1.0647963123
],
"B": [
-0.065409169,
-2.3957705741
],
"C": [
-0.3604440188,
0.5675526186000001
],
"D": [
0.4376636005,
-0.8493347762000001
],
"E": [
-3.8904904219,
-1.2805288159
... |
3obj_4rel_1extra_gen7145 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M. There is a trapezoid ABCD. There is a parallelogram EFGH. There is a right trapezoid IJKL. There are line segments AD, BC, EF, and GH. Right angle at D of trapezoid ABCD. Lines AD and BC extend to intersect at M. Lines EF and GH are... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I, J, K, L, M = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M"])
trapezoid1 = scene.add.trapezoid(A, B, C, D)
parallelogram1 = scene.add.parallelogram(E, F, G, H)
right_trapezoid1 = scene.add.right_... | {
"trapezoid1": "trapezoid(A, B, C, D)",
"parallelogram1": "parallelogram(E, F, G, H)",
"right_trapezoid1": "right_trapezoid(I, J, K, L)",
"line_AD": "line_segment(A, D)",
"line_BC": "line_segment(B, C)",
"line_EF": "line_segment(E, F)",
"line_GH": "line_segment(G, H)"
} | [
"right_angle(A, D, B)",
"line_extensions_intersect_at(line_AD, line_BC, M)",
"parallel(line_EF, line_GH)",
"is_centroid(M, trapezoid1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L",
"M"
] | [
"scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BC').length)",
"scene.constraint.eq(scene.get_object('right_trapezoid1').area, 2 * scene.get_object('parallelogram1').area)"
] | {
"points": {
"A": [
-3.1724078177,
-6.4737986948
],
"B": [
9.0708089957,
3.5514237617999997
],
"C": [
-2.5782770157,
-7.1221995753
],
"D": [
9.5892962484,
2.8410809356
],
"E": [
-2.2661209803,
2.4262704373
],
"F":... |
3obj_4rel_1extra_gen7146 | hard | Diagram description: In the diagram, a regular pentagon ABCDE is constructed. A triangle FGH is positioned such that it is similar to another triangle IJK. The line segment GH serves as a side of triangle FGH and is bisected perpendicularly by line IK. The point K is the orthocenter of triangle FGH, meaning it is the i... | 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"])
pentagon1 = scene.add.regular_pentagon(A, B, C, D, E)
triangle1 = scene.add.triangle(F, G, H)
triangle2 = scene.add.triangle(I, J, K)
line_GH = scene... | {
"pentagon1": "regular_pentagon(A, B, C, D, E)",
"triangle1": "triangle(F, G, H)",
"triangle2": "triangle(I, J, K)",
"line_GH": "line_segment(G, H)",
"line_IK": "line_segment(I, K)",
"line_HJ": "line_segment(H, J)"
} | [
"similar(triangle1, triangle2)",
"perpendicular_bisector_at(line_GH, line_IK)",
"is_orthocenter(K, triangle1)",
"lines_intersect_at(line_GH, line_HJ, J)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [] | {
"points": {
"A": [
5.1282036754,
14.5209158814
],
"B": [
-4.587539857,
18.8516578605
],
"C": [
-11.7086501011,
10.9497095332
],
"D": [
-6.3939947373,
1.7352949105
],
"E": [
4.0117531602,
3.9424218145000003
],
"F"... |
3obj_4rel_1extra_gen7147 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, M, N. There is a trapezoid with points A, B, C, D. There is a trapezoid with points E, F, G, H. There is a major arc with center I, start point J, and end point K. There is a line segment AB. There is a line segment CD. There is a line se... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I, J, K, M, N = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "M", "N"])
trapezoid1 = scene.add.trapezoid(A, B, C, D)
trapezoid2 = scene.add.trapezoid(E, F, G, H)
arc1 = scene.add.major_arc(I, J, K)
line_AB... | {
"trapezoid1": "trapezoid(A, B, C, D)",
"trapezoid2": "trapezoid(E, F, G, H)",
"arc1": "major_arc(I, J, K)",
"line_AB": "line_segment(A, B)",
"line_CD": "line_segment(C, D)",
"line_EF": "line_segment(E, F)",
"line_GH": "line_segment(G, H)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B,... | [
"parallel(line_AB, line_CD)",
"parallel(line_EF, line_GH)",
"lines_intersect_at(line_AC, line_BD, M)",
"lines_intersect_at(line_EG, line_FH, N)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"M",
"N"
] | [] | {
"points": {
"A": [
0.101676396,
1.6278998421000002
],
"B": [
0.4449294467,
1.0208960247
],
"C": [
-1.8319485465,
1.6432971527
],
"D": [
-2.5708064022,
2.9498828905
],
"E": [
1.5901597673999999,
-1.4427053409
],
"... |
3obj_4rel_1extra_gen7149 | hard | Diagram description: In the diagram, trapezoid ABCD has parallel sides AB and CD. A semicircle is constructed with diameter FG, centered at E, such that points A and G lie on the semicircle. A regular pentagon HIKLJ is positioned so that its vertices are arranged in a way that creates a complex geometric configuration.... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I, J, K, L, M = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M"])
trapezoid1 = scene.add.trapezoid(A, B, C, D)
semicircle1 = scene.add.major_arc(E, F, G)
pentagon1 = scene.add.regular_pentagon(H, I, ... | {
"trapezoid1": "trapezoid(A, B, C, D)",
"semicircle1": "major_arc(E, F, G)",
"pentagon1": "regular_pentagon(H, I, J, K, L)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EF": "line_segment(E, F)",
"line_FG": "line_segment(F, G)"
} | [
"point_lies_on(A, semicircle1)",
"point_lies_on(G, semicircle1)",
"lines_intersect_at(line_AC, line_BD, M)",
"perpendicular(line_AC, line_BD)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L",
"M"
] | [
"scene.constraint.eq(scene.get_object('trapezoid1').area, scene.get_object('pentagon1').area)"
] | {
"points": {
"A": [
0.31061986550000004,
-0.2508715875
],
"B": [
1.1891664899,
0.343827353
],
"C": [
3.672268576,
-0.6337446009000001
],
"D": [
0.8610947964000001,
-2.5366624323
],
"E": [
-0.5669773011,
0.9272540199
]... |
3obj_5rel_2extra_gen7103 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, O. There is a triangle ABC. There is a right triangle DEF. There is a circle with center O. There is a line segment AD. Point A lies on the circle. Point B lies on the circle. Point C lies on the circle. The circle is the circumcircle of triangle ABC. L... | 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.triangle(A, B, C)
right_triangleDEF = scene.add.right_triangle(D, E, F)
circleO = scene.add.circle(O)
line_AD = scene.add.line_segment(A, D)
### relationshi... | {
"triangleABC": "Triangle(A, B, C)",
"right_triangleDEF": "RightTriangle(D, E, F)",
"circleO": "Circle(O)",
"line_AD": "line_segment(A, D)"
} | [
"point_lies_on(A, circleO)",
"point_lies_on(B, circleO)",
"point_lies_on(C, circleO)",
"is_circumcircle(circleO, triangleABC)",
"tangent_to_circle(line_AD, circleO, A)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"O"
] | [
"scene.constraint.eq(scene.get_object('triangleABC').area, scene.get_object('right_triangleDEF').area)",
"scene.constraint.eq(scene.get_object('circleO').diameter, 4)"
] | {
"points": {
"A": [
0.7088491049,
2.7587586459
],
"B": [
3.8013608132,
0.9867862864
],
"C": [
3.0418379131,
2.6558366181
],
"D": [
-1.762730124,
1.1418175518
],
"E": [
-0.2959912779,
0.3776173037
],
"F": [
0... |
3obj_5rel_2extra_gen7105 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a major arc with center A, start point B, and end point C. There is a triangle with vertices D, E, F. There is a major arc with center G, start point H, and end point I. There is a line segment DE. There is a line segment EF. There is ... | 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"])
semicircle1 = scene.add.major_arc(A, B, C)
triangle1 = scene.add.triangle(D, E, F)
major_arc1 = scene.add.major_arc(G, H, I)
line_DE = scene.add.line_segment(D, E)
l... | {
"semicircle1": "major_arc(A, B, C)",
"triangle1": "triangle(D, E, F)",
"major_arc1": "major_arc(G, H, I)",
"line_DE": "line_segment(D, E)",
"line_EF": "line_segment(E, F)",
"line_FD": "line_segment(F, D)",
"line_GH": "line_segment(G, H)",
"line_HI": "line_segment(H, I)"
} | [
"translation(semicircle1, major_arc1, 3, 0)",
"parallel(line_DE, line_GH)",
"is_orthocenter(F, triangle1)",
"right_angle(D, F, E)",
"point_lies_on(I, semicircle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [
"scene.constraint.eq(scene.get_object('line_DE').length, scene.get_object('line_GH').length)",
"scene.constraint.eq(scene.angle(scene.get_object('D'), scene.get_object('F'), scene.get_object('E')), 90)"
] | {
"points": {
"A": [
2.4432653561,
-5.7687302163
],
"B": [
-2.551277753,
-2.2240408219
],
"C": [
3.9432861281,
0.1693012144
],
"D": [
-3.2956986301,
2.4710482415
],
"E": [
1.6988694322,
-1.07362783
],
"F": [
... |
3obj_5rel_2extra_gen7106 | hard | Diagram description: In the diagram, right triangle ABC has its right angle at vertex B. A minor arc EF is centered at point D. Trapezoid GHIJ has parallel sides GH and IJ. Line segment BC serves as an altitude of triangle ABC from vertex B to hypotenuse AC. Lines GH and IJ are parallel, and they intersect line AB at p... | 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"])
triangleABC = scene.add.right_triangle(A, B, C)
arc1 = scene.add.minor_arc(D, E, F)
trapezoidGHIJ = scene.add.trapezoid(G, H, I, J)
line_AB = scene.a... | {
"triangleABC": "right_triangle(A, B, C)",
"arc1": "minor_arc(D, E, F)",
"trapezoidGHIJ": "trapezoid(G, H, I, J)",
"line_AB": "line_segment(A, B)",
"line_BC": "line_segment(B, C)",
"line_AC": "line_segment(A, C)",
"line_GH": "line_segment(G, H)",
"line_IJ": "line_segment(I, J)"
} | [
"perpendicular(line_AB, line_BC)",
"is_altitude(line_BC, triangleABC, B)",
"parallel(line_GH, line_IJ)",
"lines_intersect_at(line_AB, line_GH, K)",
"point_lies_on(K, arc1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [] | {
"points": {
"A": [
8.0330410986,
4.2831324341
],
"B": [
-5.7238258472,
-3.1729069171
],
"C": [
-5.8189644968,
-2.9973591708000002
],
"D": [
-0.5597351023,
0.0405876638
],
"E": [
-0.14403308780000001,
-0.3769696723
],... |
3obj_5rel_2extra_gen7111 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, O. There is an equilateral triangle ABC. There is a rectangle DEFG. There is a circle with center O. There is a line segment AD. There is a line segment CF. There is a line segment OG. O is the orthocenter of triangle ABC. The extensions of line AD a... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, O = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "O"])
triangleABC = scene.add.equilateral_triangle(A, B, C)
rectangleDEFG = scene.add.rectangle(D, E, F, G)
circleO = scene.add.circle(O)
line_AD = scene.add.line_segment(A, D)
li... | {
"triangleABC": "equilateral_triangle(A, B, C)",
"rectangleDEFG": "rectangle(D, E, F, G)",
"circleO": "circle(O)",
"line_AD": "line_segment(A, D)",
"line_CF": "line_segment(C, F)",
"line_OG": "line_segment(O, G)"
} | [
"is_orthocenter(O, triangleABC)",
"line_extensions_intersect_at(line_AD, line_CF, G)",
"is_circumcircle(circleO, triangleABC)",
"is_midpoint(G, line_CF)",
"perpendicular(line_AD, line_CF)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"O"
] | [
"scene.constraint.eq(scene.get_object('triangleABC').circumradius, scene.get_object('circleO').radius)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 60)"
] | {
"points": {
"A": [
-2.2252149134,
0.4728336355
],
"B": [
-1.2424332017,
1.5840625336
],
"C": [
-0.7714715945,
0.1773341383
],
"D": [
-1.192763859,
-0.1377302426
],
"E": [
-1.4399682297,
-0.555746415
],
"F": [
... |
3obj_5rel_2extra_gen7113 | hard | Diagram description: In the diagram, rectangle ABCD and kite EFGH are positioned such that the diagonal AC of rectangle ABCD is perpendicular to the diagonal EG of kite EFGH. A right angle is formed at vertex B of rectangle ABCD. The diagonals AC and FH of rectangle ABCD and kite respectively intersect at point M, whic... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I, J, K, L, M = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M"])
rect1 = scene.add.rectangle(A, B, C, D)
kite1 = scene.add.kite(E, F, G, H)
rect2 = scene.add.rectangle(I, J, K, L)
line_AC = scene.ad... | {
"rect1": "rectangle(A, B, C, D)",
"kite1": "kite(E, F, G, H)",
"rect2": "rectangle(I, J, K, L)",
"line_AC": "line_segment(A, C)",
"line_EG": "line_segment(E, G)",
"line_FH": "line_segment(F, H)",
"line_IK": "line_segment(I, K)"
} | [
"perpendicular(line_AC, line_EG)",
"right_angle(A, B, C)",
"lines_intersect_at(line_AC, line_FH, M)",
"is_centroid(M, rect1)",
"parallel(line_IK, line_FH)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L",
"M"
] | [
"scene.constraint.eq(scene.get_object('rect1').area, scene.get_object('kite1').perimeter)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)"
] | {
"points": {
"A": [
1.2417837019,
-2.9820375951
],
"B": [
-2.575107821,
-1.1363940784
],
"C": [
-0.45749050820000003,
3.2429541819
],
"D": [
3.3594008322,
1.3973108511
],
"E": [
2.1453436334,
-1.0981414306
],
"F":... |
3obj_5rel_2extra_gen7114 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, M. There is a regular octagon with vertices A, B, C, D, E, F, G, H. There is a circle with center I. There is a minor arc with center I, start point J, end point K. There is a line segment AC. There is a line segment BD. There is a line s... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I, J, K, M = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "M"])
regular_octagon1 = scene.add.regular_octagon(A, B, C, D, E, F, G, H)
circle1 = scene.add.circle(I)
minor_arc1 = scene.add.minor_arc(I, J, K)
... | {
"regular_octagon1": "regular_octagon(A, B, C, D, E, F, G, H)",
"circle1": "circle(I)",
"minor_arc1": "minor_arc(I, J, K)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EF": "line_segment(E, F)",
"line_GH": "line_segment(G, H)"
} | [
"lines_intersect_at(line_AC, line_BD, M)",
"collinear(A, M, C)",
"is_centroid(I, regular_octagon1)",
"is_circumcircle(circle1, regular_octagon1)",
"point_lies_on(J, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"M"
] | [] | {
"points": {
"A": [
1.7212187973000002,
1.0326068229
],
"B": [
0.452917479,
1.4567718624000001
],
"C": [
-0.7438369596000001,
0.8598773753000001
],
"D": [
-1.168001999,
-0.408423943
],
"E": [
-0.571107512,
-1.6051783816
... |
3obj_5rel_2extra_gen7121 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is a kite ABCD. There is a minor arc FG with center E. There is a major arc HIJ with center H. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment EG. H is the centroid of kite AB... | 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"])
kite1 = scene.add.kite(A, B, C, D)
arc1 = scene.add.minor_arc(E, F, G)
semicircle1 = scene.add.major_arc(H, I, J)
line_AC = scene.add.line_segment(A, C)
line... | {
"kite1": "kite(A, B, C, D)",
"arc1": "minor_arc(E, F, G)",
"semicircle1": "major_arc(H, I, J)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EF": "line_segment(E, F)",
"line_EG": "line_segment(E, G)"
} | [
"is_centroid(H, kite1)",
"collinear(A, H, C)",
"perpendicular_bisector_at(line_AC, line_BD)",
"right_angle(F, E, G)",
"point_lies_on(F, semicircle1)"
] | [
"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('H'), scene.get_object('B')), 90)"
] | {
"points": {
"A": [
4.2550955995,
2.0035233535
],
"B": [
1.3923402582,
0.6486300259000001
],
"C": [
2.7472336178,
-2.2141303868
],
"D": [
5.6099943072,
-0.8592330297
],
"E": [
4.4467523954,
0.0594939731
],
"F": [
... |
3obj_5rel_2extra_gen7123 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is an isosceles triangle ABC with AB = BC. There is an isosceles trapezoid DEFG. There is a right triangle HIJ with angle I right. There is a line segment AB. There is a line segment BC. There is a line segment DF. There is a line segm... | 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"])
triangle_ABC = scene.add.isosceles_triangle(A, B, C)
trapezoid_DEFG = scene.add.isosceles_trapezoid(D, E, F, G)
triangle_HIJ = scene.add.right_triangle(H, I,... | {
"triangle_ABC": "isosceles_triangle(A, B, C)",
"trapezoid_DEFG": "isosceles_trapezoid(D, E, F, G)",
"triangle_HIJ": "right_triangle(H, I, J)",
"line_AB": "line_segment(A, B)",
"line_BC": "line_segment(B, C)",
"line_DF": "line_segment(D, F)",
"line_EG": "line_segment(E, G)",
"line_HI": "line_segment(H,... | [
"is_orthocenter(I, triangle_ABC)",
"line_extensions_intersect_at(line_AB, line_DF, H)",
"parallel(line_BC, line_EG)",
"perpendicular(line_HI, line_AB)",
"acute_angle(A, B, C)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J"
] | [
"scene.constraint.eq(scene.get_object('triangle_ABC').inradius, scene.get_object('triangle_HIJ').area)",
"scene.constraint.leq(scene.get_object('line_BC').length, scene.get_object('line_EG').length)"
] | {
"points": {
"A": [
-0.33878615300000003,
-2.7863200494
],
"B": [
1.4767167374,
-2.8234998004
],
"C": [
0.8697004651,
-1.1120767952
],
"D": [
1.2294150683,
-3.7250452925
],
"E": [
-0.1417021797,
-0.3659458521
],
"... |
3obj_5rel_2extra_gen7124 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a major arc with center A, start point B, end point C. There is a kite with vertices D, E, F, G. There is a circle with center H. There is a line segment DE. There is a line segment EF. There is a line segment HD. There is a line segme... | 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)
kite1 = scene.add.kite(D, E, F, G)
circle1 = scene.add.circle(H)
line_DE = scene.add.line_segment(D, E)
line_EF = scene.add... | {
"major_arc1": "major_arc(A, B, C)",
"kite1": "kite(D, E, F, G)",
"circle1": "circle(H)",
"line_DE": "line_segment(D, E)",
"line_EF": "line_segment(E, F)",
"line_HD": "line_segment(H, D)",
"line_HE": "line_segment(H, E)"
} | [
"obtuse_angle(D, H, E)",
"line_extensions_intersect_at(line_DE, line_EF, I)",
"is_radius(line_HD, circle1)",
"is_radius(line_HE, circle1)",
"point_lies_on(D, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [
"scene.constraint.eq(scene.get_object('kite1').area, 8.0)",
"scene.constraint.eq(scene.angle(scene.get_object('D'), scene.get_object('H'), scene.get_object('E')), 120)"
] | {
"points": {
"A": [
4.5216276079,
6.9077842515
],
"B": [
7.1066764748,
6.9771080772000005
],
"C": [
6.1937311508,
4.9351258429
],
"D": [
-1.7198861681,
0.5924043348
],
"E": [
-1.1402683079,
1.5912804394
],
"F": [
... |
3obj_5rel_2extra_gen7125 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M. There is a square ABCD. There is a rectangle EFGH. There is a major arc JK with center I. There is a line segment AC. There is a line segment EG. There is a line segment JL. M is the centroid of square ABCD. Line JL is the perpendic... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I, J, K, L, M = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M"])
square1 = scene.add.square(A, B, C, D)
rectangle1 = scene.add.rectangle(E, F, G, H)
major_arc1 = scene.add.major_arc(I, J, K)
line_AC... | {
"square1": "square(A, B, C, D)",
"rectangle1": "rectangle(E, F, G, H)",
"major_arc1": "major_arc(I, J, K)",
"line_AC": "line_segment(A, C)",
"line_EG": "line_segment(E, G)",
"line_perp": "line_segment(J, L)"
} | [
"perpendicular_bisector_at(line_AC, line_perp)",
"line_extensions_intersect_at(line_AC, line_EG, M)",
"is_centroid(M, square1)",
"right_angle(J, I, K)",
"point_lies_on(L, major_arc1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L",
"M"
] | [
"scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_EG').length)",
"scene.constraint.eq(scene.get_object('square1').area, 4 * scene.get_object('rectangle1').area)"
] | {
"points": {
"A": [
0.48239869080000003,
0.1828084792
],
"B": [
-0.5487002577,
-0.2814669524
],
"C": [
-0.08442535970000001,
-1.3125645512
],
"D": [
0.9466739655,
-0.8482900378
],
"E": [
3.1746592901,
0.43494857010000004
... |
3obj_5rel_2extra_gen7129 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is a triangle ABC. There is a square DEFG. There is a minor arc HIJ. There is a line segment AB. There is a line segment BC. There is a line segment AC. There is a line segment DE. There is a line segment EF. Point A lies on the minor ... | 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)
squareDEFG = scene.add.square(D, E, F, G)
minor_arcHIJ = scene.add.minor_arc(H, I, J)
lineAB = scene.add.line_segme... | {
"triangleABC": "triangle(A, B, C)",
"squareDEFG": "square(D, E, F, G)",
"minor_arcHIJ": "minor_arc(H, I, J)",
"lineAB": "line_segment(A, B)",
"lineBC": "line_segment(B, C)",
"lineAC": "line_segment(A, C)",
"lineDE": "line_segment(D, E)",
"lineEF": "line_segment(E, F)"
} | [
"point_lies_on(A, minor_arcHIJ)",
"point_lies_on(B, minor_arcHIJ)",
"parallel(lineAB, lineDE)",
"parallel(lineBC, lineEF)",
"is_orthocenter(C, triangleABC)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J"
] | [] | {
"points": {
"A": [
4.5365812414,
0.0773319962
],
"B": [
-3.755647314,
0.8898869180000001
],
"C": [
-3.77036837,
0.6904229479
],
"D": [
2.2553358237,
-1.2823126921
],
"E": [
2.4544706359,
-1.3018249684
],
"F": [
... |
3obj_5rel_2extra_gen7132 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a kite ABCD. There is a circle with center E. 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. The extensions of line segment AC and lin... | 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"])
kite1 = scene.add.kite(A, B, C, D)
circle1 = scene.add.circle(E)
minor_arc1 = scene.add.minor_arc(E, F, G)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_se... | {
"kite1": "kite(A, B, C, D)",
"circle1": "circle(E)",
"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)"
} | [
"similar(kite1, kite1)",
"line_extensions_intersect_at(line_AC, line_BD, H)",
"is_centroid(H, kite1)",
"is_radius(line_EF, circle1)",
"is_radius(line_EG, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
-3.4832926569,
-2.2800884285
],
"B": [
-0.8548646326,
-2.1372168393
],
"C": [
1.6754753277,
-2.8627689521
],
"D": [
-0.9529526746,
-3.0056407592
],
"E": [
-2.4162770781000003,
2.1463111523
],
"... |
3obj_5rel_2extra_gen7133 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a circle with center A. There is a minor arc BC with center A. There is a square DEFG. There is a line segment DE. There is a line segment EF. There is a line segment FG. There is a line segment GD. Line DE is parallel to line FG. The circle... | 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)
minor_arc1 = scene.add.minor_arc(A, B, C)
square1 = scene.add.square(D, E, F, G)
line_DE = scene.add.line_segment(D, E)
line_EF = scene.add.line_segmen... | {
"circle1": "circle(A)",
"minor_arc1": "minor_arc(A, B, C)",
"square1": "square(D, E, F, G)",
"line_DE": "line_segment(D, E)",
"line_EF": "line_segment(E, F)",
"line_FG": "line_segment(F, G)",
"line_GD": "line_segment(G, D)"
} | [
"parallel(line_DE, line_FG)",
"parallel(line_DE, line_FG)",
"is_circumcircle(circle1, square1)",
"point_lies_on(B, circle1)",
"point_lies_on(C, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [
"scene.constraint.eq(scene.get_object('line_DE').length, scene.get_object('line_EF').length)",
"scene.constraint.eq(scene.get_object('minor_arc1').central_angle, 90)"
] | {
"points": {
"A": [
0.9018330155000001,
-0.6775831076000001
],
"B": [
-0.270593158,
0.1749436842
],
"C": [
0.0493063498,
-1.8500091481
],
"D": [
1.5800891636999999,
0.6035698908
],
"E": [
-0.37931615280000003,
0.000674364... |
3obj_5rel_2extra_gen7137 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is a triangle ABC. There is a square DEFG. There is an isosceles triangle HIJ. There is a line segment AC. There is a line segment CF. There is a line segment HJ. There is a line segment HI. Point B is the orthocenter of triangle ABC. ... | 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"])
triangle1 = scene.add.triangle(A, B, C)
square1 = scene.add.square(D, E, F, G)
iso_triangle = scene.add.isosceles_triangle(H, I, J)
line_AC = scene.add.line_... | {
"triangle1": "triangle(A, B, C)",
"square1": "square(D, E, F, G)",
"iso_triangle": "isosceles_triangle(H, I, J)",
"line_AC": "line_segment(A, C)",
"line_CF": "line_segment(C, F)",
"line_HJ": "line_segment(H, J)",
"line_HI": "line_segment(H, I)"
} | [
"is_orthocenter(B, triangle1)",
"congruent(triangle1, iso_triangle)",
"perpendicular(line_AC, line_CF)",
"right_angle(A, C, F)",
"collinear(C, F, G)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J"
] | [
"scene.constraint.eq(scene.get_object('triangle1').inradius, scene.get_object('square1').inradius)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('C'), scene.get_object('F')), 90)"
] | {
"points": {
"A": [
2.8583596701,
3.6096539305
],
"B": [
1.3369194332,
2.8091580937
],
"C": [
0.5364635413000001,
4.3305946542000004
],
"D": [
-1.1469663626,
2.3048795933
],
"E": [
-0.8483363796000001,
3.2665980105
],... |
3obj_5rel_2extra_gen7138 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a square with vertices B, C, D, E. There is an equilateral triangle with vertices F, G, H. There is a line segment BC. There is a line segment CD. There is a line segment FE. There is a line segment HG. 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)
square1 = scene.add.square(B, C, D, E)
triangle1 = scene.add.equilateral_triangle(F, G, H)
line_BC = scene.add.line_segment(B, C)
line_CD = sce... | {
"circle1": "circle(A)",
"square1": "square(B, C, D, E)",
"triangle1": "equilateral_triangle(F, G, H)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_FE": "line_segment(F, E)",
"line_HG": "line_segment(H, G)"
} | [
"is_circumcircle(circle1, square1)",
"acute_angle(B, C, D)",
"right_angle(F, E, H)",
"is_median(line_FE, triangle1, F)",
"perpendicular(line_BC, line_CD)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
-1.5015076944999999,
0.5148363421000001
],
"B": [
-1.4578072008,
0.0217615203
],
"C": [
-1.9945894596,
0.47113793880000004
],
"D": [
-1.5452067198,
1.0079115544
],
"E": [
-1.0084310388,
0.5585353836
... |
3obj_5rel_2extra_gen7143 | hard | Diagram description: The diagram contains points A, B, C, D, E. There is a circle with center A. There is a circle with center B. There is a triangle with vertices C, D, E. There is a line segment CD. There is a line segment DE. There is a line segment EC. There is a line segment AC. There is a line segment BE. Line se... | 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)
circle2 = scene.add.circle(B)
triangle1 = scene.add.triangle(C, D, E)
line_CD = scene.add.line_segment(C, D)
line_DE = scene.add.line_segment(D, E)
line_EC = scene.add... | {
"circle1": "circle(A)",
"circle2": "circle(B)",
"triangle1": "triangle(C, D, E)",
"line_CD": "line_segment(C, D)",
"line_DE": "line_segment(D, E)",
"line_EC": "line_segment(E, C)",
"line_AC": "line_segment(A, C)",
"line_BE": "line_segment(B, E)"
} | [
"line_extensions_intersect_at(line_CD, line_DE, D)",
"point_lies_on(D, circle1)",
"point_lies_on(E, circle2)",
"is_circumcircle(circle1, triangle1)",
"perpendicular(line_AC, line_BE)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [
"scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BE').length)",
"scene.constraint.eq(scene.angle(scene.get_object('C'), scene.get_object('D'), scene.get_object('E')), 60)"
] | {
"points": {
"A": [
2.297843724,
0.4788221118
],
"B": [
-2.3383302047,
4.3870063401
],
"C": [
4.8730654328,
2.2733116169
],
"D": [
3.4825403821,
-2.4278003791
],
"E": [
-0.5438407885000001,
1.8117846872999999
]
},
... |
3obj_5rel_2extra_gen7144 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is a circle with center A. There is an isosceles triangle BCD. There is a regular hexagon EFGHIJ. There is a line segment BC. There is a line segment CD. There is a line segment DE. There is a line segment EF. The extension of line BC ... | 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"])
circle1 = scene.add.circle(A)
triangle1 = scene.add.isosceles_triangle(B, C, D)
hexagon1 = scene.add.regular_hexagon(E, F, G, H, I, J)
line_BC = scene.add.li... | {
"circle1": "circle(A)",
"triangle1": "isosceles_triangle(B, C, D)",
"hexagon1": "regular_hexagon(E, F, G, H, I, J)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_DE": "line_segment(D, E)",
"line_EF": "line_segment(E, F)"
} | [
"line_extension_intersects_circle_at(line_BC, circle1, B, C)",
"line_intersects_circle_at(line_CD, circle1, C, D)",
"is_circumcircle(circle1, triangle1)",
"is_centroid(A, hexagon1)",
"perpendicular(line_DE, line_EF)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J"
] | [
"scene.constraint.eq(scene.get_object('line_BC').length, scene.get_object('line_DE').length)",
"scene.constraint.leq(scene.get_object('hexagon1').area, 20)"
] | {
"points": {
"A": [
-0.3159669603,
1.8702097684
],
"B": [
0.6524231624,
1.3925280088
],
"C": [
-1.3951589189,
1.9063237688
],
"D": [
0.6821914616,
2.2820823454
],
"E": [
-1.2246807514,
3.1878514528
],
"F": [
... |
3obj_5rel_2extra_gen7148 | hard | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a circle with center A. There is a square BCDE. There is an isosceles trapezoid FGHI. There is a line segment BD. There is a line segment CF. There is a line segment GI. The circle is the circumcircle of square BCDE. Angle EBC is a rig... | 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"])
circle1 = scene.add.circle(A)
square1 = scene.add.square(B, C, D, E)
trapezoid1 = scene.add.isosceles_trapezoid(F, G, H, I)
line_BD = scene.add.line_segment(B, D)
li... | {
"circle1": "circle(A)",
"square1": "square(B, C, D, E)",
"trapezoid1": "isosceles_trapezoid(F, G, H, I)",
"line_BD": "line_segment(B, D)",
"line_CF": "line_segment(C, F)",
"line_GI": "line_segment(G, I)"
} | [
"is_circumcircle(circle1, square1)",
"right_angle(E, B, C)",
"acute_angle(F, G, H)",
"perpendicular(line_BD, line_CF)",
"parallel(line_GI, line_CF)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [
"scene.constraint.eq(scene.get_object('square1').area, scene.get_object('trapezoid1').area)",
"scene.constraint.eq(scene.angle(scene.get_object('F'), scene.get_object('G'), scene.get_object('H')), 60)"
] | {
"points": {
"A": [
-0.6939544944,
-0.15145002300000002
],
"B": [
-1.1064555252,
-0.024299280200000002
],
"C": [
-0.8210897556000001,
-0.5639270270000001
],
"D": [
-0.2814596902,
-0.2785609377
],
"E": [
-0.5668258201,
0.2... |
3obj_5rel_2extra_gen7150 | hard | 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 obtuse triangle with vertices D, E, F. There is a rhombus with vertices G, H, I, J. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line se... | 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"])
triangle1 = scene.add.triangle(A, B, C)
obtuse_triangle1 = scene.add.obtuse_triangle(D, E, F)
rhombus1 = scene.add.rhombus(G, H, I, J)
line_AD = scene.add.li... | {
"triangle1": "triangle(A, B, C)",
"obtuse_triangle1": "obtuse_triangle(D, E, F)",
"rhombus1": "rhombus(G, H, I, J)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)",
"line_GH": "line_segment(G, H)",
"line_HI": "line_segment(H, I)"
} | [
"is_orthocenter(A, triangle1)",
"translation(triangle1, obtuse_triangle1, 3, 0)",
"perpendicular(line_AD, line_GH)",
"parallel(line_BE, line_HI)",
"right_angle(B, A, C)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J"
] | [] | {
"points": {
"A": [
0.6346128904,
3.1221138001
],
"B": [
4.2145726754,
2.8849741592
],
"C": [
0.4220562997,
-0.0867247673
],
"D": [
-2.3653859715,
3.1221124914
],
"E": [
1.2145735336,
2.8849731616
],
"F": [
... |
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