unique_id stringlengths 24 24 | nl_description stringlengths 177 973 | pygeox_code stringlengths 322 1.43k | Objs unknown | Rels listlengths 1 6 | Points listlengths 4 15 | extra_rel listlengths 0 3 | possible_solution dict |
|---|---|---|---|---|---|---|---|
3obj_4rel_1extra_gen0001 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M, N, O. There is a scalene triangle with vertices A, B, C. There is a rectangle with vertices D, E, F, G. There is a square with vertices H, I, J, K. There is a line segment AL. There is a line segment CM. There is a line segment BN. ... | 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"])
triangleABC = scene.add.scalene_triangle(A, B, C)
rectangleDEFG = scene.add.rectangle(D, E, F, G)
squareHIJK = scene.... | {
"triangleABC": "scalene_triangle(A, B, C)",
"rectangleDEFG": "rectangle(D, E, F, G)",
"squareHIJK": "square(H, I, J, K)",
"line_AL": "line_segment(A, L)",
"line_CM": "line_segment(C, M)",
"line_BN": "line_segment(B, N)",
"line_HO": "line_segment(H, O)"
} | [
"is_altitude(line_AL, triangleABC, A)",
"is_altitude(line_CM, triangleABC, C)",
"similar(triangleABC, triangleABC)",
"perpendicular(line_BN, line_HO)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L",
"M",
"N",
"O"
] | [] | {
"points": {
"A": [
0.2482755562,
-0.0312224678
],
"B": [
-5.2197532709,
1.8514886797
],
"C": [
8.9862781977,
-0.9468629935
],
"D": [
0.161391636,
1.3677905586999999
],
"E": [
-0.5327630951,
1.3957064954
],
"F": [... |
3obj_4rel_1extra_gen0009 | 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 regular pentagon with vertices E, F, G, H, I.
There is a triangle with vertices B, C, D.
Point B lies on the circle.
Point C lies on the circle.
There is an acute angle at D with arms DB and DC.
The c... | 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)
triangle1 = scene.add.triangle(B, C, D)
pentagon1 = scene.add.regular_pentagon(E, F, G, H, I)
### relationships
scene.relate.point_li... | {
"circle1": "circle(A)",
"triangle1": "triangle(B, C, D)",
"pentagon1": "regular_pentagon(E, F, G, H, I)"
} | [
"point_lies_on(B, circle1)",
"point_lies_on(C, circle1)",
"acute_angle(D, B, C)",
"is_circumcircle(circle1, triangle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [] | {
"points": {
"A": [
-0.3807603409,
-1.4319277527
],
"B": [
-0.8118454101,
-1.0550407987
],
"C": [
-0.11868735720000001,
-1.9410405726
],
"D": [
0.1724941349,
-1.579533987
],
"E": [
-10.2207909589,
1.7717544385
],
... |
3obj_4rel_1extra_gen0017 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M, N. There is a quadrilateral with vertices A, B, C, D. There is a rectangle with vertices E, F, G, H. There is a right trapezoid with vertices I, J, K, L. There is a line segment AC. There is a line segment BD. There is a line segmen... | 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"])
quadrilateral1 = scene.add.quadrilateral(A, B, C, D)
rectangle1 = scene.add.rectangle(E, F, G, H)
right_trapezoid1 = scene.ad... | {
"quadrilateral1": "quadrilateral(A, B, C, D)",
"rectangle1": "rectangle(E, F, G, H)",
"right_trapezoid1": "right_trapezoid(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)"
} | [
"is_midpoint(M, line_AC)",
"is_midpoint(N, line_BD)",
"right_angle(A, B, C)",
"perpendicular(line_AC, line_BD)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L",
"M",
"N"
] | [
"scene.constraint.eq(scene.get_object('line_BD').length, scene.get_object('line_EG').length)"
] | {
"points": {
"A": [
-1.899193017,
-2.3884476728
],
"B": [
-1.7083120789000001,
-2.2409358932
],
"C": [
-2.1163885788,
-1.7128826441
],
"D": [
-0.8998714141,
-1.9810201325999999
],
"E": [
0.89862935,
1.1099586522
],
... |
3obj_4rel_1extra_gen0019 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, M, N. There is a quadrilateral ABCD. There is an equilateral triangle EFG. There is a quadrilateral HIJK. 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 segm... | 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"])
quad1 = scene.add.quadrilateral(A, B, C, D)
tri1 = scene.add.equilateral_triangle(E, F, G)
quad2 = scene.add.quadrilateral(H, I, J, K... | {
"quad1": "quadrilateral(A, B, C, D)",
"tri1": "equilateral_triangle(E, F, G)",
"quad2": "quadrilateral(H, 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)",
"line_GH": "line_segment(G, H)"
} | [
"lines_intersect_at(line_AC, line_BD, M)",
"mirror_across_line(quad1, quad2, line_EF)",
"perpendicular(line_AC, line_BD)",
"lines_intersect_at(line_EF, line_GH, N)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"M",
"N"
] | [
"scene.constraint.eq(scene.get_object('quad1').area, scene.get_object('tri1').area)",
"scene.constraint.leq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)"
] | {
"points": {
"A": [
0.5798587257,
-1.4139427747
],
"B": [
0.9015966786,
-0.7120535521
],
"C": [
-0.1320963576,
-0.8221290518000001
],
"D": [
-0.1033489194,
-1.92100665
],
"E": [
-0.40958069610000003,
-1.8757008332
],
... |
3obj_4rel_1extra_gen0021 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a major arc ABC with center A. There is a right trapezoid DEFG. There is a circle with center H. There is a line segment DE. There is a line segment EF. There is a line segment HB. Line DE is perpendicular to line EF. Point I is the mi... | 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)
right_trap1 = scene.add.right_trapezoid(D, E, F, G)
circle1 = scene.add.circle(H)
line_DE = scene.add.line_segment(D, E)
li... | {
"major_arc1": "major_arc(A, B, C)",
"right_trap1": "right_trapezoid(D, E, F, G)",
"circle1": "circle(H)",
"line_DE": "line_segment(D, E)",
"line_EF": "line_segment(E, F)",
"line_HB": "line_segment(H, B)"
} | [
"perpendicular(line_DE, line_EF)",
"is_midpoint(I, line_DE)",
"is_radius(line_HB, circle1)",
"point_lies_on(B, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [] | {
"points": {
"A": [
3.6658246814,
0.1997201579
],
"B": [
-0.3771958124,
-1.5868134359
],
"C": [
0.1345028079,
2.8581939358
],
"D": [
-0.0573424338,
2.3766990159
],
"E": [
-0.8207035467,
3.1974857313
],
"F": [
... |
3obj_4rel_1extra_gen0037 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L. There is a square with vertices A, B, C, D. There is a rectangle with vertices E, F, G, H. There is a trapezoid with vertices 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 li... | 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"])
square1 = scene.add.square(A, B, C, D)
rectangle1 = scene.add.rectangle(E, F, G, H)
trapezoid1 = scene.add.trapezoid(I, J, K, L)
line_AC = sc... | {
"square1": "square(A, B, C, D)",
"rectangle1": "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)"
} | [
"right_angle(B, A, D)",
"collinear(A, C, E)",
"parallel(line_AC, line_EG)",
"perpendicular(line_IK, line_JL)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L"
] | [
"scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_EG').length)",
"scene.constraint.leq(scene.get_object('trapezoid1').area, 12.0)"
] | {
"points": {
"A": [
-0.7982523544,
-0.3160027968
],
"B": [
0.1477065081,
-0.1837489035
],
"C": [
0.2799602752,
-1.1297076897
],
"D": [
-0.6659986065,
-1.2619614498
],
"E": [
0.4454648605,
-1.2546106021
],
"F": [
... |
3obj_4rel_1extra_gen0041 | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a circle with center A. There is a kite with vertices B, C, D, E. There is a minor arc with center A, start point F, and end point G. There is a line segment BE. There is a line segment CD. There is a line segment AF. 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"])
circle1 = scene.add.circle(A)
kite1 = scene.add.kite(B, C, D, E)
minor_arc1 = scene.add.minor_arc(A, F, G)
line_BE = scene.add.line_segment(B, E)
line_CD = scene.add.line_segment(C,... | {
"circle1": "circle(A)",
"kite1": "kite(B, C, D, E)",
"minor_arc1": "minor_arc(A, F, G)",
"line_BE": "line_segment(B, E)",
"line_CD": "line_segment(C, D)",
"line_AF": "line_segment(A, F)",
"line_AG": "line_segment(A, G)"
} | [
"is_chord(line_BE, circle1)",
"congruent(line_BE, line_CD)",
"point_lies_on(F, circle1)",
"point_lies_on(G, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [
"scene.constraint.eq(scene.get_object('line_BE').length, scene.get_object('line_CD').length)",
"scene.constraint.eq(scene.get_object('minor_arc1').central_angle, 90)",
"scene.constraint.leq(scene.get_object('line_AF').length, scene.get_object('circle1').diameter)"
] | {
"points": {
"A": [
3.009179313,
-0.6213001019000001
],
"B": [
1.2495894466,
-3.1934408513
],
"C": [
2.9955953627,
-8.31532983
],
"D": [
3.431958935,
-2.9216410466
],
"E": [
1.685951315,
2.2002477659
],
"F": [
... |
3obj_4rel_1extra_gen0042 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a major arc with center A, from B to C. There is a parallelogram with vertices D, E, F, G. There is a circle with center H. There is a line segment AD. There is a line segment HF. There is a line segment AC. Line HF is a radius of the cir... | 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)
parallelogram1 = scene.add.parallelogram(D, E, F, G)
circle1 = scene.add.circle(H)
line_AD = scene.add.line_segment(A, D)
line_HF ... | {
"semicircle1": "major_arc(A, B, C)",
"parallelogram1": "parallelogram(D, E, F, G)",
"circle1": "circle(H)",
"line_AD": "line_segment(A, D)",
"line_HF": "line_segment(H, F)",
"line_AC": "line_segment(A, C)"
} | [
"is_radius(line_HF, circle1)",
"tangent_to_circle(line_AD, circle1, A)",
"is_chord(line_AC, circle1)",
"perpendicular(line_AD, line_AC)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
1.3439685015,
0.3016228743
],
"B": [
5.4871111166,
-0.5456278509
],
"C": [
-2.6654988925,
-1.0428605266
],
"D": [
1.6424417351,
-0.588472812
],
"E": [
2.0017303709,
0.8453773326
],
"F": [
... |
3obj_4rel_1extra_gen0063 | Diagram description: The diagram contains points A, B, C, D, E, O. There is a right triangle ABC. There is a rhombus ABDE. There is a circle with center O. There are line segments AC, BE, and OA. Line OA is a radius of the circle. Point O is the midpoint of line AC. Line AC is perpendicular to line BE. The circle is th... | 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.right_triangle(A, B, C)
rhombusABDE = scene.add.rhombus(A, B, D, E)
circleO = scene.add.circle(O)
line_AC = scene.add.line_segment(A, C)
line_BE = scene.add.line_seg... | {
"triangleABC": "right_triangle(A, B, C)",
"rhombusABDE": "rhombus(A, B, D, E)",
"circleO": "circle(O)",
"line_AC": "line_segment(A, C)",
"line_BE": "line_segment(B, E)",
"line_OA": "line_segment(O, A)"
} | [
"is_radius(line_OA, circleO)",
"is_midpoint(O, line_AC)",
"perpendicular(line_AC, line_BE)",
"is_circumcircle(circleO, triangleABC)"
] | [
"A",
"B",
"C",
"D",
"E",
"O"
] | [
"scene.constraint.eq(scene.get_object('line_BE').length, scene.get_object('line_AC').length / 2)"
] | {
"points": {
"A": [
1.7236821908,
0.9792032348
],
"B": [
1.4383403859000001,
1.3681281264
],
"C": [
-0.0131469229,
0.3032179593
],
"D": [
1.4909911692,
0.8886385091000001
],
"E": [
1.7763329212,
0.4997134359
],
"O... |
3obj_4rel_1extra_gen0064 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a triangle ABC. There is a triangle DEF. There is a major arc with center G, start point H, and end point I. There is a line segment AC. There is a line segment DF. Point A lies on the major arc GHI. Point C lies on the major arc GHI. ... | 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"])
triangle_ABC = scene.add.triangle(A, B, C)
triangle_DEF = scene.add.triangle(D, E, F)
major_arc_GHI = scene.add.major_arc(G, H, I)
line_AC = scene.add.line_segment(A... | {
"triangle_ABC": "triangle(A, B, C)",
"triangle_DEF": "triangle(D, E, F)",
"major_arc_GHI": "major_arc(G, H, I)",
"line_AC": "line_segment(A, C)",
"line_DF": "line_segment(D, F)"
} | [
"point_lies_on(A, major_arc_GHI)",
"point_lies_on(C, major_arc_GHI)",
"similar(triangle_ABC, triangle_DEF)",
"perpendicular(line_AC, line_DF)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [
"scene.constraint.eq(scene.get_object('triangle_ABC').area, scene.get_object('triangle_DEF').area)"
] | {
"points": {
"A": [
0.9319756114000001,
1.7703916189000002
],
"B": [
3.2796948091,
3.6182688458000003
],
"C": [
1.1843260545,
1.1476028932
],
"D": [
1.344657532,
-1.9667875276000002
],
"E": [
1.0371225707,
1.0050525279
... |
3obj_4rel_1extra_gen0066 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M, N, O. There is a major arc with center A and endpoints B and C. There is a regular octagon with vertices D, E, F, G, H, I, J, K. There is a triangle with vertices L, M, N. There is a line segment OM. There is a line segment LN. Ther... | 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"])
major_arc1 = scene.add.major_arc(A, B, C)
regular_octagon1 = scene.add.regular_octagon(D, E, F, G, H, I, J, K)
triang... | {
"major_arc1": "major_arc(A, B, C)",
"regular_octagon1": "regular_octagon(D, E, F, G, H, I, J, K)",
"triangle1": "triangle(L, M, N)",
"line_OM": "line_segment(O, M)",
"line_LN": "line_segment(L, N)",
"line_MN": "line_segment(M, N)"
} | [
"obtuse_angle(L, M, N)",
"is_midpoint(O, line_LN)",
"mirror_across_line(major_arc1, major_arc1, line_OM)",
"is_altitude(line_MN, triangle1, M)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L",
"M",
"N",
"O"
] | [
"scene.constraint.eq(scene.get_object('triangle1').area, scene.get_object('regular_octagon1').inradius)"
] | {
"points": {
"A": [
-3.482645202,
-4.1773803308
],
"B": [
-4.3833502681,
-5.3269487302
],
"C": [
-2.5819751282,
-3.0277846908
],
"D": [
-9.2901299443,
-0.5550326724
],
"E": [
-9.812015518900001,
-2.0645195047
],
"... |
3obj_4rel_1extra_gen0067 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, M. There is a rhombus with vertices A, B, C, D. There is a quadrilateral with vertices E, F, G, H. There are line segments AC, BD, EF, and GH. The rhombus is similar to the quadrilateral. Line AC intersects line BD at point M. Line AC is perpendic... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, M = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "M"])
rhombus1 = scene.add.rhombus(A, B, C, D)
quad1 = scene.add.quadrilateral(E, F, G, H)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_segment(B, D)
li... | {
"rhombus1": "rhombus(A, B, C, D)",
"quad1": "quadrilateral(E, F, G, H)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EF": "line_segment(E, F)",
"line_GH": "line_segment(G, H)"
} | [
"similar(rhombus1, quad1)",
"lines_intersect_at(line_AC, line_BD, M)",
"perpendicular(line_AC, line_BD)",
"parallel(line_EF, line_GH)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"M"
] | [
"scene.constraint.eq(scene.get_object('line_AC').slope, scene.get_object('line_EF').slope)"
] | {
"points": {
"A": [
2.4385404189,
-1.6153620641000002
],
"B": [
2.2887838723,
-0.8789237942
],
"C": [
2.9894710553,
-1.1505857314
],
"D": [
3.1392424546,
-1.8870493771999999
],
"E": [
-0.6296226371,
-0.5381907317
],
... |
3obj_4rel_1extra_gen0073 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a right triangle BCD. There is a quadrilateral EFGH. There is a line segment BC. There is a line segment CD. There is a line segment AG. There is a line segment EH. Line AG is a radius of the circle. Point... | 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)
right_triangle1 = scene.add.right_triangle(B, C, D)
quadrilateral1 = scene.add.quadrilateral(E, F, G, H)
line_BC = scene.add.line_segment(B, C)... | {
"circle1": "circle(A)",
"right_triangle1": "right_triangle(B, C, D)",
"quadrilateral1": "quadrilateral(E, F, G, H)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_AG": "line_segment(A, G)",
"line_EH": "line_segment(E, H)"
} | [
"is_radius(line_AG, circle1)",
"collinear(A, G, H)",
"is_chord(line_BC, circle1)",
"perpendicular(line_BC, line_CD)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"scene.constraint.eq(scene.get_object('right_triangle1').perimeter, 12.0)",
"scene.constraint.leq(scene.get_object('line_BC').length, 5.0)"
] | {
"points": {
"A": [
2.5469322397000003,
-1.7931464199
],
"B": [
2.9251920965,
-4.2752561466
],
"C": [
4.2138395671,
0.08445023310000001
],
"D": [
1.9692998083000002,
0.7478941051
],
"E": [
7.5236629842,
-5.9736825425
... |
3obj_4rel_1extra_gen0090 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a parallelogram with vertices A, B, C, D. There is a right triangle with vertices E, F, G. There is a circle with center H. There is a line segment AC. There is a line segment BD. There is a line segment HF. There is a line segment FG.... | 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"])
parallelogram1 = scene.add.parallelogram(A, B, C, D)
right_triangle1 = scene.add.right_triangle(E, F, G)
circle1 = scene.add.circle(H)
line_AC = scene.add.line_segme... | {
"parallelogram1": "parallelogram(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_HF": "line_segment(H, F)",
"line_FG": "line_segment(F, G)",
"line_EG": "line_segment(E, G)"
} | [
"line_extensions_intersect_at(line_AC, line_BD, I)",
"line_extensions_intersect_at(line_HF, line_FG, F)",
"is_diameter(line_AC, circle1)",
"is_radius(line_HF, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [
"scene.constraint.eq(scene.get_object('line_HF').length, scene.get_object('line_FG').length)"
] | {
"points": {
"A": [
2.2123721354,
0.9877490924000001
],
"B": [
-1.2929086216,
7.7515460361
],
"C": [
2.719931898,
-0.0031110065
],
"D": [
6.2753090186,
-6.863648528
],
"E": [
-3.1695520452,
-2.2602238922
],
"F": [... |
3obj_4rel_1extra_gen0095 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M, N, O. There is a regular heptagon with vertices A, B, C, D, E, F, G. There is a rhomboid with vertices H, I, J, K. There is a rhomboid with vertices L, M, N, O. There is a line segment AC. There is a line segment HI. There is a line... | 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"])
heptagon1 = scene.add.regular_heptagon(A, B, C, D, E, F, G)
rhomboid1 = scene.add.rhomboid(H, I, J, K)
rhomboid2 = sc... | {
"heptagon1": "regular_heptagon(A, B, C, D, E, F, G)",
"rhomboid1": "rhomboid(H, I, J, K)",
"rhomboid2": "rhomboid(L, M, N, O)",
"line_AC": "line_segment(A, C)",
"line_HI": "line_segment(H, I)",
"line_HK": "line_segment(H, K)",
"line_MN": "line_segment(M, N)"
} | [
"mirror_across_line(rhomboid1, rhomboid2, line_AC)",
"line_extensions_intersect_at(line_HI, line_MN, B)",
"perpendicular(line_HI, line_HK)",
"acute_angle(H, I, K)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L",
"M",
"N",
"O"
] | [
"scene.constraint.eq(scene.get_object('rhomboid1').area, scene.get_object('heptagon1').area / 3)"
] | {
"points": {
"A": [
-1.8797645659,
-1.5316038437000001
],
"B": [
-2.6638063463,
-1.9439787984999999
],
"C": [
-2.8302406783,
-2.8140789249
],
"D": [
-2.2537391153,
-3.4867010808
],
"E": [
-1.3684190927,
-3.4553470639
... |
3obj_4rel_1extra_gen0104 | 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 rhombus with vertices B, C, D, E. There is a parallelogram with vertices F, G, H, I. There are line segments BC, CD, FG, GH. Line BC is parallel to line FG. Line CD is perpendicular to line BC. Line C... | 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)
rhombus1 = scene.add.rhombus(B, C, D, E)
parallelogram1 = scene.add.parallelogram(F, G, H, I)
line_BC = scene.add.line_segment(B, C)
li... | {
"circle1": "circle(A)",
"rhombus1": "rhombus(B, C, D, E)",
"parallelogram1": "parallelogram(F, G, H, I)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_FG": "line_segment(F, G)",
"line_GH": "line_segment(G, H)"
} | [
"parallel(line_BC, line_FG)",
"perpendicular(line_CD, line_BC)",
"is_chord(line_CD, circle1)",
"is_diameter(line_FG, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [
"scene.constraint.eq(scene.get_object('rhombus1').area, scene.get_object('circle1').area)"
] | {
"points": {
"A": [
-0.5860458345,
0.5254952499000001
],
"B": [
-3.5793475913,
1.051419893
],
"C": [
-1.3856905844,
1.5040291477999999
],
"D": [
-0.9330810274,
-0.6896264874
],
"E": [
-3.1267377148,
-1.1422351176
],
... |
3obj_4rel_1extra_gen0107 | 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 an obtuse triangle with vertices A, B, C. There are line segments AD, BE, and CF. Line AD is a radius of the circle with center A. Points A, D, and G are collinear. Line BE is... | 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)
triangleABC = scene.add.obtuse_triangle(A, B, C)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_segment(... | {
"circle1": "circle(A)",
"circle2": "circle(B)",
"triangleABC": "obtuse_triangle(A, B, C)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)"
} | [
"is_radius(line_AD, circle1)",
"collinear(A, D, G)",
"is_altitude(line_BE, triangleABC, B)",
"is_median(line_CF, triangleABC, C)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [
"scene.constraint.eq(scene.get_object('line_BE').length, scene.get_object('line_AD').length)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 120)"
] | {
"points": {
"A": [
4.1167489353,
-5.7389432977
],
"B": [
-1.5283086907999999,
0.8307571394000001
],
"C": [
0.2031197515,
5.7669390612
],
"D": [
2.8288713998,
-2.7781531571
],
"E": [
1.5284637929,
1.8704923886
],
... |
3obj_4rel_1extra_gen0111 | Diagram description: The diagram contains points A, B, C, D, E, F. There is a parallelogram with vertices A, B, C, D. There is a circle with center E. There is a circle with center F. There are line segments AC, BD, and EF. The angle BAD is acute. The extension of line AC intersects the circle with center E at points A... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F = scene.add.points(["A", "B", "C", "D", "E", "F"])
parallelogram1 = scene.add.parallelogram(A, B, C, D)
circle1 = scene.add.circle(E)
circle2 = scene.add.circle(F)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_segment(B, D... | {
"parallelogram1": "parallelogram(A, B, C, D)",
"circle1": "circle(E)",
"circle2": "circle(F)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line EF": "line_segment(E, F)"
} | [
"acute_angle(B, A, D)",
"line_extension_intersects_circle_at(line_AC, circle1, A, C)",
"is_diameter(line_AC, circle1)",
"perpendicular(line_AC, line_BD)"
] | [
"A",
"B",
"C",
"D",
"E",
"F"
] | [
"scene.constraint.eq(scene.get_object('circle1').area, scene.get_object('circle2').area)",
"scene.constraint.leq(scene.get_object('parallelogram1').perimeter, 20)"
] | {
"points": {
"A": [
-1.5618093119,
-0.5631094292000001
],
"B": [
-1.4463361075,
-1.6902780542
],
"C": [
-0.3314367734,
-1.8923754116
],
"D": [
-0.4469095387,
-0.765206075
],
"E": [
-0.9466230664,
-1.2277423437000001
]... |
3obj_4rel_1extra_gen0112 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a triangle with vertices A, B, C. There is a triangle with vertices D, E, F. There is a minor arc with center G, start point H, and end point I. There is a line segment AD. There is a line segment BE. There is a line segment CF. There ... | 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"])
triangle1 = scene.add.triangle(A, B, C)
triangle2 = scene.add.triangle(D, E, F)
arc1 = scene.add.minor_arc(G, H, I)
line_AD = scene.add.line_segment(A, D)
line_BE = ... | {
"triangle1": "triangle(A, B, C)",
"triangle2": "triangle(D, E, F)",
"arc1": "minor_arc(G, H, I)",
"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)"
} | [
"scale(triangle1, triangle2, 2)",
"collinear(A, D, G)",
"perpendicular(line_AD, line_BE)",
"is_altitude(line_CF, triangle1, C)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [
"scene.constraint.eq(scene.get_object('arc1').area, scene.get_object('triangle1').area)"
] | {
"points": {
"A": [
-1.9053421333,
-1.0846289347
],
"B": [
-1.4009116088,
-0.5401842496
],
"C": [
-0.0724074947,
-1.0899243642
],
"D": [
-1.5932234439,
-0.9200112713
],
"E": [
-1.2250253231000001,
-0.8736684243
],
... |
3obj_4rel_1extra_gen0113 | Diagram description: The diagram contains points A, B, C, D, E. There is an equilateral triangle with vertices A, B, C. There is a circle with center D. There is a circle with center E. There are line segments AD, BE, AC, and BC. Line AD is a radius of the circle with center D. Line BE is a radius of the circle with ce... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
triangle1 = scene.add.equilateral_triangle(A, B, C)
circle1 = scene.add.circle(D)
circle2 = scene.add.circle(E)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_segment(B, E)
line_AC... | {
"triangle1": "equilateral_triangle(A, B, C)",
"circle1": "circle(D)",
"circle2": "circle(E)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_AC": "line_segment(A, C)",
"line_BC": "line_segment(B, C)"
} | [
"is_radius(line_AD, circle1)",
"is_radius(line_BE, circle2)",
"tangent_to_circle(line_AC, circle1, A)",
"line_intersects_circle_at(line_BC, circle2, B, C)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [
"scene.constraint.eq(scene.get_object('triangle1').inradius, scene.get_object('circle1').radius)"
] | {
"points": {
"A": [
1.8606840999,
1.254917611
],
"B": [
-0.49084472640000004,
2.7617512575000003
],
"C": [
-0.6200366205,
-0.028149305700000002
],
"D": [
2.2310735678,
0.5387953160000001
],
"E": [
0.22796900590000002,
1.3... |
3obj_4rel_1extra_gen0120 | Diagram description: The diagram contains points A, B, C, D, E, F, O, P, Q, R, S, T, U. There is a triangle ABC with AB = BC. There is a regular hexagon PQRSTU. 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 perpendicular to line BE. Line ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, O, P, Q, R, S, T, U = scene.add.points(["A", "B", "C", "D", "E", "F", "O", "P", "Q", "R", "S", "T", "U"])
triangleABC = scene.add.isosceles_triangle(A, B, C)
hexagonPQRSTU = scene.add.regular_hexagon(P, Q, R, S, T, U)
circleO = scene.add.c... | {
"triangleABC": "isosceles_triangle(A, B, C)",
"hexagonPQRSTU": "regular_hexagon(P, Q, R, S, T, U)",
"circleO": "circle(O)",
"lineAD": "line_segment(A, D)",
"lineBE": "line_segment(B, E)",
"lineCF": "line_segment(C, F)"
} | [
"perpendicular(lineAD, lineBE)",
"angle_bisector(A, B, C, lineBE)",
"is_circumcircle(circleO, triangleABC)",
"is_diameter(lineCF, circleO)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"O",
"P",
"Q",
"R",
"S",
"T",
"U"
] | [
"scene.constraint.eq(scene.get_object('triangleABC').inradius, scene.get_object('hexagonPQRSTU').inradius)"
] | {
"points": {
"A": [
0.6001165794000001,
-1.3853522863
],
"B": [
-2.0994897628,
0.0990135215
],
"C": [
0.038956546200000004,
2.3167297342
],
"D": [
0.9043454403000001,
-3.3924085575
],
"E": [
2.2239274509,
0.7543555191
... |
3obj_4rel_1extra_gen0132 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M. There is a rhomboid ABCD. There is a parallelogram EFGH. There is a quadrilateral IJKL. There is a line segment AC. There is a line segment EG. There is a line segment IK. There is a line segment JL. There is a line segment BD. Ther... | 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"])
rhomboid1 = scene.add.rhomboid(A, B, C, D)
parallelogram1 = scene.add.parallelogram(E, F, G, H)
quadrilateral1 = scene.add.quadrilate... | {
"rhomboid1": "rhomboid(A, B, C, D)",
"parallelogram1": "parallelogram(E, F, G, H)",
"quadrilateral1": "quadrilateral(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)",
"line_BD": "line_segment(B, D)",
"lin... | [
"line_extensions_intersect_at(line_AC, line_EG, M)",
"is_centroid(M, quadrilateral1)",
"perpendicular(line_BD, line_FH)",
"parallel(line_AC, line_IK)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L",
"M"
] | [
"scene.constraint.eq(scene.get_object('line_BD').length, scene.get_object('line_FH').length)",
"scene.constraint.leq(scene.get_object('line_AC').length, scene.get_object('line_EG').length)",
"scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('D')), 60)"
] | {
"points": {
"A": [
-1.8700419937000001,
0.8704373797
],
"B": [
0.8015709841,
3.6206273406
],
"C": [
3.2601059931,
2.9999032214
],
"D": [
0.588494528,
0.24971605670000002
],
"E": [
4.8419503224,
-0.0461156199
],
"... |
3obj_4rel_1extra_gen0151 | 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 semicircle with center C and endpoints D and E. There is a line segment AC. There is a line segment BE. There is a line segment CD. There is a line segment DE. Line AC inter... | 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)
semicircle1 = scene.add.semicircle(C, D, E)
line_AC = scene.add.line_segment(A, C)
line_BE = scene.add.line_segment(B, E)... | {
"circle1": "circle(A)",
"circle2": "circle(B)",
"semicircle1": "semicircle(C, D, E)",
"line_AC": "line_segment(A, C)",
"line_BE": "line_segment(B, E)",
"line_CD": "line_segment(C, D)",
"line_DE": "line_segment(D, E)"
} | [
"lines_intersect_at(line_AC, line_BE, F)",
"line_extensions_intersect_at(line_CD, line_DE, G)",
"is_diameter(line_CD, circle1)",
"is_radius(line_BE, circle2)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [] | {
"points": {
"A": [
-1.2264851742,
-3.425361649
],
"B": [
-1.5328710392,
-3.6433446469
],
"C": [
-0.6752391575000001,
-3.0331476606
],
"D": [
-1.7777330934000002,
-3.8175710782000003
],
"E": [
0.4272559018,
-2.248723219
... |
3obj_4rel_1extra_gen0177 | 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 an equilateral triangle DEF. There is a right trapezoid GHIJ. There are line segments AC, DF, GI, and HJ. Line AC and line DF intersect at point K. Point K lies on line AC. Triangle ABC and t... | 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)
triangle2 = scene.add.equilateral_triangle(D, E, F)
trapezoid1 = scene.add.right_trapezoid(G, H, ... | {
"triangle1": "equilateral_triangle(A, B, C)",
"triangle2": "equilateral_triangle(D, E, F)",
"trapezoid1": "right_trapezoid(G, H, I, J)",
"line_AC": "line_segment(A, C)",
"line_DF": "line_segment(D, F)",
"line_GI": "line_segment(G, I)",
"line_HJ": "line_segment(H, J)"
} | [
"line_extensions_intersect_at(line_AC, line_DF, K)",
"point_lies_on(K, line_AC)",
"mirror_across_line(triangle1, triangle2, line_GI)",
"perpendicular(line_GI, line_HJ)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [
"scene.constraint.eq(scene.get_object('triangle1').area, scene.get_object('trapezoid1').area)"
] | {
"points": {
"A": [
-0.4972627047,
1.0837587919
],
"B": [
0.0459475621,
1.6034246954
],
"C": [
-0.6757013006,
1.8140255891
],
"D": [
-0.5640334319,
1.3570212485
],
"E": [
0.1576150475,
1.1464223906
],
"F": [
... |
3obj_4rel_1extra_gen0182 | Diagram description: The diagram contains points A, B, C, D, E. There is a circle with center A. There is an isosceles triangle with vertices B, C, D. There is a circle with center E. There is a line segment BC. There is a line segment DE. There is a line segment CD. The circle with center A is the circumcircle of the ... | 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)
isosceles_triangle1 = scene.add.isosceles_triangle(B, C, D)
circle2 = scene.add.circle(E)
line_BC = scene.add.line_segment(B, C)
line_DE = scene.add.line_segment(D, E)... | {
"circle1": "circle(A)",
"isosceles_triangle1": "isosceles_triangle(B, C, D)",
"circle2": "circle(E)",
"line_BC": "line_segment(B, C)",
"line_DE": "line_segment(D, E)",
"line_CD": "line_segment(C, D)"
} | [
"is_circumcircle(circle1, isosceles_triangle1)",
"angle_bisector(B, D, C, line_DE)",
"is_radius(line_DE, circle2)",
"is_diameter(line_BC, circle1)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [] | {
"points": {
"A": [
1.3699976155,
-2.2968921026
],
"B": [
0.3491555209,
2.9146433482000003
],
"C": [
2.3908439857,
-7.5084326007
],
"D": [
0.153907555,
2.8725734072
],
"E": [
3.5303402784999998,
0.6932720661
]
},
... |
3obj_4rel_1extra_gen0196 | Diagram description: The diagram contains points A, B, C, D, E, F, O, M. There is an obtuse triangle ABC with vertices A, B, C. There is a triangle DEF with vertices D, E, F. There is a circle with center O. There is a line AD. There is a line BE. There is a line CF. There is a line OM. M is the centroid of triangle AB... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, O, M = scene.add.points(["A", "B", "C", "D", "E", "F", "O", "M"])
triangleABC = scene.add.obtuse_triangle(A, B, C)
triangleDEF = scene.add.triangle(D, E, F)
circleO = scene.add.circle(O)
line_AD = scene.add.line_segment(A, D)
line_BE = sce... | {
"triangleABC": "obtuse_triangle(A, B, C)",
"triangleDEF": "triangle(D, E, F)",
"circleO": "circle(O)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)",
"line_OM": "line_segment(O, M)"
} | [
"is_centroid(M, triangleABC)",
"angle_bisector(A, B, C, line_BE)",
"is_altitude(line_AD, triangleABC, A)",
"is_circumcircle(circleO, triangleABC)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"O",
"M"
] | [
"scene.constraint.eq(scene.get_object('triangleABC').area, 2 * scene.get_object('triangleDEF').area)",
"scene.constraint.leq(scene.get_object('line_BE').length, scene.get_object('triangleABC').circumradius)"
] | {
"points": {
"A": [
1.2890606895,
-5.8351237833
],
"B": [
-2.4818570359,
2.6863619114
],
"C": [
2.3782296714,
3.5920938436
],
"D": [
-0.3722811575,
3.079506405
],
"E": [
1.5333662331,
0.5705794915
],
"F": [
... |
3obj_4rel_1extra_gen0200 | 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. There is an isosceles trapezoid DEFG. There is a line segment BE. There is a line segment CF. There is a line segment DE. There is a line segment GF. The angle BAC is acute. Line BE is a chord... | 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)
isosceles_trapezoid1 = scene.add.isosceles_trapezoid(D, E, F, G)
line_BE = scene.add.line_segment(B, E)
line_... | {
"circle1": "circle(A)",
"minor_arc1": "minor_arc(A, B, C)",
"isosceles_trapezoid1": "isosceles_trapezoid(D, E, F, G)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)",
"line_DE": "line_segment(D, E)",
"line_GF": "line_segment(G, F)"
} | [
"acute_angle(B, A, C)",
"is_chord(line_BE, circle1)",
"perpendicular(line_BE, line_CF)",
"is_diameter(line_DE, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [] | {
"points": {
"A": [
1.4306729029,
-3.0159399235
],
"B": [
-0.1860223477,
-2.8883124731
],
"C": [
0.4360921,
-4.2968774113
],
"D": [
2.3503612403,
-4.3516667148
],
"E": [
0.5109847087,
-1.6802132203
],
"F": [
... |
3obj_4rel_1extra_gen0208 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a right triangle ABC. There is a right trapezoid DEFG. There is a scalene triangle HIJ. There is a line segment AC. There is a line segment DF. There is a line segment BI. Line AC intersects line DF at point K. Line AC is paralle... | 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.right_triangle(A, B, C)
trapezoid1 = scene.add.right_trapezoid(D, E, F, G)
triangle2 = scene.add.scalene_triangle(H, I, J)
line... | {
"triangle1": "right_triangle(A, B, C)",
"trapezoid1": "right_trapezoid(D, E, F, G)",
"triangle2": "scalene_triangle(H, I, J)",
"line_AC": "line_segment(A, C)",
"line_DF": "line_segment(D, F)",
"line_BI": "line_segment(B, I)"
} | [
"lines_intersect_at(line_AC, line_DF, K)",
"parallel(line_AC, line_DF)",
"is_altitude(line_BI, triangle1, B)",
"obtuse_angle(J, I, H)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [
"scene.constraint.eq(scene.get_object('triangle1').area, scene.get_object('triangle2').area)",
"scene.constraint.leq(scene.get_object('trapezoid1').area, 12.0)"
] | {
"points": {
"A": [
0.2969433396,
1.3891676911
],
"B": [
-1.63202095,
0.2934643329
],
"C": [
-0.8208706098,
-1.1345500737
],
"D": [
-0.1445257237,
0.39245190420000003
],
"E": [
-0.7239089001,
0.3777660154
],
"F": ... |
3obj_4rel_1extra_gen0223 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a regular pentagon with vertices A, B, C, D, E. There is a square with vertices F, G, H, I. There is a circle with center J. There is a line segment AC. There is a line segment FG. There is a line segment JH. Line AC intersects l... | 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)
square1 = scene.add.square(F, G, H, I)
circle1 = scene.add.circle(J)
line_AC = scene.add.line_s... | {
"pentagon1": "regular_pentagon(A, B, C, D, E)",
"square1": "square(F, G, H, I)",
"circle1": "circle(J)",
"line_AC": "line_segment(A, C)",
"line_FG": "line_segment(F, G)",
"line_JH": "line_segment(J, H)"
} | [
"lines_intersect_at(line_AC, line_FG, K)",
"acute_angle(A, K, F)",
"is_circumcircle(circle1, pentagon1)",
"is_radius(line_JH, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [
"scene.constraint.eq(scene.get_object('circle1').area, scene.get_object('square1').perimeter)"
] | {
"points": {
"A": [
3.1364590881,
0.6316804522
],
"B": [
1.954171486,
0.7494053545
],
"C": [
1.4768614892,
-0.3386379782
],
"D": [
2.3641552902000003,
-1.1288106413
],
"E": [
3.389843014,
-0.5291208714
],
"F": [
... |
3obj_4rel_1extra_gen0233 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M. There is an isosceles triangle ABC. There is a regular hexagon with vertices D, E, F, G, H, I. There is a trapezoid JKLM. There is a line segment AB. There is a line segment BC. There is a line segment CD. There is a line segment DE... | 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"])
triangle_ABC = scene.add.isosceles_triangle(A, B, C)
hexagon_DEF_GHIJKL = scene.add.regular_hexagon(D, E, F, G, H, I)
trapezoid_JKLM ... | {
"triangle_ABC": "isosceles_triangle(A, B, C)",
"hexagon_DEF_GHIJKL": "regular_hexagon(D, E, F, G, H, I)",
"trapezoid_JKLM": "trapezoid(J, K, L, M)",
"line_AB": "line_segment(A, B)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_DE": "line_segment(D, E)",
"line_EF": "line_segm... | [
"right_angle(A, B, C)",
"parallel(line_AB, line_KL_parallel_line)",
"is_altitude(line_BL, triangle_ABC, B)",
"is_median(line_BL, triangle_ABC, B)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L",
"M"
] | [] | {
"points": {
"A": [
1.040336378,
-1.5733421144
],
"B": [
1.2536101795999999,
-1.3627715559
],
"C": [
1.0430396348,
-1.1494977164
],
"D": [
-2.7229463451,
-0.9630056482
],
"E": [
-3.9560801421000003,
-7.1309970787
],
... |
3obj_4rel_1extra_gen0234 | Diagram description: The diagram contains points A, B, C, D, O. There is a triangle ABC. There is a rhomboid ABCD. There is a circle with center O. There is a line segment AC. There is a line segment BD. There is a line segment AD. There is a line segment BC. The extensions of line AC and line BD intersect at point O. ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, O = scene.add.points(["A", "B", "C", "D", "O"])
triangleABC = scene.add.triangle(A, B, C)
rhomboidABCD = scene.add.rhomboid(A, B, C, D)
circleO = scene.add.circle(O)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.add.line_segment(B, D)
l... | {
"triangleABC": "triangle(A, B, C)",
"rhomboidABCD": "rhomboid(A, B, C, D)",
"circleO": "circle(O)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_AD": "line_segment(A, D)",
"line_BC": "line_segment(B, C)"
} | [
"line_extensions_intersect_at(line_AC, line_BD, O)",
"line_extension_intersects_circle_at(line_AD, circleO, A, D)",
"is_altitude(line_BC, triangleABC, B)",
"is_diameter(line_AC, circleO)"
] | [
"A",
"B",
"C",
"D",
"O"
] | [] | {
"points": {
"A": [
0.4175806649,
3.21216942
],
"B": [
-5.1613989583,
-4.1043613307
],
"C": [
-4.9998262898,
-4.2223442812
],
"D": [
0.5766289488,
3.090897659
],
"O": [
-2.2911124529,
-0.5050948343
]
},
"circles":... |
3obj_4rel_1extra_gen0248 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a kite B, C, D, E. There is an equilateral triangle F, G, H. There is a line segment BD. There is a line segment CF. There is a line segment GE. There is a line segment HF. The extension of line BD interse... | 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)
kite1 = scene.add.kite(B, C, D, E)
triangle1 = scene.add.equilateral_triangle(F, G, H)
line_BD = scene.add.line_segment(B, D)
line_CF = scene.a... | {
"circle1": "circle(A)",
"kite1": "kite(B, C, D, E)",
"triangle1": "equilateral_triangle(F, G, H)",
"line_BD": "line_segment(B, D)",
"line_CF": "line_segment(C, F)",
"line_GE": "line_segment(G, E)",
"line_HF": "line_segment(H, F)"
} | [
"line_extension_intersects_circle_at(line_BD, circle1, B, D)",
"is_orthocenter(C, triangle1)",
"is_chord(line_CF, circle1)",
"perpendicular(line_CF, line_GE)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"scene.constraint.eq(scene.get_object('triangle1').area, scene.get_object('circle1').area)",
"scene.constraint.leq(scene.get_object('line_HF').slope, 0)"
] | {
"points": {
"A": [
-1.3564170554000001,
0.2981328144
],
"B": [
-0.5697415382000001,
0.4061155158
],
"C": [
-1.7830398077,
-0.3715774664
],
"D": [
-1.5910626878,
1.0567232123
],
"E": [
-2.2096622643,
-1.0412895495
],
... |
3obj_4rel_1extra_gen0256 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, M. There is a square with points A, B, C, D. There is a square 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 AC. There is a line segment EG. There is a line segment IK.... | 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"])
square1 = scene.add.square(A, B, C, D)
square2 = scene.add.square(E, F, G, H)
semicircle1 = scene.add.major_arc(I, J, K)
line_AC = scene.add.... | {
"square1": "square(A, B, C, D)",
"square2": "square(E, F, G, H)",
"semicircle1": "major_arc(I, J, K)",
"line_AC": "line_segment(A, C)",
"line_EG": "line_segment(E, G)",
"line_IK": "line_segment(I, K)"
} | [
"congruent(square1, square2)",
"line_extensions_intersect_at(line_AC, line_EG, M)",
"mirror_across_line(square1, square2, line_IK)",
"perpendicular(line_AC, line_EG)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"M"
] | [
"scene.constraint.eq(scene.get_object('square1').area, 4 * scene.get_object('semicircle1').radius)"
] | {
"points": {
"A": [
1.6475639219,
2.6832662341
],
"B": [
-2.4758861099000002,
2.3791902176
],
"C": [
-2.1718117758,
-1.744262468
],
"D": [
1.9516376385,
-1.440186474
],
"E": [
-2.6765521512,
2.3643917796
],
"F": [... |
3obj_4rel_1extra_gen0260 | 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 a square BCDE. There is a regular pentagon FGHIJ. There is a line segment AB. There is a line segment AC. There is a line segment BD. There is a line segment FG. The circle is the circumcircle of the... | 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)
square1 = scene.add.square(B, C, D, E)
pentagon1 = scene.add.regular_pentagon(F, G, H, I, J)
line_AB = scene.add.line_segment(A... | {
"circle1": "circle(A)",
"square1": "square(B, C, D, E)",
"pentagon1": "regular_pentagon(F, G, H, I, J)",
"line_AB": "line_segment(A, B)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_FG": "line_segment(F, G)"
} | [
"is_circumcircle(circle1, square1)",
"perpendicular(line_AB, line_AC)",
"is_diameter(line_BD, circle1)",
"is_radius(line_AB, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J"
] | [
"scene.constraint.eq(scene.get_object('circle1').area, scene.get_object('square1').inradius * scene.get_object('pentagon1').perimeter)"
] | {
"points": {
"A": [
0.0790898756,
0.728136042
],
"B": [
-0.120077871,
1.4376309009
],
"C": [
0.7885846894,
0.9273038603
],
"D": [
0.27825757830000003,
0.018641367000000002
],
"E": [
-0.6304050051,
0.5289684256
],
... |
3obj_4rel_1extra_gen0267 | 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 is a circle with center G. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment DE. There is an acute angle at B in triang... | 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)
circle1 = scene.add.circle(G)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.... | {
"triangle1": "isosceles_triangle(A, B, C)",
"triangle2": "right_triangle(D, E, F)",
"circle1": "circle(G)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)",
"line_DE": "line_segment(D, E)"
} | [
"acute_angle(A, B, C)",
"is_altitude(line_AD, triangle1, A)",
"is_chord(line_DE, circle1)",
"perpendicular(line_BE, line_CF)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [
"scene.constraint.eq(scene.get_object('triangle1').inradius, scene.get_object('triangle2').inradius)",
"scene.constraint.leq(scene.get_object('line_AD').slope, 1.0)"
] | {
"points": {
"A": [
1.469458638,
-1.0858970326
],
"B": [
1.0181228718,
-1.8906880824
],
"C": [
0.8687688962000001,
-0.9801460772
],
"D": [
0.90139851,
-1.1790743044
],
"E": [
1.0622349813,
-1.6940008180000001
],
"... |
3obj_4rel_1extra_gen0268 | Diagram description: The diagram contains points A, B, C, D, E. There is a triangle ABC. There is a circle with center D. There is a circle with center E. There is a line segment AD. There is a line segment BE. There is a line segment CD. The circle with center D is the circumcircle of triangle ABC. Line BE is the perp... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E = scene.add.points(["A", "B", "C", "D", "E"])
triangle1 = scene.add.triangle(A, B, C)
circle1 = scene.add.circle(D)
circle2 = scene.add.circle(E)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_segment(B, E)
line_CD = scene.add... | {
"triangle1": "triangle(A, B, C)",
"circle1": "circle(D)",
"circle2": "circle(E)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CD": "line_segment(C, D)"
} | [
"is_circumcircle(circle1, triangle1)",
"perpendicular_bisector_at(line_AD, line_BE)",
"is_chord(line_CD, circle2)",
"is_radius(line_AD, circle1)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [
"scene.constraint.eq(scene.get_object('triangle1').perimeter, 2 * scene.get_object('circle1').area / scene.get_object('triangle1').circumradius)"
] | {
"points": {
"A": [
0.15372771370000002,
-0.1754446638
],
"B": [
0.4105113368,
-0.0607394635
],
"C": [
0.4571590566,
-0.3996942209
],
"D": [
0.3357531797,
-0.24390735970000002
],
"E": [
0.2600780883,
-0.4310406585
]
... |
3obj_4rel_1extra_gen0271 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a triangle ABC. There is an equilateral triangle DEF. There is a circle with center G. There is a line AD. There is a line BE. There is a line CF. There is a line DE. line AD is an altitude of triangle ABC from vertex A. line BE is an alt... | 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"])
triangle1 = scene.add.triangle(A, B, C)
equilateral_triangle1 = scene.add.equilateral_triangle(D, E, F)
circle1 = scene.add.circle(G)
line_AD = scene.add.line_segment(A, D)
... | {
"triangle1": "triangle(A, B, C)",
"equilateral_triangle1": "equilateral_triangle(D, E, F)",
"circle1": "circle(G)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)",
"line_DE": "line_segment(D, E)"
} | [
"is_altitude(line_AD, triangle1, A)",
"is_altitude(line_BE, triangle1, B)",
"lines_intersect_at(line_AD, line_BE, H)",
"is_circumcircle(circle1, triangle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"scene.constraint.eq(scene.get_object('triangle1').inradius, scene.get_object('equilateral_triangle1').perimeter / 6)"
] | {
"points": {
"A": [
-0.7412046447,
-3.0837310437
],
"B": [
-1.6825982959,
-2.4310610987
],
"C": [
-0.6169969606,
-1.7216055753
],
"D": [
-1.3314078366,
-2.1972464352
],
"E": [
-0.6899433465,
-2.5215784101
],
"F": ... |
3obj_4rel_1extra_gen0281 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a square with vertices A, B, C, D. There is a circle with center E. There is an isosceles triangle with vertices F, G, 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. 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"])
square1 = scene.add.square(A, B, C, D)
circle1 = scene.add.circle(E)
triangle1 = scene.add.isosceles_triangle(F, G, H)
line_AC = scene.add.line_segment(A, C)
line_BD = scene... | {
"square1": "square(A, B, C, D)",
"circle1": "circle(E)",
"triangle1": "isosceles_triangle(F, G, 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)"
} | [
"is_chord(line_AC, circle1)",
"lines_intersect_at(line_AC, line_BD, E)",
"is_radius(line_EF, circle1)",
"is_altitude(line_FG, triangle1, F)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"scene.constraint.eq(scene.get_object('line_AC').length, 2 * scene.get_object('line_EF').length)",
"scene.constraint.eq(scene.get_object('triangle1').area, (1/2) * scene.get_object('line_FG').length * scene.get_object('line_FG').length)"
] | {
"points": {
"A": [
-0.9306751597,
-2.5704539658
],
"B": [
-1.4370793438,
-1.7323431351
],
"C": [
-0.5989685769,
-1.2259390632
],
"D": [
-0.0925643907,
-2.0640499511
],
"E": [
-0.7648219726000001,
-1.8981962524
],
... |
3obj_4rel_1extra_gen0288 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a kite with vertices A, B, C, D. There is a circle with center E. There is a parallelogram 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. Line A... | 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"])
kite1 = scene.add.kite(A, B, C, D)
circle1 = scene.add.circle(E)
parallelogram1 = scene.add.parallelogram(F, G, H, I)
line_AC = scene.add.line_segment(A, C)
line_BD ... | {
"kite1": "kite(A, B, C, D)",
"circle1": "circle(E)",
"parallelogram1": "parallelogram(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)"
} | [
"perpendicular(line_AC, line_BD)",
"is_radius(line_EF, circle1)",
"parallel(line_GH, line_AC)",
"point_lies_on(A, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [
"scene.constraint.eq(scene.get_object('kite1').area, scene.get_object('parallelogram1').area)"
] | {
"points": {
"A": [
0.1404774259,
0.9105676323
],
"B": [
0.8869341148000001,
-1.6280305327
],
"C": [
0.3357815222,
0.9600011144
],
"D": [
0.5997942025,
-0.4935849248
],
"E": [
-0.6676974988000001,
-0.8516097996
],
... |
3obj_4rel_1extra_gen0296 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, K, L. There is a kite with points A, B, C, D. There is a trapezoid with points E, F, G, H. There is a circle with center 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. There is... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, I, K, L = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "K", "L"])
kite1 = scene.add.kite(A, B, C, D)
trapezoid1 = scene.add.trapezoid(E, F, G, H)
circle1 = scene.add.circle(I)
line_AC = scene.add.line_segment(A, C)
... | {
"kite1": "kite(A, B, C, D)",
"trapezoid1": "trapezoid(E, F, G, H)",
"circle1": "circle(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)",
"line_KL": "line_segment(K, L)"
} | [
"tangent_to_circle(line_AC, circle1, A)",
"line_extension_intersects_circle_at(line_BD, circle1, B, D)",
"is_diameter(line_EF, circle1)",
"perpendicular(line_AC, line_BD)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"K",
"L"
] | [
"scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_EF').length)",
"scene.constraint.eq(scene.get_object('circle1').area, 4 * 3.14159)"
] | {
"points": {
"A": [
-0.1469711024,
0.4775277317
],
"B": [
-2.8270359448,
1.1239216405
],
"C": [
-3.609169059,
-1.5212372001999999
],
"D": [
-2.9273328314000002,
1.2976655834
],
"E": [
0.8148473407,
2.5969165485
],
... |
3obj_4rel_1extra_gen0305 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is a minor arc with center A, start point B, and end point C. There is a rhomboid with vertices D, E, F, G. There is an isosceles triangle with vertices H, I, J. There are line segments DE, EF, FG, GD, HI, IJ, and HJ. Line DE is parall... | 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"])
arc1 = scene.add.minor_arc(A, B, C)
rhomboid1 = scene.add.rhomboid(D, E, F, G)
triangle1 = scene.add.isosceles_triangle(H, I, J)
line_DE = scene.add.line_seg... | {
"arc1": "minor_arc(A, B, C)",
"rhomboid1": "rhomboid(D, E, F, G)",
"triangle1": "isosceles_triangle(H, I, J)",
"line_DE": "line_segment(D, E)",
"line_EF": "line_segment(E, F)",
"line_FG": "line_segment(F, G)",
"line_GD": "line_segment(G, D)",
"line_HI": "line_segment(H, I)",
"line_IJ": "line_segment... | [
"parallel(line_DE, line_FG)",
"is_altitude(line_HI, triangle1, H)",
"point_lies_on(B, arc1)",
"point_lies_on(C, arc1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J"
] | [
"scene.constraint.eq(scene.get_object('line_HI').length, scene.get_object('line_IJ').length)",
"scene.constraint.eq(scene.angle(scene.get_object('H'), scene.get_object('I'), scene.get_object('J')), 90)"
] | {
"points": {
"A": [
7.5385054915000005,
6.3416784309
],
"B": [
5.1589265868,
-5.0555664598
],
"C": [
-4.1039144313,
6.4584912196
],
"D": [
-8.3905250607,
-5.8360476114
],
"E": [
-2.8247248132,
0.2130560595
],
"F":... |
3obj_4rel_1extra_gen0307 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J.
There is a regular pentagon ABCDE.
There is a rhombus FGHI.
There is a circle with center J.
There is a line segment AC.
There is a line segment FH.
There is a line segment JG.
Point G lies on the circle.
Point H lies on the circle.
The circ... | 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"])
pentagon1 = scene.add.regular_pentagon(A, B, C, D, E)
rhombus1 = scene.add.rhombus(F, G, H, I)
circle1 = scene.add.circle(J)
line_AC = scene.add.line_segment... | {
"pentagon1": "regular_pentagon(A, B, C, D, E)",
"rhombus1": "rhombus(F, G, H, I)",
"circle1": "circle(J)",
"line_AC": "line_segment(A, C)",
"line_FH": "line_segment(F, H)",
"line_JG": "line_segment(J, G)"
} | [
"point_lies_on(G, circle1)",
"point_lies_on(H, circle1)",
"is_circumcircle(circle1, pentagon1)",
"is_radius(line_JG, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J"
] | [] | {
"points": {
"A": [
-6.2239542944,
2.2507946805
],
"B": [
-4.5854883967,
-0.006467828300000001
],
"C": [
-1.9323903716,
0.8542733645
],
"D": [
-1.9311515143,
3.6435031860000002
],
"E": [
-4.5834838835,
4.5066008253
],... |
3obj_4rel_1extra_gen0310 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is an isosceles triangle ABC. There is an isosceles trapezoid ABCD. There is a right trapezoid EFGH. There is a line segment AD. There is a line segment BC. There is a line segment EF. There is a line segment GH. F is the orthocenter of tria... | 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"])
triangleABC = scene.add.isosceles_triangle(A, B, C)
trapezoidABCD = scene.add.isosceles_trapezoid(A, B, C, D)
trapezoidEFGH = scene.add.right_trapezoid(E, F, G, H)
line_AD =... | {
"triangleABC": "isosceles_triangle(A, B, C)",
"trapezoidABCD": "isosceles_trapezoid(A, B, C, D)",
"trapezoidEFGH": "right_trapezoid(E, F, G, H)",
"line_AD": "line_segment(A, D)",
"line_BC": "line_segment(B, C)",
"line_EF": "line_segment(E, F)",
"line_GH": "line_segment(G, H)"
} | [
"is_orthocenter(F, triangleABC)",
"point_lies_on(F, line_AD)",
"perpendicular(line_AD, line_BC)",
"parallel(line_EF, line_GH)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
-0.6208516651,
0.5451742196
],
"B": [
0.340210532,
-0.677671091
],
"C": [
0.5253191564,
0.8665849673
],
"D": [
0.9234042156000001,
0.3600655356
],
"E": [
-0.42677745,
1.8891928964
],
"F": [
... |
3obj_4rel_1extra_gen0311 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is an equilateral triangle ABC. There is a circle with center D. There is a square EFGH. There is a line segment AD. There is a line segment BD. There is a line segment CD. There is a line segment EF. There is a line segment FG. Point A lies... | 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"])
triangle1 = scene.add.equilateral_triangle(A, B, C)
circle1 = scene.add.circle(D)
square1 = scene.add.square(E, F, G, H)
line_AD = scene.add.line_segment(A, D)
line_BD = sce... | {
"triangle1": "equilateral_triangle(A, B, C)",
"circle1": "circle(D)",
"square1": "square(E, F, G, H)",
"line_AD": "line_segment(A, D)",
"line_BD": "line_segment(B, D)",
"line_CD": "line_segment(C, D)",
"line_EF": "line_segment(E, F)",
"line_FG": "line_segment(F, G)"
} | [
"point_lies_on(A, circle1)",
"point_lies_on(B, circle1)",
"point_lies_on(C, circle1)",
"is_circumcircle(circle1, triangle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BD').length)"
] | {
"points": {
"A": [
2.1411089934,
2.056334467
],
"B": [
1.4850575095,
2.6111688537
],
"C": [
1.3325825568,
1.7655944956
],
"D": [
1.6529165071,
2.1443660415
],
"E": [
-1.5754126084,
-0.3706078423
],
"F": [
-... |
3obj_4rel_1extra_gen0314 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K.
There is a quadrilateral ABCD.
There is a major arc with points E, F, G.
There is a rectangle HIJK.
There is a line segment AC.
There is a line segment BD.
There is a line segment EF.
Quadrilateral ABCD is congruent to rectangle HIJK.
The... | 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"])
quad1 = scene.add.quadrilateral(A, B, C, D)
semicircle1 = scene.add.major_arc(E, F, G)
rect1 = scene.add.rectangle(H, I, J, K)
line_AC = scene.add.li... | {
"quad1": "Quadrilateral(A, B, C, D)",
"semicircle1": "MajorArc(E, F, G)",
"rect1": "Rectangle(H, I, J, K)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EF": "line_segment(E, F)"
} | [
"congruent(quad1, rect1)",
"acute_angle(A, B, C)",
"perpendicular(line_AC, line_BD)",
"mirror_across_line(quad1, rect1, line_EF)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [] | {
"points": {
"A": [
-2.455020618,
2.3974794804
],
"B": [
3.9392857274,
2.7653787819
],
"C": [
4.307183428,
-3.6289277359
],
"D": [
-2.0871223478,
-3.9968262695
],
"E": [
3.7023186131,
2.0581731993
],
"F": [
... |
3obj_4rel_1extra_gen0319 | 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 rhombus HIJK. There is a right isosceles triangle EFG. 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. There 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"])
rhombus1 = scene.add.rhombus(A, B, C, D)
triangle1 = scene.add.right_isosceles_triangle(E, F, G)
rhombus2 = scene.add.rhombus(H, I, J, K)
line_AC = s... | {
"rhombus1": "rhombus(A, B, C, D)",
"triangle1": "right_isosceles_triangle(E, F, G)",
"rhombus2": "rhombus(H, 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)",
"line_EG": "line_segment(E, G)",
"line_HI": "lin... | [
"perpendicular(line_AC, line_BD)",
"is_orthocenter(F, triangle1)",
"mirror_across_line(rhombus1, rhombus2, line_EG)",
"parallel(line_EF, line_IJ)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [
"scene.constraint.eq(scene.get_object('rhombus1').area, scene.get_object('triangle1').area)",
"scene.constraint.leq(scene.get_object('line_AC').length, 2 * scene.get_object('line_EF').length)"
] | {
"points": {
"A": [
0.4920509199,
-1.7540318175
],
"B": [
0.8107038082,
-1.6229074259
],
"C": [
0.9473858039,
-1.3066004869
],
"D": [
0.6287331071000001,
-1.4377235278
],
"E": [
1.5861346985,
-1.4870381632
],
"F":... |
3obj_4rel_1extra_gen0328 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, M. There is a square ABCD. There is a rhombus EFGH. There is an isosceles triangle IJK. There is a line segment AC. There is a line segment EG. There is a line segment IJ. There is a line segment JK. There is a line segment KI. The extens... | 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"])
square1 = scene.add.square(A, B, C, D)
rhombus1 = scene.add.rhombus(E, F, G, H)
triangle1 = scene.add.isosceles_triangle(I, J, K)
line_AC = s... | {
"square1": "square(A, B, C, D)",
"rhombus1": "rhombus(E, F, G, H)",
"triangle1": "isosceles_triangle(I, J, K)",
"line_AC": "line_segment(A, C)",
"line_EG": "line_segment(E, G)",
"line_IJ": "line_segment(I, J)",
"line_JK": "line_segment(J, K)",
"line_KI": "line_segment(K, I)"
} | [
"line_extensions_intersect_at(line_AC, line_EG, M)",
"point_lies_on(M, line_AC)",
"point_lies_on(M, line_EG)",
"rotation_around_point(line_IJ, line_JK, J, 90)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"M"
] | [
"scene.constraint.eq(scene.get_object('triangle1').area, scene.get_object('square1').area / 2)"
] | {
"points": {
"A": [
-1.7071007043000002,
1.1585271313
],
"B": [
-1.024578074,
0.2626492272
],
"C": [
-1.9204560828,
-0.4198732806
],
"D": [
-2.6029785511,
0.4760047228
],
"E": [
-1.8319295324,
0.6655506797
],
"F":... |
3obj_4rel_1extra_gen0332 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is a right trapezoid ABCD. There is a parallelogram EFGH. There is a circle with center I. 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 EF. Ther... | 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.right_trapezoid(A, B, C, D)
parallelogram1 = scene.add.parallelogram(E, F, G, H)
circle1 = scene.add.circle(I)
line_AB = scene.add.lin... | {
"trapezoid1": "right_trapezoid(A, B, C, D)",
"parallelogram1": "parallelogram(E, F, G, H)",
"circle1": "circle(I)",
"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_FG": "line_se... | [
"similar(trapezoid1, parallelogram1)",
"is_midpoint(J, line_AB)",
"perpendicular(line_AB, line_BC)",
"tangent_to_circle(line_BC, circle1, B)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J"
] | [] | {
"points": {
"A": [
-0.5816594851,
0.5582544810000001
],
"B": [
1.2869330693,
0.37033733750000003
],
"C": [
1.5370208920000001,
2.8571445236
],
"D": [
-0.3315846262,
3.0450787253
],
"E": [
0.6960989105000001,
3.58021242
... |
3obj_4rel_1extra_gen0335 | Diagram description: The diagram contains points A, B, C, O, H, M, D, E, F. There is a triangle with points A, B, C. There is a circle with center O. There is an equilateral triangle with points D, E, F. There is a line segment AH. There is a line segment BM. Line AH is an altitude of triangle ABC from vertex A. H is t... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O, H, M, D, E, F = scene.add.points(["A", "B", "C", "O", "H", "M", "D", "E", "F"])
triangleABC = scene.add.triangle(A, B, C)
circleO = scene.add.circle(O)
equilateral_triangleDEF = scene.add.equilateral_triangle(D, E, F)
line_altitude = scene.add.l... | {
"triangleABC": "triangle(A, B, C)",
"circleO": "circle(O)",
"equilateral_triangleDEF": "equilateral_triangle(D, E, F)",
"line_altitude": "line_segment(A, H)",
"line_median": "line_segment(B, M)"
} | [
"is_altitude(line_altitude, triangleABC, A)",
"is_orthocenter(H, triangleABC)",
"is_circumcircle(circleO, triangleABC)",
"is_median(line_median, triangleABC, B)"
] | [
"A",
"B",
"C",
"O",
"H",
"M",
"D",
"E",
"F"
] | [] | {
"points": {
"A": [
9.8549003045,
9.4609070349
],
"B": [
-5.2155553463,
-2.2082884106
],
"C": [
-5.5709718249,
-1.7289780650000002
],
"O": [
2.2585898542000002,
3.705158188
],
"H": [
-5.4503907333,
-1.8883020546
],
... |
3obj_4rel_1extra_gen0342 | 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 kite with vertices B, C, D, E. There is a rhombus with vertices F, G, H, I. There is a line segment BD. There is a line segment FH. There is a line segment AG. There is a line segment BF. Line BD and ... | 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)
kite1 = scene.add.kite(B, C, D, E)
rhombus1 = scene.add.rhombus(F, G, H, I)
line_BD = scene.add.line_segment(B, D)
line_FH = scene.add.... | {
"circle1": "circle(A)",
"kite1": "kite(B, C, D, E)",
"rhombus1": "rhombus(F, G, H, I)",
"line_BD": "line_segment(B, D)",
"line_FH": "line_segment(F, H)",
"line_AG": "line_segment(A, G)",
"line_BF": "line_segment(B, F)"
} | [
"lines_intersect_at(line_BD, line_FH, A)",
"lines_intersect_at(line_AG, line_BF, C)",
"is_diameter(line_BD, circle1)",
"is_radius(line_AG, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [] | {
"points": {
"A": [
-1.1831409931,
-0.3190090149
],
"B": [
-0.8212720184000001,
0.9152941403
],
"C": [
-0.9910502456,
-0.37532305260000004
],
"D": [
-1.5450097586,
-1.5533119166
],
"E": [
7.5620802851,
-2.8829059533
]... |
3obj_5rel_2extra_gen0001 | 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 triangle BCD. There is a triangle EFG. There is a line segment BC. There is a line segment EF. There is a line segment BD. There is a line segment CF. Triangle BCD is similar to triangle EFG. Extensio... | 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)
triangle1 = scene.add.triangle(B, C, D)
triangle2 = scene.add.triangle(E, F, G)
line_BC = scene.add.line_segment(B, C)
line_EF = scene.... | {
"circle1": "circle(A)",
"triangle1": "triangle(B, C, D)",
"triangle2": "triangle(E, F, G)",
"line_BC": "line_segment(B, C)",
"line_EF": "line_segment(E, F)",
"line_BD": "line_segment(B, D)",
"line_CF": "line_segment(C, F)"
} | [
"similar(triangle1, triangle2)",
"line_extensions_intersect_at(line_BC, line_EF, H)",
"is_circumcircle(circle1, triangle1)",
"is_orthocenter(I, triangle1)",
"perpendicular(line_BD, line_CF)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [
"scene.constraint.eq(scene.get_object('triangle1').circumradius, 3.0)",
"scene.constraint.leq(scene.get_object('line_BC').length, 4.0)"
] | {
"points": {
"A": [
4.2991158128,
-1.7906626127
],
"B": [
1.8200187515000001,
-3.4800102766
],
"C": [
1.3039987948,
-1.6200707258
],
"D": [
4.8730574868000005,
1.1539516752
],
"E": [
-5.3728118031,
3.3833905479
],
... |
3obj_5rel_2extra_gen0003 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L. There is a quadrilateral with vertices A, B, C, D. There is an equilateral triangle with vertices E, F, G. There is an equilateral triangle with vertices H, I, J. There is a line segment AC. There is a line segment BD. There is a line ... | 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"])
quad1 = scene.add.quadrilateral(A, B, C, D)
tri1 = scene.add.equilateral_triangle(E, F, G)
tri2 = scene.add.equilateral_triangle(H, I, J)
lin... | {
"quad1": "quadrilateral(A, B, C, D)",
"tri1": "equilateral_triangle(E, F, G)",
"tri2": "equilateral_triangle(H, I, J)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EF": "line_segment(E, F)",
"line_HI": "line_segment(H, I)"
} | [
"mirror_across_line(tri1, tri2, line_AC)",
"lines_intersect_at(line_AC, line_BD, K)",
"perpendicular(line_AC, line_BD)",
"line_extensions_intersect_at(line_EF, line_HI, L)",
"is_centroid(K, quad1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L"
] | [] | {
"points": {
"A": [
0.8061497294000001,
1.1146707611
],
"B": [
0.6519857388,
0.1320640844
],
"C": [
-0.33970366890000003,
0.2083172978
],
"D": [
-0.1855587187,
1.1909266425
],
"E": [
-0.1243262786,
-0.0439293422
],
... |
3obj_5rel_2extra_gen0017 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a rectangle with points A, B, C, D. There is a rhombus with points E, F, G, H. There is a circle with center I. There is a line segment AC. There is a line segment EG. There is a line segment IF. Line AC is a diameter of the circle. Li... | 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)
rhombus1 = scene.add.rhombus(E, F, G, H)
circle1 = scene.add.circle(I)
line_AC = scene.add.line_segment(A, C)
line_EG = ... | {
"rectangle1": "rectangle(A, B, C, D)",
"rhombus1": "rhombus(E, F, G, H)",
"circle1": "circle(I)",
"line_AC": "line_segment(A, C)",
"line_EG": "line_segment(E, G)",
"line_IF": "line_segment(I, F)"
} | [
"is_diameter(line_AC, circle1)",
"is_radius(line_IF, circle1)",
"perpendicular(line_AC, line_EG)",
"is_circumcircle(circle1, rectangle1)",
"point_lies_on(F, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [] | {
"points": {
"A": [
-1.0037557048,
0.029187090500000002
],
"B": [
-0.8509022279,
-0.9618778555
],
"C": [
1.1377479285,
-0.6551654099
],
"D": [
0.9848945622,
0.3358991503
],
"E": [
0.1709304047,
1.0162399649
],
"F"... |
3obj_5rel_2extra_gen0021 | Diagram description: The diagram contains points A, B, C, D, E, F, G, O. There is a triangle ABC. There is a circle with center O. There is a right triangle DEF. There is a line segment AD. There is a line segment BE. There is a line segment CF. Triangle ABC has a circumcircle centered at O. Line AD is tangent to the c... | 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.triangle(A, B, C)
circleO = scene.add.circle(O)
right_triangleDEF = scene.add.right_triangle(D, E, F)
line_AD = scene.add.line_segment(A, D)
line_BE ... | {
"triangleABC": "triangle(A, B, C)",
"circleO": "circle(O)",
"right_triangleDEF": "right_triangle(D, E, F)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)"
} | [
"is_circumcircle(circleO, triangleABC)",
"tangent_to_circle(line_AD, circleO, A)",
"line_extension_intersects_circle_at(line_BE, circleO, B, G)",
"is_altitude(line_CF, triangleABC, C)",
"is_median(line_BE, triangleABC, B)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"O"
] | [
"scene.constraint.eq(scene.get_object('right_triangleDEF').inradius, scene.get_object('triangleABC').inradius)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('O'), scene.get_object('B')), 60)"
] | {
"points": {
"A": [
0.1664528817,
0.8137552555
],
"B": [
-1.2215795149,
1.8339641827
],
"C": [
0.0847969892,
-0.7324935571000001
],
"D": [
-1.9870260235,
5.7232056214
],
"E": [
0.1256546288,
0.040608310200000004
],
... |
3obj_5rel_2extra_gen0032 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a regular heptagon ABCDEFG. There is a circle with center H. There is a right isosceles triangle IJK. There is a line segment HI. There is a line segment HJ. There is a line segment IK. There is a line segment JK. The circle is t... | 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"])
heptagon1 = scene.add.regular_heptagon(A, B, C, D, E, F, G)
circle1 = scene.add.circle(H)
triangle1 = scene.add.right_isosceles_triangle(I, J, K)
lin... | {
"heptagon1": "regular_heptagon(A, B, C, D, E, F, G)",
"circle1": "circle(H)",
"triangle1": "right_isosceles_triangle(I, J, K)",
"line_HI": "line_segment(H, I)",
"line_HJ": "line_segment(H, J)",
"line_IK": "line_segment(I, K)",
"line_JK": "line_segment(J, K)"
} | [
"is_incircle(circle1, heptagon1)",
"line_extensions_intersect_at(line_HI, line_HJ, H)",
"is_radius(line_HI, circle1)",
"is_radius(line_HJ, circle1)",
"right_angle(I, H, J)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [] | {
"points": {
"A": [
1.0910207377,
4.786772752
],
"B": [
0.5456444523,
5.9192582777
],
"C": [
-0.6798049372,
6.1989591041
],
"D": [
-1.662539046,
5.415254804
],
"E": [
-1.662539046,
4.1582907
],
"F": [
-0.679... |
3obj_5rel_2extra_gen0035 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a right trapezoid ABCD. There is a rectangle EFGH. There is a circle with center I. 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 EF. There is a ... | 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"])
trapezoid1 = scene.add.right_trapezoid(A, B, C, D)
rectangle1 = scene.add.rectangle(E, F, G, H)
circle1 = scene.add.circle(I)
line_AB = scene.add.line_segment(A, B)
... | {
"trapezoid1": "right_trapezoid(A, B, C, D)",
"rectangle1": "rectangle(E, F, G, H)",
"circle1": "circle(I)",
"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_FG": "line_segment(F,... | [
"line_intersects_circle_at(line_AC, circle1, A, C)",
"collinear(A, I, C)",
"perpendicular(line_AB, line_BC)",
"is_diameter(line_AC, circle1)",
"is_radius(line_EI, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [] | {
"points": {
"A": [
0.4682997038,
-0.11775404910000001
],
"B": [
0.2191096153,
-0.22859098290000002
],
"C": [
0.41921892600000005,
-0.6784854771000001
],
"D": [
0.6684076797,
-0.5676490493
],
"E": [
0.16658335870000002,
-... |
3obj_5rel_2extra_gen0042 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is a parallelogram ABCD. There is an isosceles 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. I... | 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"])
parallelogram1 = scene.add.parallelogram(A, B, C, D)
triangle1 = scene.add.isosceles_triangle(E, F, G)
circle1 = scene.add.circle(H)
line_AC = scene.add.line... | {
"parallelogram1": "parallelogram(A, B, C, D)",
"triangle1": "isosceles_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_midpoint(I, line_AC)",
"is_midpoint(J, line_BD)",
"collinear(A, I, C)",
"collinear(B, J, D)",
"is_circumcircle(circle1, triangle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J"
] | [] | {
"points": {
"A": [
-7.9887459761,
7.7132670356
],
"B": [
-4.3996915124000004,
4.6389116936
],
"C": [
7.3354174006,
-5.4018779943
],
"D": [
3.4391186313,
-2.0646128918
],
"E": [
7.9378841877,
-6.9005275331
],
"F":... |
3obj_5rel_2extra_gen0043 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a right trapezoid ABCD. There is a regular hexagon EFGHIJ. There is a circle with center K. There is a line AB. There is a line CD. There is a line KG. There is a line KH. The extended line AB intersects the circle at points A an... | 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.right_trapezoid(A, B, C, D)
hexagon1 = scene.add.regular_hexagon(E, F, G, H, I, J)
circle1 = scene.add.circle(K)
line_AB = sce... | {
"trapezoid1": "right_trapezoid(A, B, C, D)",
"hexagon1": "regular_hexagon(E, F, G, H, I, J)",
"circle1": "circle(K)",
"line_AB": "line_segment(A, B)",
"line_CD": "line_segment(C, D)",
"line_KG": "line_segment(K, G)",
"line_KH": "line_segment(K, H)"
} | [
"line_extension_intersects_circle_at(line_AB, circle1, A, B)",
"parallel(line_AB, line_CD)",
"is_radius(line_KG, circle1)",
"is_radius(line_KH, circle1)",
"perpendicular(line_KG, line_KH)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [
"scene.constraint.eq(scene.get_object('hexagon1').perimeter, 12)",
"scene.constraint.eq(scene.get_object('trapezoid1').area, 2 * scene.get_object('hexagon1').area)"
] | {
"points": {
"A": [
-0.1721883578,
-3.4324109985
],
"B": [
-2.808051497,
-2.4122298614
],
"C": [
-2.3225231,
3.4827479749
],
"D": [
1.8754011948,
1.8579886679
],
"E": [
-0.2988881843,
-0.48527533570000003
],
"F": ... |
3obj_5rel_2extra_gen0044 | 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 rhombus EFGH. There is a rhombus 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. There is a line segment IK. There is a line... | 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)
rhombus1 = scene.add.rhombus(E, F, G, H)
rhombus2 = scene.add.rhombus(I, J, K, L)
line_A... | {
"trapezoid1": "trapezoid(A, B, C, D)",
"rhombus1": "rhombus(E, F, G, H)",
"rhombus2": "rhombus(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_IK": "line_segment(I, K)",
"line_JL": "line_segment(J... | [
"lines_intersect_at(line_AC, line_BD, M)",
"is_midpoint(M, line_AC)",
"is_midpoint(M, line_BD)",
"mirror_across_line(rhombus1, rhombus2, line_AC)",
"perpendicular(line_AC, line_BD)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L",
"M"
] | [
"scene.constraint.eq(scene.get_object('rhombus1').area, scene.get_object('rhombus2').area)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('M'), scene.get_object('B')), 90)"
] | {
"points": {
"A": [
-2.4828058167,
0.8595608919000001
],
"B": [
-0.5443037192,
2.611508966
],
"C": [
1.2707292815,
0.7319355233
],
"D": [
-0.6677819282,
-1.0200253545
],
"E": [
0.2159217321,
1.1662398183
],
"F": [... |
3obj_5rel_2extra_gen0045 | 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 a major arc with center F, start point G, and end point H. There are line segments BC, CD, DE, EB, BD, and CF. Line BC intersects the circle at points B and C. L... | 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)
semicircle1 = scene.add.major_arc(F, G, H)
line_BC = scene.add.line_segment(B, C)
line_CD = scene.add.li... | {
"circle1": "circle(A)",
"square1": "square(B, C, D, E)",
"semicircle1": "major_arc(F, G, H)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_DE": "line_segment(D, E)",
"line_EB": "line_segment(E, B)",
"line_BD": "line_segment(B, D)",
"line_CF": "line_segment(C, F)"
} | [
"line_intersects_circle_at(line_BC, circle1, B, C)",
"is_diameter(line_BD, circle1)",
"perpendicular(line_BC, line_CD)",
"point_lies_on(F, circle1)",
"point_lies_on(G, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"scene.constraint.eq(scene.get_object('line_BC').length, scene.get_object('line_CD').length)",
"scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('C'), scene.get_object('D')), 90)"
] | {
"points": {
"A": [
0.7523805028,
-0.453008795
],
"B": [
1.8398032492,
0.7565722960000001
],
"C": [
1.9619611555,
-1.5404323386
],
"D": [
-0.33504300330000003,
-1.6625902115
],
"E": [
-0.4572008846,
0.6344147819
],
... |
3obj_5rel_2extra_gen0077 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a rhomboid BCDE. There is a minor arc FG. There is a line segment BD. There is a line segment CF. There is a line segment AG. There is a line segment FE. Line BD intersects line CF at point H. Points B, H,... | 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)
rhomboid1 = scene.add.rhomboid(B, C, D, E)
minor_arc1 = scene.add.minor_arc(A, F, G)
line_BD = scene.add.line_segment(B, D)
line_CF = scene.add... | {
"circle1": "circle(A)",
"rhomboid1": "rhomboid(B, C, D, E)",
"minor_arc1": "minor_arc(A, F, G)",
"line_BD": "line_segment(B, D)",
"line_CF": "line_segment(C, F)",
"line_AG": "line_segment(A, G)",
"line_FE": "line_segment(F, E)"
} | [
"lines_intersect_at(line_BD, line_CF, H)",
"collinear(B, H, D)",
"is_chord(line_BD, circle1)",
"point_lies_on(F, circle1)",
"point_lies_on(G, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
0.3326615596,
2.5066500885
],
"B": [
1.0596788278,
-1.94286905
],
"C": [
3.1801484723,
1.1935433846
],
"D": [
0.2531643337,
7.01447159
],
"E": [
-1.8673053377,
3.8780592394
],
"F": [
-1.3... |
3obj_5rel_2extra_gen0083 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a trapezoid ABCD. There is a trapezoid EFGH. There is a circle with center I. There is a line segment AB. There is a line segment CD. There is a line segment EF. There is a line segment GH. There is a line segment IF. There is a line s... | 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"])
trapezoid1 = scene.add.trapezoid(A, B, C, D)
trapezoid2 = scene.add.trapezoid(E, F, G, H)
circle1 = scene.add.circle(I)
line_AB = scene.add.line_segment(A, B)
line_C... | {
"trapezoid1": "trapezoid(A, B, C, D)",
"trapezoid2": "trapezoid(E, F, G, H)",
"circle1": "circle(I)",
"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_IF": "line_segment(I, F)",
"line_IH": "line_segment(I, H)",
... | [
"perpendicular_bisector_at(line_AB, line_IF)",
"similar(trapezoid1, trapezoid2)",
"is_radius(line_IF, circle1)",
"is_radius(line_IH, circle1)",
"point_lies_on(F, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [
"scene.constraint.eq(scene.get_object('line_IF').length, scene.get_object('line_IH').length)",
"scene.constraint.leq(scene.get_object('trapezoid1').area, 20)"
] | {
"points": {
"A": [
1.0403855756,
-0.8323515572
],
"B": [
-1.7594503434000002,
3.6072847292
],
"C": [
0.1299618398,
-2.6360608889
],
"D": [
-3.0227577109,
2.3631599667
],
"E": [
-4.3135388664,
-2.0368315261
],
"F"... |
3obj_5rel_2extra_gen0092 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is a parallelogram with vertices A, B, C, D. There is a semicircle with center E and endpoints F and G. There is a semicircle with center H and endpoints I and J. There is a line segment AC. There is a line segment BD. Point F lies on ... | 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"])
parallelogram1 = scene.add.parallelogram(A, B, C, D)
semicircle1 = scene.add.major_arc(E, F, G)
semicircle2 = scene.add.major_arc(H, I, J)
line_AC = scene.ad... | {
"parallelogram1": "parallelogram(A, B, C, D)",
"semicircle1": "MajorArc(E, F, G)",
"semicircle2": "MajorArc(H, I, J)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)"
} | [
"point_lies_on(F, semicircle1)",
"point_lies_on(G, semicircle1)",
"point_lies_on(I, semicircle2)",
"point_lies_on(J, semicircle2)",
"right_angle(F, E, G)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J"
] | [
"scene.constraint.eq(scene.get_object('semicircle1').radius, 3.0)",
"scene.constraint.leq(scene.get_object('parallelogram1').perimeter, 20.0)"
] | {
"points": {
"A": [
0.5786584219,
-0.4410408945
],
"B": [
-3.359931822,
1.9847390652999999
],
"C": [
-3.7664678706,
0.7909883589000001
],
"D": [
0.1721223586,
-1.6347915895
],
"E": [
1.6937345629,
-1.3194242219
],
... |
3obj_5rel_2extra_gen0124 | Diagram description: The diagram contains points A, B, C, O, D, E, F. There is an obtuse triangle ABC. There is a circle with center O. There is an acute triangle DEF. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment OA. There is a line segment OB. There is a l... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O, D, E, F = scene.add.points(["A", "B", "C", "O", "D", "E", "F"])
triangle1 = scene.add.obtuse_triangle(A, B, C)
circle1 = scene.add.circle(O)
triangle2 = scene.add.acute_triangle(D, E, F)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add... | {
"triangle1": "obtuse_triangle(A, B, C)",
"circle1": "circle(O)",
"triangle2": "acute_triangle(D, E, F)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)",
"line_OA": "line_segment(O, A)",
"line_OB": "line_segment(O, B)",
"line_OC": "line_segment(O, C)... | [
"is_circumcircle(circle1, triangle1)",
"is_chord(line_AD, circle1)",
"is_altitude(line_BE, triangle1, B)",
"is_median(line_CF, triangle1, C)",
"perpendicular(line_OA, line_BE)"
] | [
"A",
"B",
"C",
"O",
"D",
"E",
"F"
] | [] | {
"points": {
"A": [
0.2095819194,
3.1625649529
],
"B": [
0.0809286499,
2.4207053675
],
"C": [
-1.4806738641,
2.691518954
],
"O": [
-0.6355454183,
2.9270425475
],
"D": [
0.0301783755,
3.498464766
],
"E": [
-0... |
3obj_5rel_2extra_gen0125 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a right triangle with vertices B, C, D. There is a trapezoid with vertices E, F, G, H. There is a line segment BC. There is a line segment CD. There is a line segment EF. There is a line segment FG. Point ... | 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)
right_triangle1 = scene.add.right_triangle(B, C, D)
trapezoid1 = scene.add.trapezoid(E, F, G, H)
line_BC = scene.add.line_segment(B, C)
line_CD... | {
"circle1": "circle(A)",
"right_triangle1": "right_triangle(B, C, D)",
"trapezoid1": "trapezoid(E, F, G, H)",
"line_BC": "line_segment(B, C)",
"line_CD": "line_segment(C, D)",
"line_EF": "line_segment(E, F)",
"line_FG": "line_segment(F, G)"
} | [
"point_lies_on(B, circle1)",
"point_lies_on(C, circle1)",
"is_chord(line_BC, circle1)",
"perpendicular(line_BC, line_CD)",
"lines_intersect_at(line_BC, line_FG, C)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"scene.constraint.eq(scene.get_object('line_BC').length, scene.get_object('line_CD').length)",
"scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('C'), scene.get_object('D')), 90)"
] | {
"points": {
"A": [
-0.2516531433,
2.1501841532
],
"B": [
-2.3576650819,
1.4146395864
],
"C": [
1.5848528367,
3.4165008051
],
"D": [
3.5867139994,
-0.526016979
],
"E": [
-3.0171047545,
-2.1761354345
],
"F": [
... |
3obj_5rel_2extra_gen0127 | Diagram description: The diagram contains points A, B, C, O, D, E, F. There is a triangle ABC with vertices A, B, C. There is a circle with center O. There is a minor arc EF with center D. There is a line segment AD. There is a line segment BE. The circle is the circumcircle of triangle ABC. Line AD is tangent to the c... | 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)
minor_arc_DE = scene.add.minor_arc(D, E, F)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_s... | {
"triangleABC": "triangle(A, B, C)",
"circleO": "circle(O)",
"minor_arc_DE": "minor_arc(D, E, F)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)"
} | [
"is_circumcircle(circleO, triangleABC)",
"tangent_to_circle(line_AD, circleO, A)",
"is_midpoint(E, line_AD)",
"is_altitude(line_BE, triangleABC, B)",
"point_lies_on(F, circleO)"
] | [
"A",
"B",
"C",
"O",
"D",
"E",
"F"
] | [] | {
"points": {
"A": [
2.8637303124,
-1.2973972505
],
"B": [
-9.6425066187,
4.8081039052
],
"C": [
2.7786310687,
-1.4783753474
],
"O": [
-3.4778682237,
1.5740771513
],
"D": [
3.0317110961,
-0.9264654033
],
"E": [
... |
3obj_5rel_2extra_gen0132 | 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 trapezoid BCDE. There is an isosceles trapezoid FGHI. There is a line segment BD. There is a line segment CE. There is a line segment FH. There is a line segment GI. Line BD intersects the circle at p... | 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)
trapezoid1 = scene.add.trapezoid(B, C, D, E)
isosceles_trapezoid1 = scene.add.isosceles_trapezoid(F, G, H, I)
line_BD = scene.add.line_... | {
"circle1": "circle(A)",
"trapezoid1": "trapezoid(B, C, D, E)",
"isosceles_trapezoid1": "isosceles_trapezoid(F, G, H, I)",
"line_BD": "line_segment(B, D)",
"line_CE": "line_segment(C, E)",
"line_FH": "line_segment(F, H)",
"line_GI": "line_segment(G, I)"
} | [
"line_intersects_circle_at(line_BD, circle1, B, D)",
"tangent_to_circle(line_CE, circle1, C)",
"parallel(line_BD, line_FH)",
"is_diameter(line_GI, circle1)",
"perpendicular(line_CE, line_BD)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [] | {
"points": {
"A": [
0.018220669800000002,
0.09380463500000001
],
"B": [
0.5050175241,
-0.5874553911
],
"C": [
0.07227345140000001,
0.9293694228
],
"D": [
0.5887273978,
0.7066783581
],
"E": [
0.5337124919,
0.8995200001
... |
3obj_5rel_2extra_gen0137 | Diagram description: The diagram contains points A, B, C, O, M, N, P. There is a triangle ABC. There is a circle with center O. There is an isosceles trapezoid MNOP. There is a line AB. There is a line AC. There is a line BC. There is a line MO. There is a line NO. The circle with center O is the circumcircle of triang... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O, M, N, P = scene.add.points(["A", "B", "C", "O", "M", "N", "P"])
triangleABC = scene.add.triangle(A, B, C)
circleO = scene.add.circle(O)
isosceles_trapezoidMNOP = scene.add.isosceles_trapezoid(M, N, O, P)
line_AC = scene.add.line_segment(A, C)
li... | {
"triangleABC": "Triangle(A, B, C)",
"circleO": "Circle(O)",
"isosceles_trapezoidMNOP": "IsoscelesTrapezoid(M, N, O, P)",
"line_AC": "line_segment(A, C)",
"line_BC": "line_segment(B, C)",
"line_AB": "line_segment(A, B)",
"line_MO": "line_segment(M, O)",
"line_NO": "line_segment(N, O)"
} | [
"is_circumcircle(circleO, triangleABC)",
"point_lies_on(A, circleO)",
"point_lies_on(C, circleO)",
"is_midpoint(M, line_AC)",
"is_midpoint(P, line_BC)"
] | [
"A",
"B",
"C",
"O",
"M",
"N",
"P"
] | [
"scene.constraint.eq(scene.get_object('line_BC').length, scene.get_object('line_AC').length)",
"scene.constraint.eq(scene.get_object('triangleABC').inradius, 2.0)"
] | {
"points": {
"A": [
-0.5780456303,
-5.1412225111
],
"B": [
-6.6098913127,
-0.325882396
],
"C": [
-0.1819475412,
1.5404458248
],
"O": [
-2.7374317757,
-1.6606369035
],
"M": [
-0.38000678520000003,
-1.8003878529000001
]... |
3obj_5rel_2extra_gen0153 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is an obtuse triangle with vertices A, B, C. There is an isosceles triangle with vertices D, E, F. There is an obtuse triangle with vertices G, H, I. There is a line segment AD. There is a line segment BE. There is a line segment CF. Ther... | 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"])
triangle1 = scene.add.obtuse_triangle(A, B, C)
triangle2 = scene.add.isosceles_triangle(D, E, F)
triangle3 = scene.add.obtuse_triangle(G, H, I)
line_AD = scene.add.l... | {
"triangle1": "obtuse_triangle(A, B, C)",
"triangle2": "isosceles_triangle(D, E, F)",
"triangle3": "obtuse_triangle(G, H, I)",
"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)",
"line_IG"... | [
"similar(triangle1, triangle3)",
"collinear(A, D, G)",
"perpendicular(line_AD, line_BE)",
"is_altitude(line_CF, triangle1, C)",
"is_orthocenter(F, triangle2)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [
"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('B'), scene.get_object('C')), 120)"
] | {
"points": {
"A": [
-1.5586056658,
1.8375930159
],
"B": [
-0.7563276267,
1.3094244951
],
"C": [
-1.0258260201,
-3.2831417480000002
],
"D": [
1.2378734728,
-0.141681559
],
"E": [
-2.7354068859,
-1.4868456847
],
"F"... |
3obj_5rel_2extra_gen0164 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a right isosceles triangle ABC with AB = BC and right angle at B. There is a square DEFG. There is a circle with center H. There is a line segment AC. There is a line segment BD. There is a line segment HF. Line HF is a radius of the circ... | 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"])
triangleABC = scene.add.right_isosceles_triangle(A, B, C)
squareDEFG = scene.add.square(D, E, F, G)
circleH = scene.add.circle(H)
line_AC = scene.add.line_segment(A, C)
line... | {
"triangleABC": "right_isosceles_triangle(A, B, C)",
"squareDEFG": "square(D, E, F, G)",
"circleH": "circle(H)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_HF": "line_segment(H, F)"
} | [
"is_radius(line_HF, circleH)",
"is_circumcircle(circleH, squareDEFG)",
"perpendicular(line_AC, line_BD)",
"is_altitude(line_BD, triangleABC, B)",
"is_incircle(circleH, triangleABC)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
-0.342362538,
0.5032109654
],
"B": [
0.10715216570000001,
-1.0974306329
],
"C": [
-1.4934893278,
-1.5469449092
],
"D": [
-0.9179258851000001,
-0.5218673669
],
"E": [
-0.2549200102,
-0.3356735798
],... |
3obj_5rel_2extra_gen0165 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a rectangle with points A, B, C, D. There is a circle with center E. There is an isosceles triangle with vertices F, G, H. There is a line segment AC. There is a line segment EG. There is a line segment FH. The circle is the circumcircle ... | 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"])
rectangle1 = scene.add.rectangle(A, B, C, D)
circle1 = scene.add.circle(E)
triangle1 = scene.add.isosceles_triangle(F, G, H)
line_AC = scene.add.line_segment(A, C)
line_EG =... | {
"rectangle1": "rectangle(A, B, C, D)",
"circle1": "circle(E)",
"triangle1": "isosceles_triangle(F, G, H)",
"line_AC": "line_segment(A, C)",
"line_EG": "line_segment(E, G)",
"line_FH": "line_segment(F, H)"
} | [
"is_circumcircle(circle1, rectangle1)",
"is_orthocenter(G, triangle1)",
"collinear(A, E, C)",
"is_diameter(line_AC, circle1)",
"perpendicular(line_EG, line_FH)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
-1.127866605,
5.1495211426
],
"B": [
-1.1167893044,
4.6111809816000005
],
"C": [
-0.5279694907,
4.6232968094
],
"D": [
-0.5390469474,
5.1616371381
],
"E": [
-0.8279181097,
4.8864090432000005
],
... |
3obj_5rel_2extra_gen0167 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a right triangle ABC with right angle at B. There is a rhombus DEFG. There is a circle with center H. There is a line segment AC. There is a line segment HD. There is a line segment HF. Line AC is tangent to the circle at A. Points A, H, ... | 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"])
triangle1 = scene.add.right_triangle(A, B, C)
rhombus1 = scene.add.rhombus(D, E, F, G)
circle1 = scene.add.circle(H)
line_AC = scene.add.line_segment(A, C)
line_HD = scene.a... | {
"triangle1": "right_triangle(A, B, C)",
"rhombus1": "rhombus(D, E, F, G)",
"circle1": "circle(H)",
"line_AC": "line_segment(A, C)",
"line_HD": "line_segment(H, D)",
"line_HF": "line_segment(H, F)"
} | [
"tangent_to_circle(line_AC, circle1, A)",
"collinear(A, H, D)",
"is_radius(line_HD, circle1)",
"is_radius(line_HF, circle1)",
"perpendicular(line_HD, line_HF)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
1.5776005338,
-0.0253775389
],
"B": [
1.6516310122,
0.257613307
],
"C": [
-0.611991649,
0.849775276
],
"D": [
1.3875840301,
-0.5007950876
],
"E": [
2.0561153625,
-1.6002719511999999
],
"F": [
... |
3obj_5rel_2extra_gen0181 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, O, I, J, K. There is a regular octagon with vertices A, B, C, D, E, F, G, H. There is a circle with center O. There is a scalene triangle with vertices I, J, K. There is a line segment OI. There is a line segment OJ. There is a line segment OK. Th... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, E, F, G, H, O, I, J, K = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "O", "I", "J", "K"])
regular_octagon1 = scene.add.regular_octagon(A, B, C, D, E, F, G, H)
circle1 = scene.add.circle(O)
scalene_triangle1 = scene.add.scalene_tria... | {
"regular_octagon1": "regular_octagon(A, B, C, D, E, F, G, H)",
"circle1": "circle(O)",
"scalene_triangle1": "scalene_triangle(I, J, K)",
"line_OI": "line_segment(O, I)",
"line_OJ": "line_segment(O, J)",
"line_OK": "line_segment(O, K)",
"line_IJ": "line_segment(I, J)",
"line_JK": "line_segment(J, K)",
... | [
"is_circumcircle(circle1, regular_octagon1)",
"is_radius(line_OI, circle1)",
"is_radius(line_OJ, circle1)",
"is_radius(line_OK, circle1)",
"line_extension_intersects_circle_at(line_IJ, circle1, I, J)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"O",
"I",
"J",
"K"
] | [] | {
"points": {
"A": [
2.0727433478,
3.4448131148
],
"B": [
-0.0699751011,
3.5597553019
],
"C": [
-1.6663822464,
2.1259009564999998
],
"D": [
-1.7813244335,
-0.0168174924
],
"E": [
-0.3474700881,
-1.6132246377000001
],
... |
3obj_5rel_2extra_gen0190 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a trapezoid ABCD. There is a rhomboid EFGH. There is a circle with center I. There is a line segment AB. There is a line segment CD. There is a line segment EF. There is a line segment FG. There is a line segment IJ. Line AB is 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"])
trapezoid1 = scene.add.trapezoid(A, B, C, D)
rhomboid1 = scene.add.rhomboid(E, F, G, H)
circle1 = scene.add.circle(I)
line_AB = scene.add.line_segmen... | {
"trapezoid1": "trapezoid(A, B, C, D)",
"rhomboid1": "rhomboid(E, F, G, H)",
"circle1": "circle(I)",
"line_AB": "line_segment(A, B)",
"line_CD": "line_segment(C, D)",
"line_EF": "line_segment(E, F)",
"line_FG": "line_segment(F, G)",
"line_IJ": "line_segment(I, J)"
} | [
"parallel(line_AB, line_CD)",
"line_intersects_circle_at(line_EF, circle1, J, K)",
"right_angle(A, B, C)",
"perpendicular(line_AB, line_EF)",
"is_radius(line_IJ, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [
"scene.constraint.eq(scene.get_object('trapezoid1').area, scene.get_object('rhomboid1').area)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)"
] | {
"points": {
"A": [
-3.9610470169000003,
0.0137961954
],
"B": [
-0.342490295,
-1.8253626002
],
"C": [
1.2661039961,
1.339556808
],
"D": [
2.3342979704999998,
0.796638512
],
"E": [
0.2253295257,
2.501807892
],
"F":... |
3obj_5rel_2extra_gen0198 | 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 trapezoid BCDE. There is a square FGHI. There is a line segment BD. There is a line segment FH. There is a line segment CG. Line BD is the perpendicular bisector of line CG. Point G lies on the circle... | 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)
trapezoid1 = scene.add.trapezoid(B, C, D, E)
square1 = scene.add.square(F, G, H, I)
line_BD = scene.add.line_segment(B, D)
line_FH = sc... | {
"circle1": "circle(A)",
"trapezoid1": "trapezoid(B, C, D, E)",
"square1": "square(F, G, H, I)",
"line_BD": "line_segment(B, D)",
"line_FH": "line_segment(F, H)",
"line_CG": "line_segment(C, G)"
} | [
"perpendicular_bisector_at(line_BD, line_CG)",
"point_lies_on(G, circle1)",
"is_diameter(line_FH, circle1)",
"is_circumcircle(circle1, square1)",
"line_intersects_circle_at(line_CG, circle1, C, G)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [] | {
"points": {
"A": [
2.2456296555,
-1.0941925007
],
"B": [
2.0612904272,
-1.2000262098
],
"C": [
1.7804862799999999,
-1.2440999528
],
"D": [
1.1825490418,
-1.7045193995
],
"E": [
3.0956561259,
-1.4042470908
],
"F":... |
3obj_5rel_2extra_gen0212 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a trapezoid ABCD. There is a circle with center E. There is a right triangle FGH. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment FH. Line AC is perpendicular to line BD. Point G... | 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)
circle1 = scene.add.circle(E)
right_triangle1 = scene.add.right_triangle(F, G, H)
line_AC = scene.add.line_segment(A, C)
line_BD... | {
"trapezoid1": "trapezoid(A, B, C, D)",
"circle1": "circle(E)",
"right_triangle1": "right_triangle(F, G, H)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EF": "line_segment(E, F)",
"line_FH": "line_segment(F, H)"
} | [
"perpendicular(line_AC, line_BD)",
"is_orthocenter(G, right_triangle1)",
"is_chord(line_FH, circle1)",
"point_lies_on(F, circle1)",
"point_lies_on(H, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)",
"scene.constraint.eq(scene.get_object('right_triangle1').area, 6)"
] | {
"points": {
"A": [
1.9099804186,
-0.9002787596
],
"B": [
3.8682172383,
-2.6898686541
],
"C": [
3.172559208,
-0.8434644617
],
"D": [
3.8114029492,
-1.4272898239
],
"E": [
-1.1482606565,
-1.9834836895999999
],
"F":... |
3obj_5rel_2extra_gen0219 | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a triangle ABC. There is a circle with center D. There is a scalene triangle EFG. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment EG. There is a line segment FG. Line AD is a radius... | 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.triangle(A, B, C)
circle1 = scene.add.circle(D)
scalene1 = scene.add.scalene_triangle(E, F, G)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_... | {
"triangle1": "Triangle(A, B, C)",
"circle1": "Circle(D)",
"scalene1": "ScaleneTriangle(E, F, G)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)",
"line_EG": "line_segment(E, G)",
"line_FG": "line_segment(F, G)"
} | [
"is_radius(line_AD, circle1)",
"congruent(line_BE, line_CF)",
"is_altitude(line_BE, triangle1, B)",
"is_circumcircle(circle1, triangle1)",
"is_incircle(circle1, scalene1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [] | {
"points": {
"A": [
-2.0316135796,
3.1872208623000002
],
"B": [
-1.3213734332,
3.0945305638
],
"C": [
-2.4286767128,
2.3290991518
],
"D": [
-1.7551244103,
2.5383630889
],
"E": [
-1.9416910626,
3.3815590134
],
"F":... |
3obj_5rel_2extra_gen0231 | 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 AD. circle with center A is the circumc... | 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_AD": "line_segment(A, D)"
} | [
"is_circumcircle(circle1, triangle1)",
"is_incircle(circle2, triangle1)",
"right_angle(D, C, E)",
"obtuse_angle(E, C, D)",
"is_radius(line_AD, circle1)"
] | [
"A",
"B",
"C",
"D",
"E"
] | [
"scene.constraint.eq(scene.get_object('circle1').diameter, 4.0)",
"scene.constraint.leq(scene.get_object('triangle1').area, 6.0)"
] | {
"points": {
"A": [
-1.8278387033999999,
0.38561177820000003
],
"B": [
-1.3538210649,
-0.3033065911
],
"C": [
-0.5867588792,
-1.1827372424
],
"D": [
-0.3851447771,
1.7707595389000002
],
"E": [
-3.2704448221,
-0.9996259222... |
3obj_5rel_2extra_gen0233 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L. There is a right trapezoid ABCD. There is a right trapezoid EFGH. There is a major arc IJK. There is a line segment AD. There is a line segment EH. There is a line segment IJ. There is a line segment JK. The angle ADB is acute. The ext... | 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"])
trapezoid1 = scene.add.right_trapezoid(A, B, C, D)
trapezoid2 = scene.add.right_trapezoid(E, F, G, H)
semicircle1 = scene.add.major_arc(I, J,... | {
"trapezoid1": "right_trapezoid(A, B, C, D)",
"trapezoid2": "right_trapezoid(E, F, G, H)",
"semicircle1": "major_arc(I, J, K)",
"line_AD": "line_segment(A, D)",
"line_EH": "line_segment(E, H)",
"line_IJ": "line_segment(I, J)",
"line_JK": "line_segment(J, K)"
} | [
"acute_angle(A, D, B)",
"line_extensions_intersect_at(line_AD, line_EH, L)",
"mirror_across_line(trapezoid1, trapezoid2, line_IJ)",
"perpendicular(line_AD, line_IJ)",
"point_lies_on(J, semicircle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L"
] | [
"scene.constraint.eq(scene.get_object('trapezoid1').area, scene.get_object('trapezoid2').area)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('D'), scene.get_object('B')), 60)"
] | {
"points": {
"A": [
-0.4886955214,
-0.056953163
],
"B": [
2.1346893878,
0.7128266507000001
],
"C": [
-1.4746768245,
1.2987500456
],
"D": [
-0.9331300697,
1.4576511069
],
"E": [
-1.0872879036,
1.9830142546
],
"F": ... |
3obj_5rel_2extra_gen0235 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a quadrilateral with vertices A, B, C, D. There is a rhombus with vertices E, F, G, H. There is an obtuse triangle with vertices I, J, K. There is a line segment AC. There is a line segment BD. There is a line segment EG. There 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"])
quadrilateral1 = scene.add.quadrilateral(A, B, C, D)
rhombus1 = scene.add.rhombus(E, F, G, H)
obtuse_triangle1 = scene.add.obtuse_triangle(I, J, K)
l... | {
"quadrilateral1": "quadrilateral(A, B, C, D)",
"rhombus1": "rhombus(E, F, G, H)",
"obtuse_triangle1": "obtuse_triangle(I, J, K)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EG": "line_segment(E, G)",
"line_FH": "line_segment(F, H)"
} | [
"similar(quadrilateral1, rhombus1)",
"point_lies_on(A, line_AC)",
"point_lies_on(C, line_AC)",
"perpendicular(line_AC, line_BD)",
"obtuse_angle(J, K, I)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [
"scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)",
"scene.constraint.leq(scene.get_object('obtuse_triangle1').area, 10)"
] | {
"points": {
"A": [
-2.4587861285,
2.445631068
],
"B": [
1.8611181306,
1.6306405448999999
],
"C": [
1.0461484181,
-2.6893640569
],
"D": [
-3.2738820592,
-1.8742992272999999
],
"E": [
0.1648793213,
-0.9748981561000001
... |
3obj_5rel_2extra_gen0244 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a circle with center A. There is a regular pentagon with vertices B, C, D, E, F. There is a square with vertices G, H, I, J. There is a line segment BD. There is a line segment GI. Line BD and line GI intersect at point K. Points... | 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"])
circle1 = scene.add.circle(A)
pentagon1 = scene.add.regular_pentagon(B, C, D, E, F)
square1 = scene.add.square(G, H, I, J)
line_BD = scene.add.line_s... | {
"circle1": "circle(A)",
"pentagon1": "regular_pentagon(B, C, D, E, F)",
"square1": "square(G, H, I, J)",
"line_BD": "line_segment(B, D)",
"line_GI": "line_segment(G, I)"
} | [
"lines_intersect_at(line_BD, line_GI, K)",
"collinear(B, K, D)",
"perpendicular(line_BD, line_GI)",
"is_circumcircle(circle1, pentagon1)",
"is_incircle(circle1, square1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [] | {
"points": {
"A": [
0.49690271090000004,
1.7236339226
],
"B": [
0.3735577031,
2.3623158636
],
"C": [
-0.1486375257,
1.8036901128
],
"D": [
0.2212799347,
1.1344280871
],
"E": [
0.972096727,
1.2794271587
],
"F": [
... |
3obj_5rel_2extra_gen0246 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a regular pentagon with vertices A, B, C, D, E. There is a rectangle with vertices F, G, H, I. There is a circle with center J. There are line segments AC, FG, JH, JI. The extensions of line AC and line FG intersect at point K. A... | 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)
rectangle1 = scene.add.rectangle(F, G, H, I)
circle1 = scene.add.circle(J)
line_AC = scene.add.... | {
"pentagon1": "regular_pentagon(A, B, C, D, E)",
"rectangle1": "rectangle(F, G, H, I)",
"circle1": "circle(J)",
"line_AC": "line_segment(A, C)",
"line_FG": "line_segment(F, G)",
"line_JH": "line_segment(J, H)",
"line_JI": "line_segment(J, I)"
} | [
"line_extensions_intersect_at(line_AC, line_FG, K)",
"acute_angle(A, K, F)",
"is_circumcircle(circle1, pentagon1)",
"is_radius(line_JH, circle1)",
"perpendicular(line_JI, line_FG)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [
"scene.constraint.eq(scene.get_object('pentagon1').diagonal, 2 * scene.get_object('circle1').radius)",
"scene.constraint.leq(scene.get_object('line_JI').length, scene.get_object('rectangle1').perimeter / 8)"
] | {
"points": {
"A": [
0.6929876772,
2.5094047838
],
"B": [
0.8532702947,
2.116402081
],
"C": [
1.2765681288000001,
2.1473953948
],
"D": [
1.3778979601,
2.5595530189
],
"E": [
1.0172254059,
2.7832871256000002
],
"F":... |
3obj_5rel_2extra_gen0255 | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a major arc with center A from B to C. There is a circle with center D. There is a major arc with center E from F to G. There is a line segment AD. There is a line segment BD. There is a line segment EG. Line AD is a radius of the circle. 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"])
semicircle1 = scene.add.major_arc(A, B, C)
circle1 = scene.add.circle(D)
semicircle2 = scene.add.major_arc(E, F, G)
line_AD = scene.add.line_segment(A, D)
line_BD = scene.add.line_s... | {
"semicircle1": "major_arc(A, B, C)",
"circle1": "circle(D)",
"semicircle2": "major_arc(E, F, G)",
"line_AD": "line_segment(A, D)",
"line_BD": "line_segment(B, D)",
"line_EG": "line_segment(E, G)"
} | [
"is_radius(line_AD, circle1)",
"lines_intersect_at(line_AD, line_BD, D)",
"is_chord(line_EG, circle1)",
"perpendicular(line_AD, line_BD)",
"point_lies_on(F, semicircle2)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [] | {
"points": {
"A": [
0.36014683680000004,
0.7379360373
],
"B": [
-0.0388826118,
-1.3682132516
],
"C": [
-1.0355000624,
-0.8891039275
],
"D": [
-0.2348263603,
0.6810465872
],
"E": [
-0.0080220937,
0.12806432310000002
],... |
3obj_5rel_2extra_gen0266 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a kite with vertices A, B, C, D. There is a regular pentagon with vertices E, F, G, H, I. There is a circle with center J. There is a line segment AC. There is a line segment BD. There is a line segment EG. There is a line segmen... | 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"])
kite1 = scene.add.kite(A, B, C, D)
pentagon1 = scene.add.regular_pentagon(E, F, G, H, I)
circle1 = scene.add.circle(J)
line_AC = scene.add.line_segme... | {
"kite1": "kite(A, B, C, D)",
"pentagon1": "regular_pentagon(E, F, G, H, I)",
"circle1": "circle(J)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EG": "line_segment(E, G)",
"line_JE": "line_segment(J, E)"
} | [
"perpendicular_bisector_at(line_AC, line_BD)",
"line_extensions_intersect_at(line_AC, line_EG, K)",
"angle_bisector(A, B, D, line_BD)",
"is_circumcircle(circle1, pentagon1)",
"is_radius(line_JE, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [] | {
"points": {
"A": [
-3.6473449457,
0.7941101259000001
],
"B": [
-9.7968969731,
-4.533849597
],
"C": [
-3.7776590126,
0.9445173542
],
"D": [
2.5005770537,
6.1206636453
],
"E": [
3.7161256066,
1.2501138733000001
],
... |
3obj_5rel_2extra_gen0275 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, O, P, Q. There is a rectangle with vertices A, B, C, D. There is a quadrilateral with vertices E, F, G, H. There is a quadrilateral with vertices I, J, K, L. 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, K, L, O, P, Q = scene.add.points(["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "O", "P", "Q"])
rectangle1 = scene.add.rectangle(A, B, C, D)
quad1 = scene.add.quadrilateral(E, F, G, H)
quad2 = scene.add.quadrilate... | {
"rectangle1": "rectangle(A, B, C, D)",
"quad1": "quadrilateral(E, F, G, H)",
"quad2": "quadrilateral(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_IK": "line_segment(I, K)",
"line_JL": "line_seg... | [
"lines_intersect_at(line_AC, line_BD, O)",
"lines_intersect_at(line_EG, line_FH, P)",
"lines_intersect_at(line_IK, line_JL, Q)",
"acute_angle(A, O, B)",
"right_angle(E, P, F)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L",
"O",
"P",
"Q"
] | [
"scene.constraint.eq(scene.get_object('rectangle1').perimeter, scene.get_object('quad1').perimeter)",
"scene.constraint.leq(scene.get_object('line_AC').length, scene.get_object('line_EG').length)"
] | {
"points": {
"A": [
-2.4186953344,
2.9334166230000003
],
"B": [
-1.7694852058000001,
2.5101079711
],
"C": [
-3.2964270508,
0.1683033428
],
"D": [
-3.9456369573,
0.5916119534000001
],
"E": [
0.43813845090000003,
3.48904217... |
3obj_5rel_2extra_gen0299 | 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 circle with center D. There is an isosceles trapezoid with vertices E, F, G, H. There is a line segment AD. There is a line segment BD. There is a line segment EF. Ther... | 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)
circle1 = scene.add.circle(D)
trapezoid1 = scene.add.isosceles_trapezoid(E, F, G, H)
line_AD = scene.add.line_segment(A, D)
line_B... | {
"semicircle1": "major_arc(A, B, C)",
"circle1": "circle(D)",
"trapezoid1": "isosceles_trapezoid(E, F, G, H)",
"line_AD": "line_segment(A, D)",
"line_BD": "line_segment(B, D)",
"line_EF": "line_segment(E, F)",
"line_GH": "line_segment(G, H)"
} | [
"point_lies_on(A, circle1)",
"point_lies_on(B, circle1)",
"is_radius(line_AD, circle1)",
"is_radius(line_BD, circle1)",
"point_lies_on(E, semicircle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"scene.constraint.eq(scene.get_object('line_EF').length, scene.get_object('line_AD').length)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('D'), scene.get_object('B')), 90)"
] | {
"points": {
"A": [
-5.4889736453,
-2.6665419833
],
"B": [
1.1503855248,
-2.7748881006
],
"C": [
-2.4178895152,
-8.5539243369
],
"D": [
-2.2234671378,
-6.04039463
],
"E": [
0.7515248278000001,
-4.9356846425
],
"F"... |
3obj_5rel_2extra_gen0302 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a rhomboid ABCD. There is a minor arc 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 FG. Line AC and line BD intersect at I. Angle AIB is a right angle. Line FG 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"])
rhomboid1 = scene.add.rhomboid(A, B, C, D)
arc1 = scene.add.minor_arc(E, F, G)
circle1 = scene.add.circle(H)
line_AC = scene.add.line_segment(A, C)
line_BD = scene.a... | {
"rhomboid1": "rhomboid(A, B, C, D)",
"arc1": "minor_arc(E, F, G)",
"circle1": "circle(H)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_FG": "line_segment(F, G)"
} | [
"lines_intersect_at(line_AC, line_BD, I)",
"right_angle(A, I, B)",
"is_chord(line_FG, circle1)",
"point_lies_on(F, circle1)",
"point_lies_on(G, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [
"scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)",
"scene.constraint.eq(scene.get_object('arc1').area, (1/2) * scene.get_object('circle1').area)"
] | {
"points": {
"A": [
0.171162758,
-1.2756500607999999
],
"B": [
0.1368314974,
-1.6080372102
],
"C": [
0.4697894675,
-1.6423776679
],
"D": [
0.5039945866000001,
-1.3099616647
],
"E": [
2.0622916519,
-0.5100522626
],
... |
3obj_5rel_2extra_gen0306 | Diagram description: The diagram contains points A, B, C, O, H, Q, M, N, P. There is a triangle ABC. There is a quadrilateral MNOP. There is a circle with center O. There are line segments AH and BC. The circle is the circumcircle of triangle ABC. H is the orthocenter of triangle ABC. Line AH and line BC intersect at H... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, O, H, Q, M, N, P = scene.add.points(["A", "B", "C", "O", "H", "Q", "M", "N", "P"])
triangleABC = scene.add.triangle(A, B, C)
circleO = scene.add.circle(O)
quadrilateralMNOP = scene.add.quadrilateral(M, N, O, P)
lineAH = scene.add.line_segment(A, H)... | {
"triangleABC": "triangle(A, B, C)",
"circleO": "circle(O)",
"quadrilateralMNOP": "quadrilateral(M, N, O, P)",
"lineAH": "line_segment(A, H)",
"lineBC": "line_segment(B, C)"
} | [
"is_circumcircle(circleO, triangleABC)",
"is_orthocenter(H, triangleABC)",
"lines_intersect_at(lineAH, lineBC, H)",
"is_midpoint(Q, lineBC)",
"point_lies_on(Q, lineBC)"
] | [
"A",
"B",
"C",
"O",
"H",
"Q",
"M",
"N",
"P"
] | [] | {
"points": {
"A": [
7.7832950113,
-9.3960178327
],
"B": [
-2.0167546153,
3.6318917225
],
"C": [
-1.3744057355,
4.1029279888
],
"O": [
3.1220823484,
-2.7024385207
],
"H": [
-1.8536696869,
3.74595445
],
"Q": [
... |
3obj_5rel_2extra_gen0311 | Diagram description: The diagram contains points A, B, C, D, O. There is a triangle ABC. There is a kite ABCD. There is a circle with center O. There is a line segment AD. There is a line segment BC. There is a line segment AC. There is a line segment OA. There is a line segment OC. Point A lies on the circle. Point C ... | from pygeox import GeoScene
scene = GeoScene()
### objects
A, B, C, D, O = scene.add.points(["A", "B", "C", "D", "O"])
triangleABC = scene.add.triangle(A, B, C)
kiteABCD = scene.add.kite(A, B, C, D)
circleO = scene.add.circle(O)
line_AD = scene.add.line_segment(A, D)
line_BC = scene.add.line_segment(B, C)
line_AC =... | {
"triangleABC": "triangle(A, B, C)",
"kiteABCD": "kite(A, B, C, D)",
"circleO": "circle(O)",
"line_AD": "line_segment(A, D)",
"line_BC": "line_segment(B, C)",
"line_AC": "line_segment(A, C)",
"line_OA": "line_segment(O, A)",
"line_OC": "line_segment(O, C)"
} | [
"point_lies_on(A, circleO)",
"point_lies_on(C, circleO)",
"is_radius(line_OA, circleO)",
"is_radius(line_OC, circleO)",
"congruent(line_AD, line_AC)"
] | [
"A",
"B",
"C",
"D",
"O"
] | [] | {
"points": {
"A": [
-0.5758437712000001,
0.36255390260000003
],
"B": [
4.6550736022,
0.0108454568
],
"C": [
0.3386851603,
-2.9648873974
],
"D": [
2.7630694991,
-0.5091613612
],
"O": [
0.9143516378000001,
-1.0172713757
... |
3obj_5rel_2extra_gen0319 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a square with vertices A, B, C, D. There is a parallelogram with vertices E, F, G, H. There is a right triangle with vertices I, J, K. There is a line segment AC. There is a line segment EG. There is a line segment IJ. Square ABC... | 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"])
square1 = scene.add.square(A, B, C, D)
parallelogram1 = scene.add.parallelogram(E, F, G, H)
right_triangle1 = scene.add.right_triangle(I, J, K)
line_... | {
"square1": "square(A, B, C, D)",
"parallelogram1": "parallelogram(E, F, G, H)",
"right_triangle1": "right_triangle(I, J, K)",
"line_AC": "line_segment(A, C)",
"line_EG": "line_segment(E, G)",
"line_IJ": "line_segment(I, J)"
} | [
"similar(square1, parallelogram1)",
"collinear(A, C, E)",
"perpendicular(line_AC, line_EG)",
"is_altitude(line_IJ, right_triangle1, I)",
"is_orthocenter(J, right_triangle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [] | {
"points": {
"A": [
-3.3786892934,
-4.9810233188
],
"B": [
-3.3517573112,
-3.7759570577
],
"C": [
-2.1464379495,
-3.803005658
],
"D": [
-2.1733638727,
-5.0080669559
],
"E": [
1.6617904893,
-0.162342009
],
"F": [
... |
3obj_5rel_2extra_gen0328 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a minor arc BC. There is a parallelogram DEFG. There is a line segment BE. There is a line segment CF. There is a line segment DE. There is a line segment AF. Points B, A, and C are collinear. Line BE is a... | 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)
minor_arc1 = scene.add.minor_arc(A, B, C)
parallelogram1 = scene.add.parallelogram(D, E, F, G)
line_BE = scene.add.line_segment(B, E)
line_CF =... | {
"circle1": "circle(A)",
"minor_arc1": "minor_arc(A, B, C)",
"parallelogram1": "parallelogram(D, E, F, G)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)",
"line_DE": "line_segment(D, E)",
"line_AF": "line_segment(A, F)"
} | [
"collinear(B, A, C)",
"lines_intersect_at(line_BE, line_CF, H)",
"is_chord(line_BE, circle1)",
"is_radius(line_AF, circle1)",
"perpendicular(line_DE, line_AF)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
0.2619977321,
1.4782572650999999
],
"B": [
-3.2430313021,
1.5911438709999999
],
"C": [
3.7670268175,
1.3653707967
],
"D": [
0.8103059655,
-2.3530089491
],
"E": [
0.0816644613,
-2.0239494016
],
... |
3obj_5rel_2extra_gen0330 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a trapezoid ABCD. There is a circle with center E. There is an isosceles trapezoid FGHI. There is a line segment AC. There is a line segment BD. There is a line segment EF. Line AC intersects the circle at points A and C. Trapezoid ABC... | 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"])
trapezoid1 = scene.add.trapezoid(A, B, C, D)
circle1 = scene.add.circle(E)
isosceles_trapezoid1 = scene.add.isosceles_trapezoid(F, G, H, I)
line_AC = scene.add.line_... | {
"trapezoid1": "trapezoid(A, B, C, D)",
"circle1": "circle(E)",
"isosceles_trapezoid1": "isosceles_trapezoid(F, G, H, I)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EF": "line_segment(E, F)"
} | [
"line_intersects_circle_at(line_AC, circle1, A, C)",
"similar(trapezoid1, isosceles_trapezoid1)",
"perpendicular(line_AC, line_BD)",
"is_radius(line_EF, circle1)",
"point_lies_on(F, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [
"scene.constraint.eq(scene.get_object('trapezoid1').area, scene.get_object('isosceles_trapezoid1').area)",
"scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('E'), scene.get_object('F')), 90)"
] | {
"points": {
"A": [
0.6533501856,
-2.2288220667
],
"B": [
1.0405380315,
0.5447298294
],
"C": [
0.4801749972,
-1.9991206216
],
"D": [
0.8110763447,
0.37143717130000004
],
"E": [
-0.2097854156,
-2.6988294499
],
"F":... |
3obj_5rel_2extra_gen0331 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is an acute triangle with vertices B, C, D. There is a rhombus with vertices E, F, G, H. There is a line segment BD. There is a line segment CF. Line BD is an altitude of the acute triangle from vertex B. 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"])
circle1 = scene.add.circle(A)
acute_tri1 = scene.add.acute_triangle(B, C, D)
rhombus1 = scene.add.rhombus(E, F, G, H)
line_BD = scene.add.line_segment(B, D)
line_CF = scene.... | {
"circle1": "circle(A)",
"acute_tri1": "acute_triangle(B, C, D)",
"rhombus1": "rhombus(E, F, G, H)",
"line_BD": "line_segment(B, D)",
"line_CF": "line_segment(C, F)"
} | [
"is_altitude(line_BD, acute_tri1, B)",
"is_circumcircle(circle1, acute_tri1)",
"perpendicular(line_BD, line_CF)",
"point_lies_on(F, circle1)",
"is_midpoint(G, line_CF)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
0.40618428830000003,
-0.2674757927
],
"B": [
-6.9059385566,
1.9081913716
],
"C": [
7.6587236239,
-2.6328181305
],
"D": [
-6.9606390991,
1.7150946539
],
"E": [
-1.8150082580000002,
-4.0573055776
],
... |
3obj_5rel_2extra_gen0333 | Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a triangle with points A, B, C. There is a circle with center G. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment GE. There is a line segment AG. Line AD is a median of triangle ABC ... | 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.triangle(A, B, C)
circle1 = scene.add.circle(G)
line_AD = scene.add.line_segment(A, D)
line_BE = scene.add.line_segment(B, E)
line_CF = scene.add.line_segment(... | {
"triangle1": "triangle(A, B, C)",
"circle1": "circle(G)",
"line_AD": "line_segment(A, D)",
"line_BE": "line_segment(B, E)",
"line_CF": "line_segment(C, F)",
"line_GE": "line_segment(G, E)",
"line_AG": "line_segment(A, G)"
} | [
"is_median(line_AD, triangle1, A)",
"is_median(line_BE, triangle1, B)",
"is_centroid(G, triangle1)",
"is_circumcircle(circle1, triangle1)",
"angle_bisector(G, A, F, line_AG)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [] | {
"points": {
"A": [
5.4924412249,
7.1393894612
],
"B": [
7.4723937883,
-5.6021424296
],
"C": [
-4.5520720119,
-0.9460416925
],
"D": [
1.4601710008,
-3.274101481
],
"E": [
0.4701898815,
3.0966727178
],
"F": [
... |
3obj_5rel_2extra_gen0351 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a rectangle with vertices A, B, C, D. There is an equilateral triangle with vertices E, F, G. There is a circle with center H. There is a line segment AC. There is a line segment EF. There is a line segment HD. Line AC is a diameter of 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"])
rectangle1 = scene.add.rectangle(A, B, C, D)
triangle1 = scene.add.equilateral_triangle(E, F, G)
circle1 = scene.add.circle(H)
line_AC = scene.add.line_segment(A, C)
line_EF... | {
"rectangle1": "rectangle(A, B, C, D)",
"triangle1": "equilateral_triangle(E, F, G)",
"circle1": "circle(H)",
"line_AC": "line_segment(A, C)",
"line_EF": "line_segment(E, F)",
"line_HD": "line_segment(H, D)"
} | [
"is_diameter(line_AC, circle1)",
"is_centroid(H, triangle1)",
"perpendicular(line_AC, line_EF)",
"point_lies_on(D, circle1)",
"is_radius(line_HD, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
0.1435732171,
0.7929608484
],
"B": [
0.053265432,
0.529858892
],
"C": [
0.40588593310000004,
0.4088250856
],
"D": [
0.49619303340000004,
0.6719259456000001
],
"E": [
0.5016309054,
1.072946099
],
... |
3obj_5rel_2extra_gen0354 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is an isosceles trapezoid ABCD. There is an equilateral 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 HG. Line AC intersects 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"])
trapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)
triangle1 = scene.add.equilateral_triangle(E, F, G)
circle1 = scene.add.circle(H)
line_AC = scene.add.line_seg... | {
"trapezoid1": "isosceles_trapezoid(A, B, C, D)",
"triangle1": "equilateral_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_HG": "line_segment(H, G)"
} | [
"lines_intersect_at(line_AC, line_BD, I)",
"is_centroid(I, trapezoid1)",
"is_circumcircle(circle1, triangle1)",
"is_radius(line_HG, circle1)",
"perpendicular(line_AC, line_BD)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [
"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": [
-2.4907696667,
-4.3309980202
],
"B": [
-4.8733705363,
-2.0278405736
],
"C": [
-2.570223026,
0.3547722448
],
"D": [
-0.187618427,
-1.9483871847
],
"E": [
-0.6998908598,
0.730170359
],
"F": [
... |
3obj_5rel_2extra_gen0355 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a major arc BC on the circle. There is a trapezoid DEFG. There is a line segment DE. There is a line segment GF. There is a line segment DF. There is a line segment EG. Point B lies on the circle. Point C ... | 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)
major_arc1 = scene.add.major_arc(A, B, C)
trapezoid1 = scene.add.trapezoid(D, E, F, G)
line_DE = scene.add.line_segment(D, E)
line_GF = scene.a... | {
"circle1": "circle(A)",
"major_arc1": "major_arc(A, B, C)",
"trapezoid1": "trapezoid(D, E, F, G)",
"line_DE": "line_segment(D, E)",
"line_GF": "line_segment(G, F)",
"line_DF": "line_segment(D, F)",
"line_EG": "line_segment(E, G)"
} | [
"point_lies_on(B, circle1)",
"point_lies_on(C, circle1)",
"line_extensions_intersect_at(line_DE, line_GF, H)",
"is_chord(line_DF, circle1)",
"is_diameter(line_EG, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
-3.3262589378,
-2.8805771416
],
"B": [
-3.1341879737,
-2.772703615
],
"C": [
-3.5331725304,
-2.9561804209
],
"D": [
-3.3016124335,
-2.6621519689
],
"E": [
-3.4974175254,
-2.7420914875999998
],
... |
3obj_5rel_2extra_gen0360 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a rhombus with vertices A, B, C, D. There is a circle with center E. There is a minor arc with center E, starting at F and ending at G. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line se... | 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"])
rhombus1 = scene.add.rhombus(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.l... | {
"rhombus1": "rhombus(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)"
} | [
"perpendicular_bisector_at(line_AC, line_BD)",
"lines_intersect_at(line_AC, line_BD, H)",
"is_radius(line_EF, circle1)",
"is_radius(line_EG, circle1)",
"point_lies_on(F, circle1)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [] | {
"points": {
"A": [
-1.7371481151000001,
-0.8660986047
],
"B": [
-0.09667682300000001,
1.3337529050999999
],
"C": [
2.1197187963,
-0.2842962144
],
"D": [
0.47924754540000003,
-2.4841476992000002
],
"E": [
0.1657141596,
0.... |
3obj_5rel_2extra_gen0370 | Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a quadrilateral ABCD. There is a rhombus EFGH. There is a circle with center I. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment IH. Point A lies on the circle. Point C lies on... | 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"])
quadrilateral1 = scene.add.quadrilateral(A, B, C, D)
rhombus1 = scene.add.rhombus(E, F, G, H)
circle1 = scene.add.circle(I)
line_AC = scene.add.line_segment(A, C)
li... | {
"quadrilateral1": "quadrilateral(A, B, C, D)",
"rhombus1": "rhombus(E, F, G, H)",
"circle1": "circle(I)",
"line_AC": "line_segment(A, C)",
"line_BD": "line_segment(B, D)",
"line_EF": "line_segment(E, F)",
"line_IH": "line_segment(I, H)"
} | [
"point_lies_on(A, circle1)",
"point_lies_on(C, circle1)",
"is_diameter(line_AC, circle1)",
"perpendicular(line_AC, line_BD)",
"right_angle(B, A, D)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [] | {
"points": {
"A": [
1.4844147259,
0.5866589051000001
],
"B": [
-0.273647374,
2.4143099883
],
"C": [
0.9772454611,
-1.49244025
],
"D": [
2.6444108833,
1.7024874863
],
"E": [
3.0725277272,
1.4281767753
],
"F": [
... |
3obj_5rel_2extra_gen0395 | 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 rectangle B C D E. There is a kite F G H I. There is a line segment BD. There is a line segment FH. There is a line segment AC. Point B lies on the circle with center A. Point D lies on the circle wit... | 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)
rectangle1 = scene.add.rectangle(B, C, D, E)
kite1 = scene.add.kite(F, G, H, I)
line_BD = scene.add.line_segment(B, D)
line_FH = scene.... | {
"circle1": "circle(A)",
"rectangle1": "rectangle(B, C, D, E)",
"kite1": "kite(F, G, H, I)",
"line_BD": "line_segment(B, D)",
"line_FH": "line_segment(F, H)",
"line_AC": "line_segment(A, C)"
} | [
"point_lies_on(B, circle1)",
"point_lies_on(D, circle1)",
"is_diameter(line_BD, circle1)",
"is_radius(line_AC, circle1)",
"perpendicular(line_BD, line_FH)"
] | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I"
] | [] | {
"points": {
"A": [
0.2023665663,
2.8853520326
],
"B": [
0.48076083950000004,
2.9785564746
],
"C": [
0.42051649700000004,
2.6888802725
],
"D": [
-0.0760280956,
2.7921472278
],
"E": [
-0.015783358600000002,
3.0818244509
... |
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