image
stringlengths 34
43
| conversations
listlengths 2
2
|
|---|---|
geometry3k/train/243/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(1)), MeasureOf(Angle(F, A, B))); Equals(MeasureOf(Angle(2)), MeasureOf(Angle(A, B, F))); Equals(MeasureOf(Angle(3)), MeasureOf(Angle(B, F, A))); Equals(MeasureOf(Angle(A, F, D)), MeasureOf(Angle(4))); Equals(MeasureOf(Angle(5)), MeasureOf(Angle(A, D, F))); Equals(MeasureOf(Angle(6)), MeasureOf(Angle(C, F, D))); PointLiesOnLine(F, Line(C, A)); PointLiesOnLine(F, Line(B, D)); "
}
] |
geometry3k/train/244/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Perpendicular(Line(Q, N), Line(K, N)); Perpendicular(Line(P, M), Line(R, M)); PointLiesOnLine(Q, Line(R, P)); PointLiesOnLine(Q, Line(N, M)); PointLiesOnLine(N, Line(K, L)); PointLiesOnLine(R, Line(M, L)); PointLiesOnLine(P, Line(K, M)); "
}
] |
geometry3k/train/245/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Parallel(Line(T, S), Line(L, W)); PointLiesOnLine(L, Line(T, R)); PointLiesOnLine(W, Line(R, S)); "
}
] |
geometry3k/train/246/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, B)), \\frac{5}{3}x+11); Equals(LengthOf(Line(D, B)), 3y-9); Equals(LengthOf(Line(D, A)), x+2); Equals(LengthOf(Line(D, Y)), 2y+6); Equals(LengthOf(Line(D, Y)), LengthOf(Line(D, B))); Equals(LengthOf(Line(A, Y)), LengthOf(Line(A, C))); PointLiesOnLine(D, Line(Y, B)); PointLiesOnLine(A, Line(Y, C)); "
}
] |
geometry3k/train/248/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(Q, U, v)), 26); Equals(MeasureOf(Angle(Q, V, A)), 167); Equals(MeasureOf(Angle(T, V, U)), x); Equals(MeasureOf(Angle(S, V, T)), 77); Equals(MeasureOf(Angle(A, V, C)), x); PointLiesOnCircle(U, Circle(V, radius_)); PointLiesOnCircle(S, Circle(V, radius_)); PointLiesOnCircle(A, Circle(V, radius_)); PointLiesOnCircle(T, Circle(V, radius_)); PointLiesOnCircle(Q, Circle(V, radius_)); "
}
] |
geometry3k/train/249/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, B)), 4); Equals(MeasureOf(Angle(E, B, C)), 30); Equals(MeasureOf(Angle(A, B, E)), 30); Equals(MeasureOf(Angle(D, B, A)), 30); Equals(MeasureOf(Angle(D, B, F)), 30); Equals(LengthOf(Line(B, F)), x); Perpendicular(Line(E, B), Line(E, C)); Perpendicular(Line(E, A), Line(A, B)); Perpendicular(Line(D, B), Line(A, D)); Perpendicular(Line(D, F), Line(B, F)); "
}
] |
geometry3k/train/250/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, C)), 15); Equals(LengthOf(Line(A, C)), 6); Equals(LengthOf(Line(A, B)), x); Perpendicular(Line(B, C), Line(A, C)); "
}
] |
geometry3k/train/251/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(B, A, D)), MeasureOf(Angle(4))); Equals(MeasureOf(Angle(A, D, G)), MeasureOf(Angle(1))); Equals(MeasureOf(Angle(2)), MeasureOf(Angle(F, G, B))); Equals(MeasureOf(Angle(3)), MeasureOf(Angle(G, C, B))); Perpendicular(Line(F, G), Line(D, F)); Perpendicular(Line(C, B), Line(G, B)); Perpendicular(Line(G, C), Line(F, G)); PointLiesOnLine(B, Line(G, A)); PointLiesOnLine(F, Line(A, D)); "
}
] |
geometry3k/train/252/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(F, W)), x); Equals(LengthOf(Line(W', W)), 4); Equals(LengthOf(Line(F, W')), 10); PointLiesOnLine(D, Line(N, F)); PointLiesOnLine(W, Line(F, W')); "
}
] |
geometry3k/train/254/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Arc(U, R)), 179); Equals(MeasureOf(Arc(R, T)), 71); PointLiesOnLine(T, Line(S, U)); PointLiesOnCircle(R, Circle(O, radius_)); PointLiesOnCircle(U, Circle(O, radius_)); PointLiesOnCircle(T, Circle(O, radius_)); "
}
] |
geometry3k/train/255/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, B)), 21); Equals(LengthOf(Line(B, C)), 15); Equals(LengthOf(Line(A, C)), 16); Perpendicular(Line(B, C), Line(A, C)); "
}
] |
geometry3k/train/256/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(G, F)), 5x-9); Equals(LengthOf(Line(G, H)), x+7); PointLiesOnCircle(H, Circle(J, radius_)); PointLiesOnCircle(F, Circle(J, radius_)); "
}
] |
geometry3k/train/257/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(Y, Z)), 5x-7); Equals(LengthOf(Line(Z, X)), 3x+5); Perpendicular(Line(X, W), Line(Z, X)); Perpendicular(Line(Y, Z), Line(Y, W)); PointLiesOnLine(X, Line(W, E)); PointLiesOnLine(Y, Line(N, W)); PointLiesOnLine(Z, Line(A, W)); "
}
] |
geometry3k/train/259/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, D)), 8); Equals(LengthOf(Line(C, A)), x); Equals(MeasureOf(Angle(A, C, B)), 43); Equals(LengthOf(Line(D, B)), y); Perpendicular(Line(C, A), Line(A, B)); Perpendicular(Line(D, B), Line(B, C)); PointLiesOnLine(A, Line(C, D)); "
}
] |
geometry3k/train/260/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(i, A, D)), MeasureOf(Angle(2))); Equals(MeasureOf(Angle(1)), MeasureOf(Angle(D, B, G))); Equals(MeasureOf(Angle(D, F, G)), 65); Equals(MeasureOf(Angle(F, I, C)), 112); Equals(MeasureOf(Angle(B, D, F)), 47); PointLiesOnLine(I, Line(A, C)); PointLiesOnLine(F, Line(A, D)); PointLiesOnLine(B, Line(F, G)); PointLiesOnLine(F, Line(B, I)); PointLiesOnLine(B, Line(I, G)); PointLiesOnLine(F, Line(I, G)); "
}
] |
geometry3k/train/261/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(B, C, D)), y^{2}); Equals(MeasureOf(Angle(C, A, E)), 2x); Equals(MeasureOf(Angle(B, D, C)), 68); Equals(MeasureOf(Angle(D, B, C)), 3x-15); Parallel(Line(E, A), Line(B, D)); PointLiesOnLine(E, Line(B, C)); PointLiesOnLine(A, Line(C, D)); "
}
] |
geometry3k/train/262/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, E)), 6.25); Equals(LengthOf(Line(A, B)), 10); Equals(LengthOf(Line(D, E)), x-1); Equals(LengthOf(Line(B, C)), x+2); PointLiesOnLine(B, Line(A, C)); PointLiesOnLine(E, Line(A, D)); "
}
] |
geometry3k/train/263/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, D)), 5+x); Equals(LengthOf(Line(B, D)), x); Equals(LengthOf(Line(C, F)), 5+x); Equals(LengthOf(Line(B, F)), 5); PointLiesOnLine(D, Line(A, B)); PointLiesOnLine(F, Line(B, C)); PointLiesOnCircle(A, Circle(E, radius_)); PointLiesOnCircle(C, Circle(E, radius_)); PointLiesOnCircle(D, Circle(E, radius_)); PointLiesOnCircle(F, Circle(E, radius_)); "
}
] |
geometry3k/train/264/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(A, Line(F, D)); PointLiesOnLine(A, Line(P, G)); PointLiesOnCircle(L, Circle(A, radius_)); PointLiesOnCircle(F, Circle(A, radius_)); PointLiesOnCircle(P, Circle(A, radius_)); PointLiesOnCircle(G, Circle(A, radius_)); PointLiesOnCircle(D, Circle(A, radius_)); "
}
] |
geometry3k/train/265/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(K, Line(G, J)); PointLiesOnLine(K, Line(H, F)); "
}
] |
geometry3k/train/266/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, B)), 13); Equals(LengthOf(Line(A, C)), 7); Equals(LengthOf(Line(F, E)), 14); Equals(LengthOf(Line(C, B)), 10); "
}
] |
geometry3k/train/270/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, F)), x+4); Equals(LengthOf(Line(D, C)), 2x); Equals(LengthOf(Line(B, D)), x); Equals(LengthOf(Line(B, F)), 8); PointLiesOnLine(F, Line(A, B)); PointLiesOnLine(D, Line(B, C)); PointLiesOnCircle(A, Circle(E, radius_)); PointLiesOnCircle(C, Circle(E, radius_)); PointLiesOnCircle(D, Circle(E, radius_)); PointLiesOnCircle(F, Circle(E, radius_)); "
}
] |
geometry3k/train/271/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(D, F, C)), 145); Equals(MeasureOf(Angle(B, F, D)), 165); Equals(MeasureOf(Angle(C, F, B)), x); PointLiesOnCircle(B, Circle(F, radius_)); PointLiesOnCircle(C, Circle(F, radius_)); PointLiesOnCircle(D, Circle(F, radius_)); "
}
] |
geometry3k/train/272/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(K, L)), LengthOf(Line(A, J))); Equals(MeasureOf(Arc(J, D)), 3x+54); Equals(MeasureOf(Arc(K, C)), 5x); PointLiesOnCircle(L, Circle(C, radius_)); PointLiesOnCircle(K, Circle(C, radius_)); PointLiesOnCircle(A, Circle(D, radius_)); PointLiesOnCircle(J, Circle(D, radius_)); "
}
] |
geometry3k/train/274/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(A, D, G)), b); Equals(MeasureOf(Angle(C, E, F)), d); PointLiesOnLine(D, Line(A, H)); PointLiesOnLine(E, Line(D, C)); PointLiesOnLine(E, Line(F, H)); PointLiesOnLine(D, Line(G, C)); PointLiesOnLine(E, Line(C, G)); PointLiesOnLine(D, Line(E, G)); "
}
] |
geometry3k/train/275/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(Z, Line(Y, V)); PointLiesOnLine(Z, Line(W, U)); PointLiesOnCircle(V, Circle(Z, radius_)); PointLiesOnCircle(W, Circle(Z, radius_)); PointLiesOnCircle(Y, Circle(Z, radius_)); PointLiesOnCircle(U, Circle(Z, radius_)); PointLiesOnCircle(X, Circle(Z, radius_)); "
}
] |
geometry3k/train/277/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Arc(C, A)), 60); PointLiesOnCircle(B, Circle(D, radius_)); PointLiesOnCircle(A, Circle(D, radius_)); PointLiesOnCircle(C, Circle(D, radius_)); "
}
] |
geometry3k/train/278/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(J, L)), 4); Equals(LengthOf(Line(J, M)), x); Perpendicular(Line(L, M), Line(M, J)); Equals(LengthOf(Line(D, C)), 6-x); Equals(LengthOf(Line(D, G)), 2); Perpendicular(Line(D, G), Line(C, G)); PointLiesOnLine(M, Line(L, K)); PointLiesOnLine(G, Line(C, E)); "
}
] |
geometry3k/train/279/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(A, B, C)), x-8); Equals(MeasureOf(Angle(F, A, B)), x+2); Equals(MeasureOf(Angle(B, C, D)), x+7); Equals(MeasureOf(Angle(A, F, E)), x-4); Equals(MeasureOf(Angle(F, E, D)), x+6); Equals(MeasureOf(Angle(C, E, D)), x-3); "
}
] |
geometry3k/train/281/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, C)), 5); Equals(LengthOf(Line(B, C)), 3); Perpendicular(Line(A, C), Line(B, C)); "
}
] |
geometry3k/train/282/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, C)), b+5); Equals(LengthOf(Line(A, E)), b); Perpendicular(Line(C, B), Line(B, E)); PointLiesOnLine(B, Line(A, E)); "
}
] |
geometry3k/train/285/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(W, R)), x+6); Equals(LengthOf(Line(T, R)), 2x+6); Equals(LengthOf(Line(T, V)), 10); Equals(LengthOf(Line(W, S)), 8); Equals(MeasureOf(Angle(V, T, R)), MeasureOf(Angle(S, W, T))); PointLiesOnLine(R, Line(W, T)); PointLiesOnLine(R, Line(V, S)); "
}
] |
geometry3k/train/286/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(E, F, A)), 63); Perpendicular(Line(D, F), Line(F, E)); PointLiesOnLine(F, Line(A, C)); PointLiesOnCircle(D, Circle(F, radius_)); PointLiesOnCircle(E, Circle(F, radius_)); PointLiesOnCircle(B, Circle(F, radius_)); PointLiesOnCircle(A, Circle(F, radius_)); PointLiesOnCircle(C, Circle(F, radius_)); "
}
] |
geometry3k/train/287/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, A)), y); Equals(MeasureOf(Angle(C, A, B)), 45); Equals(LengthOf(Line(C, B)), x); Equals(LengthOf(Line(A, C)), 7\\sqrt{2}); Perpendicular(Line(A, C), Line(C, B)); "
}
] |
geometry3k/train/288/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(E, B, F)), 4x); Equals(MeasureOf(Arc(E, F)), 35); Equals(MeasureOf(Arc(C, D)), 9x+26); PointLiesOnLine(E, Line(B, C)); PointLiesOnLine(F, Line(B, D)); PointLiesOnCircle(C, Circle(A, radius_)); PointLiesOnCircle(D, Circle(A, radius_)); PointLiesOnCircle(E, Circle(A, radius_)); PointLiesOnCircle(F, Circle(A, radius_)); "
}
] |
geometry3k/train/290/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, A)), 8); Equals(LengthOf(Line(B, C)), 10); Equals(LengthOf(Line(D, A)), 4); Perpendicular(Line(A, C), Line(C, B)); Perpendicular(Line(A, D), Line(A, C)); "
}
] |
geometry3k/train/291/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, A)), 13); Equals(LengthOf(Line(B, C)), 15); Equals(LengthOf(Line(C, A)), 12); "
}
] |
geometry3k/train/292/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, B)), 12); Equals(LengthOf(Line(C, E)), x); Equals(LengthOf(Line(B, E)), 15); PointLiesOnLine(F, Line(E, B)); PointLiesOnCircle(C, Circle(E, radius_)); PointLiesOnCircle(F, Circle(E, radius_)); "
}
] |
geometry3k/train/293/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(C, G, B)), 100); Equals(MeasureOf(Angle(1)), MeasureOf(Angle(C, G, A))); Equals(MeasureOf(Angle(C, A, B)), MeasureOf(Angle(3))); Equals(MeasureOf(Angle(D, C, F)), 75); Equals(MeasureOf(Angle(2)), MeasureOf(Angle(F, C, A))); PointLiesOnLine(G, Line(A, B)); PointLiesOnLine(C, Line(D, A)); PointLiesOnLine(G, Line(E, C)); PointLiesOnLine(C, Line(G, F)); PointLiesOnLine(C, Line(E, F)); PointLiesOnLine(G, Line(F, E)); "
}
] |
geometry3k/train/295/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(E, A)), 2x+1); Equals(LengthOf(Line(E, B)), 3x-5); Perpendicular(Line(C, A), Line(E, A)); Perpendicular(Line(E, D), Line(E, B)); Equals(LengthOf(Line(D, C)), LengthOf(Line(B, D))); PointLiesOnLine(E, Line(A, B)); PointLiesOnLine(D, Line(B, C)); "
}
] |
geometry3k/train/296/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, Y)), 8); Equals(LengthOf(Line(B, A)), x); Perpendicular(Line(Y, B), Line(A, B)); Equals(LengthOf(Line(A, B)), LengthOf(Line(B, Y))); "
}
] |
geometry3k/train/298/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(G, H, I)), 98); Equals(MeasureOf(Angle(H, G, J)), 87); Equals(MeasureOf(Angle(I, J, G)), y+30); Equals(MeasureOf(Angle(L, O, N)), 60); Equals(MeasureOf(Angle(M, L, O)), x-4); Equals(MeasureOf(Angle(L, M, N)), MeasureOf(Angle(I, H, G))); Equals(MeasureOf(Angle(J, I, H)), MeasureOf(Angle(O, N, M))); Equals(MeasureOf(Angle(I, J, G)), MeasureOf(Angle(L, O, N))); "
}
] |
geometry3k/train/300/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(S, T)), 20); Equals(LengthOf(Line(T, C)), 12); Equals(LengthOf(Line(R, C)), x); PointLiesOnLine(C, Line(R, T)); PointLiesOnCircle(S, Circle(R, radius_)); PointLiesOnCircle(C, Circle(R, radius_)); "
}
] |
geometry3k/train/301/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, B)), x); Equals(LengthOf(Line(C, A)), 11); Equals(MeasureOf(Angle(B, C, A)), 28); Equals(LengthOf(Line(C, B)), 9); "
}
] |
geometry3k/train/302/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, C)), 5y); Equals(LengthOf(Line(A, Y)), 2x-5); Equals(LengthOf(Line(C, B)), 3x-18); Equals(LengthOf(Line(Y, B)), 2x+12); "
}
] |
geometry3k/train/303/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(B, A, D)), 65); Equals(MeasureOf(Angle(D, A, E)), 110); Equals(MeasureOf(Angle(E, A, C)), x); Perpendicular(Line(A, B), Line(A, C)); PointLiesOnCircle(B, Circle(A, radius_)); PointLiesOnCircle(C, Circle(A, radius_)); PointLiesOnCircle(D, Circle(A, radius_)); PointLiesOnCircle(E, Circle(A, radius_)); "
}
] |
geometry3k/train/304/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(J, P)), x); Equals(LengthOf(Line(M, L)), 2.7); PointLiesOnLine(P, Line(K, M)); PointLiesOnLine(J, Line(K, L)); PointLiesOnLine(H, Line(M, L)); "
}
] |
geometry3k/train/305/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Parallel(Line(P, Q), Line(T, R)); PointLiesOnLine(T, Line(P, S)); PointLiesOnLine(R, Line(Q, S)); "
}
] |
geometry3k/train/306/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Perpendicular(Line(X, B), Line(O, X)); PointLiesOnLine(X, Line(Y, O)); PointLiesOnLine(X, Line(A, B)); PointLiesOnCircle(Y, Circle(O, radius_)); PointLiesOnCircle(A, Circle(O, radius_)); PointLiesOnCircle(B, Circle(O, radius_)); "
}
] |
geometry3k/train/307/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(P, Line(Q, T)); PointLiesOnLine(M, Line(R, S)); "
}
] |
geometry3k/train/308/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Perpendicular(Line(G, C), Line(F, C)); PointLiesOnLine(C, Line(D, G)); PointLiesOnLine(C, Line(E, H)); PointLiesOnCircle(D, Circle(C, radius_)); PointLiesOnCircle(G, Circle(C, radius_)); PointLiesOnCircle(F, Circle(C, radius_)); PointLiesOnCircle(E, Circle(C, radius_)); PointLiesOnCircle(H, Circle(C, radius_)); "
}
] |
geometry3k/train/309/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(T, S, R)), 125); Equals(LengthOf(Line(T, S)), 6.8); Equals(MeasureOf(Angle(R, T, S)), 24); Equals(LengthOf(Line(T, R)), x); "
}
] |
geometry3k/train/310/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Arc(R, S, T)), 7.94); Equals(MeasureOf(Angle(N, S, T)), 70); PointLiesOnCircle(R, Circle(S, radius_)); PointLiesOnCircle(T, Circle(S, radius_)); "
}
] |
geometry3k/train/311/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(2)), MeasureOf(Angle(C, B, D))); Equals(MeasureOf(Angle(B, C, D)), 70); Equals(MeasureOf(Angle(1)), MeasureOf(Angle(C, D, B))); Equals(MeasureOf(Angle(B, D, A)), MeasureOf(Angle(3))); Equals(MeasureOf(Angle(B, A, D)), 40); PointLiesOnLine(D, Line(A, C)); "
}
] |
geometry3k/train/312/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Perpendicular(Line(N, J), Line(J, K)); Perpendicular(Line(K, M), Line(M, N)); PointLiesOnLine(Q, Line(N, K)); PointLiesOnLine(Q, Line(J, M)); "
}
] |
geometry3k/train/314/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, E)), x); Equals(LengthOf(Line(E, C)), x+3); Equals(LengthOf(Line(D, E)), x+10); Equals(LengthOf(Line(E, A)), x+1); PointLiesOnLine(E, Line(B, D)); PointLiesOnLine(E, Line(C, A)); PointLiesOnCircle(B, Circle(F, radius_)); PointLiesOnCircle(C, Circle(F, radius_)); PointLiesOnCircle(A, Circle(F, radius_)); PointLiesOnCircle(D, Circle(F, radius_)); "
}
] |
geometry3k/train/315/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(R, S)), 8); Equals(LengthOf(Line(R, Q)), 4); Equals(LengthOf(Line(K, J)), 6); Equals(LengthOf(Line(K, L)), 12); Equals(MeasureOf(Angle(R, Q, S)), 80); Equals(MeasureOf(Angle(R, S, Q)), x); Equals(MeasureOf(Angle(K, L, J)), 30); Equals(MeasureOf(Angle(J, K, L)), y); Equals(MeasureOf(Angle(L, J, K)), MeasureOf(Angle(S, Q, R))); Equals(MeasureOf(Angle(R, S, Q)), MeasureOf(Angle(J, L, K))); Equals(MeasureOf(Angle(L, K, J)), MeasureOf(Angle(Q, R, S))); "
}
] |
geometry3k/train/316/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(E, D)), x-4); Equals(LengthOf(Line(A, B)), x); Equals(LengthOf(Line(E, F)), 3); Equals(LengthOf(Line(B, C)), 5); Equals(MeasureOf(Angle(E, D, F)), MeasureOf(Angle(C, A, B))); Equals(MeasureOf(Angle(C, B, A)), MeasureOf(Angle(F, E, D))); "
}
] |
geometry3k/train/317/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, C)), 19); Equals(LengthOf(Line(A, B)), 7); Equals(LengthOf(Line(A, C)), x); Perpendicular(Line(A, B), Line(A, C)); "
}
] |
geometry3k/train/318/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(S, Q, R)), 33); Equals(LengthOf(Line(P, R)), y+4); Equals(MeasureOf(Angle(T, Q, S)), 95); Equals(LengthOf(Line(Q, T)), 5x); Equals(LengthOf(Line(S, R)), 27); Equals(LengthOf(Line(T, P)), 2y-5); Equals(MeasureOf(Angle(T, S, Q)), 3z); PointLiesOnLine(P, Line(T, R)); PointLiesOnLine(P, Line(S, Q)); "
}
] |
geometry3k/train/320/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(D, A)), 8); Equals(LengthOf(Line(D, H)), x); Equals(MeasureOf(Angle(B, A, D)), 30); Equals(MeasureOf(Angle(C, B, A)), 45); Equals(LengthOf(Line(H, F)), 6); Perpendicular(Line(D, H), Line(A, H)); Perpendicular(Line(F, C), Line(B, F)); Parallel(Line(C, D), Line(B, A)); PointLiesOnLine(F, Line(A, B)); PointLiesOnLine(H, Line(A, B)); PointLiesOnLine(H, Line(A, F)); PointLiesOnLine(F, Line(B, H)); "
}
] |
geometry3k/train/321/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, G)), 10); Equals(LengthOf(Line(E, G)), 10); PointLiesOnLine(E, Line(D, F)); PointLiesOnLine(B, Line(A, C)); PointLiesOnCircle(D, Circle(G, radius_)); PointLiesOnCircle(A, Circle(G, radius_)); PointLiesOnCircle(F, Circle(G, radius_)); PointLiesOnCircle(C, Circle(G, radius_)); "
}
] |
geometry3k/train/322/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(B, Line(U, V)); PointLiesOnLine(A, Line(R, S)); "
}
] |
geometry3k/train/323/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, E)), x+7); Equals(LengthOf(Line(E, C)), 9); Equals(LengthOf(Line(E, F)), x); Equals(LengthOf(Line(B, E)), 4); PointLiesOnLine(E, Line(A, B)); PointLiesOnLine(E, Line(F, C)); PointLiesOnCircle(A, Circle(D, radius_)); PointLiesOnCircle(B, Circle(D, radius_)); PointLiesOnCircle(C, Circle(D, radius_)); PointLiesOnCircle(F, Circle(D, radius_)); "
}
] |
geometry3k/train/324/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(DiameterOf(Circle(C))), 12); PointLiesOnLine(C, Line(A, B)); PointLiesOnLine(C, Line(E, H)); PointLiesOnLine(C, Line(J, F)); PointLiesOnCircle(A, Circle(C, radius_)); PointLiesOnCircle(B, Circle(C, radius_)); PointLiesOnCircle(E, Circle(C, radius_)); PointLiesOnCircle(F, Circle(C, radius_)); PointLiesOnCircle(H, Circle(C, radius_)); PointLiesOnCircle(J, Circle(C, radius_)); "
}
] |
geometry3k/train/325/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(N, Line(R, A)); PointLiesOnLine(M, Line(T, V)); "
}
] |
geometry3k/train/327/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Perpendicular(Line(G, C), Line(G, D)); PointLiesOnLine(G, Line(D, A)); PointLiesOnLine(G, Line(B, F)); PointLiesOnCircle(D, Circle(G, radius_)); PointLiesOnCircle(A, Circle(G, radius_)); PointLiesOnCircle(C, Circle(G, radius_)); PointLiesOnCircle(B, Circle(G, radius_)); PointLiesOnCircle(F, Circle(G, radius_)); "
}
] |
geometry3k/train/328/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(Y, W)), 40); Equals(LengthOf(Line(Z, W)), 3x-6); Equals(LengthOf(Line(Y, U)), 32); Equals(LengthOf(Line(U, Z)), x+6); Perpendicular(Line(Z, U), Line(U, W)); Equals(MeasureOf(Angle(Z, W, U)), MeasureOf(Angle(W, Y, U))); PointLiesOnLine(U, Line(Y, Z)); "
}
] |
geometry3k/train/331/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(M, P)), 36); Equals(LengthOf(Line(N, P)), 15); Equals(LengthOf(Line(M, N)), 39); Perpendicular(Line(M, P), Line(N, P)); "
}
] |
geometry3k/train/332/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, E)), 2); Equals(LengthOf(Line(E, C)), 5); Equals(LengthOf(Line(D, E)), 4); Equals(LengthOf(Line(B, E)), x); PointLiesOnLine(E, Line(A, B)); PointLiesOnLine(E, Line(D, C)); PointLiesOnCircle(A, Circle(X, radius_)); PointLiesOnCircle(B, Circle(X, radius_)); PointLiesOnCircle(C, Circle(X, radius_)); PointLiesOnCircle(D, Circle(X, radius_)); "
}
] |
geometry3k/train/333/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(A, H, K)), 6y+10); Equals(MeasureOf(Angle(M, I, H)), 8x-12); Equals(MeasureOf(Angle(G, I, D)), 4x); PointLiesOnLine(H, Line(A, G)); PointLiesOnLine(I, Line(A, G)); PointLiesOnLine(H, Line(I, A)); PointLiesOnLine(I, Line(G, H)); PointLiesOnLine(I, Line(M, D)); PointLiesOnLine(H, Line(K, O)); "
}
] |
geometry3k/train/335/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(D, C, A)), 66); Equals(MeasureOf(Angle(A, D, C)), MeasureOf(Angle(3))); Equals(MeasureOf(Angle(4)), MeasureOf(Angle(B, D, A))); Equals(MeasureOf(Angle(1)), MeasureOf(Angle(C, A, D))); Equals(MeasureOf(Angle(A, B, D)), 24); Equals(MeasureOf(Angle(D, A, B)), MeasureOf(Angle(2))); Equals(LengthOf(Line(A, D)), LengthOf(Line(C, D))); PointLiesOnLine(D, Line(C, B)); "
}
] |
geometry3k/train/336/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(S, U, V)), 2x+15); Equals(MeasureOf(Angle(S, T, B)), 3x-5); PointLiesOnLine(B, Line(V, T)); PointLiesOnLine(B, Line(U, S)); PointLiesOnCircle(V, Circle(A, radius_)); PointLiesOnCircle(T, Circle(A, radius_)); PointLiesOnCircle(S, Circle(A, radius_)); PointLiesOnCircle(U, Circle(A, radius_)); "
}
] |
geometry3k/train/337/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(E, A, B)), MeasureOf(Angle(6))); Equals(MeasureOf(Angle(C, B, A)), 36); Equals(MeasureOf(Angle(E, B, D)), 42); Equals(MeasureOf(Angle(5)), MeasureOf(Angle(D, E, B))); Equals(MeasureOf(Angle(4)), MeasureOf(Angle(C, E, D))); Equals(MeasureOf(Angle(7)), MeasureOf(Angle(B, D, E))); Equals(MeasureOf(Angle(C, D, E)), 57); Equals(MeasureOf(Angle(E, C, D)), 28); PointLiesOnLine(E, Line(D, A)); PointLiesOnLine(E, Line(B, C)); "
}
] |
geometry3k/train/339/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(D, A, B)), 74); Equals(MeasureOf(Angle(B, C, D)), x); Equals(MeasureOf(Angle(A, D, C)), 105); Equals(LengthOf(Line(D, A)), LengthOf(Line(B, A))); Equals(LengthOf(Line(C, D)), LengthOf(Line(C, B))); "
}
] |
geometry3k/train/340/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(E, A)), 12); Equals(LengthOf(Line(D, E)), 24); Equals(LengthOf(Line(C, E)), 24); Equals(LengthOf(Line(E, B)), x); PointLiesOnLine(E, Line(D, C)); PointLiesOnLine(F, Line(E, B)); PointLiesOnLine(E, Line(A, F)); PointLiesOnLine(F, Line(A, B)); PointLiesOnLine(E, Line(B, A)); PointLiesOnCircle(D, Circle(F, radius_)); PointLiesOnCircle(A, Circle(F, radius_)); PointLiesOnCircle(B, Circle(F, radius_)); PointLiesOnCircle(C, Circle(F, radius_)); "
}
] |
geometry3k/train/341/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(R, T)), y+3); Equals(LengthOf(Line(S, T)), 49); Equals(LengthOf(Line(S, R)), x); Equals(LengthOf(Line(W, V)), 20); Equals(LengthOf(Line(V, U)), 21); Equals(LengthOf(Line(U, W)), 29); Equals(MeasureOf(Angle(U, V, W)), MeasureOf(Angle(S, T, R))); Equals(MeasureOf(Angle(T, S, R)), MeasureOf(Angle(U, W, V))); Equals(MeasureOf(Angle(W, U, V)), MeasureOf(Angle(S, R, T))); "
}
] |
geometry3k/train/343/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(E, D)), 3); PointLiesOnLine(F, Line(A, C)); PointLiesOnLine(I, Line(A, E)); PointLiesOnLine(B, Line(E, D)); PointLiesOnCircle(B, Circle(V, radius_)); PointLiesOnCircle(F, Circle(V, radius_)); PointLiesOnCircle(I, Circle(V, radius_)); "
}
] |
geometry3k/train/345/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(K, G, L)), x); Equals(MeasureOf(Arc(H, J)), 47); Equals(MeasureOf(Arc(K, L)), 116); PointLiesOnLine(G, Line(J, L)); PointLiesOnLine(G, Line(H, K)); PointLiesOnCircle(J, Circle(A, radius_)); PointLiesOnCircle(L, Circle(A, radius_)); PointLiesOnCircle(K, Circle(A, radius_)); PointLiesOnCircle(H, Circle(A, radius_)); "
}
] |
geometry3k/train/346/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(Q, Line(R, A)); PointLiesOnLine(P, Line(A, R)); PointLiesOnLine(Q, Line(R, P)); PointLiesOnLine(R, Line(A, B)); PointLiesOnLine(Q, Line(A, B)); PointLiesOnLine(P, Line(B, A)); PointLiesOnLine(P, Line(A, Q)); PointLiesOnLine(R, Line(Q, B)); PointLiesOnLine(R, Line(P, B)); PointLiesOnLine(Q, Line(P, B)); "
}
] |
geometry3k/train/348/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, C)), x-3); Equals(LengthOf(Line(B, C)), 4x-21); Equals(LengthOf(Line(A, B)), 2x-7); "
}
] |
geometry3k/train/349/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, B)), z); Equals(LengthOf(Line(A, C)), y); Equals(LengthOf(Line(X, C)), 36); Equals(LengthOf(Line(B, A)), 6x); Perpendicular(Line(C, B), Line(C, A)); Perpendicular(Line(X, B), Line(C, X)); PointLiesOnLine(X, Line(B, A)); "
}
] |
geometry3k/train/352/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(C, A, D)), MeasureOf(Angle(1))); Equals(MeasureOf(Angle(2)), MeasureOf(Angle(B, A, E))); Equals(MeasureOf(Angle(D, C, E)), MeasureOf(Angle(7))); Equals(MeasureOf(Angle(C, E, D)), MeasureOf(Angle(8))); Equals(MeasureOf(Angle(B, E, D)), MeasureOf(Angle(5))); Equals(MeasureOf(Angle(C, D, A)), MeasureOf(Angle(3))); Equals(MeasureOf(Angle(D, B, E)), MeasureOf(Angle(6))); Equals(MeasureOf(Angle(E, D, B)), MeasureOf(Angle(4))); Perpendicular(Line(D, B), Line(B, A)); PointLiesOnLine(E, Line(C, B)); PointLiesOnLine(E, Line(A, D)); "
}
] |
geometry3k/train/353/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, C)), 7); Equals(LengthOf(Line(A, B)), 5); Equals(LengthOf(Line(B, C)), 6); Equals(LengthOf(Line(D, E)), 3); "
}
] |
geometry3k/train/354/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, B)), y); Equals(LengthOf(Line(C, A)), 14); Equals(MeasureOf(Angle(C, A, B)), 30); Equals(LengthOf(Line(A, B)), x); Perpendicular(Line(A, B), Line(C, B)); "
}
] |
geometry3k/train/356/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(E, C)), 3x); Equals(LengthOf(Line(A, F)), 10z-40); Equals(LengthOf(Line(B, E)), 4y); Equals(LengthOf(Line(A, D)), 2z); PointLiesOnLine(F, Line(A, C)); PointLiesOnLine(E, Line(C, B)); PointLiesOnLine(D, Line(B, A)); PointLiesOnCircle(E, Circle(G, radius_)); PointLiesOnCircle(F, Circle(G, radius_)); PointLiesOnCircle(D, Circle(G, radius_)); "
}
] |
geometry3k/train/357/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, B)), y); Equals(LengthOf(Line(D, C)), 2\\sqrt{3}); Equals(LengthOf(Line(D, B)), x); Equals(LengthOf(Line(D, A)), 2); Perpendicular(Line(B, C), Line(C, D)); Perpendicular(Line(D, C), Line(D, B)); PointLiesOnLine(D, Line(B, A)); "
}
] |
geometry3k/train/358/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(E, F, D)), 2x); Equals(MeasureOf(Angle(C, E, B)), 40); Equals(MeasureOf(Angle(F, E, D)), y); Equals(MeasureOf(Angle(D, E, F)), Angle(F, D, E)); PointLiesOnLine(E, Line(F, B)); PointLiesOnLine(E, Line(D, C)); "
}
] |
geometry3k/train/360/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Perpendicular(Line(E, G), Line(G, K)); Perpendicular(Line(K, A), Line(A, H)); Perpendicular(Line(E, F), Line(N, F)); Perpendicular(Line(D, N), Line(H, D)); Equals(LengthOf(Line(D, F)), 25); PointLiesOnLine(H, Line(A, D)); PointLiesOnLine(K, Line(G, A)); PointLiesOnLine(E, Line(F, G)); PointLiesOnLine(N, Line(D, F)); PointLiesOnCircle(E, Circle(O, radius_)); PointLiesOnCircle(H, Circle(O, radius_)); PointLiesOnCircle(K, Circle(O, radius_)); PointLiesOnCircle(N, Circle(O, radius_)); "
}
] |
geometry3k/train/361/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(D, A)), 8); Equals(LengthOf(Line(B, D)), 25); Equals(LengthOf(Line(A, C)), x); Equals(LengthOf(Line(D, C)), z); Equals(LengthOf(Line(C, B)), y); Perpendicular(Line(D, C), Line(D, B)); Perpendicular(Line(C, B), Line(A, C)); PointLiesOnLine(D, Line(B, A)); "
}
] |
geometry3k/train/362/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(J, C, B)), 105); Equals(MeasureOf(Angle(C, I, K)), x); Equals(MeasureOf(Angle(F, N, K)), 125); Parallel(Line(F, H), Line(B, D)); PointLiesOnLine(E, Line(H, F)); PointLiesOnLine(C, Line(D, B)); PointLiesOnLine(C, Line(J, I)); PointLiesOnLine(E, Line(I, K)); "
}
] |
geometry3k/train/363/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, A)), 24); Equals(LengthOf(Line(C, B)), 10); Equals(LengthOf(Line(A, B)), 26); Perpendicular(Line(C, A), Line(C, B)); "
}
] |
geometry3k/train/364/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(P, Line(D, B)); PointLiesOnLine(P, Line(C, A)); "
}
] |
geometry3k/train/365/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, C)), 3); Equals(MeasureOf(Angle(B, A, C)), 45); Equals(LengthOf(Line(A, B)), h); Perpendicular(Line(B, C), Line(A, C)); "
}
] |
geometry3k/train/366/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(E, A)), x-1); Equals(LengthOf(Line(D, C)), 5); Equals(LengthOf(Line(A, B)), 2); Equals(LengthOf(Line(D, E)), x+5); Parallel(Line(C, D), Line(B, A)); PointLiesOnLine(E, Line(D, A)); PointLiesOnLine(E, Line(B, C)); "
}
] |
geometry3k/train/368/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, B)), 23); Equals(MeasureOf(Angle(B, D, E)), 45); Equals(LengthOf(Line(E, D)), 5); Perpendicular(Line(E, A), Line(E, B)); PointLiesOnLine(E, Line(A, D)); "
}
] |
geometry3k/train/369/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(C, F, D)), 3x); Equals(MeasureOf(Angle(B, F, C)), 6x); Equals(MeasureOf(Angle(A, F, E)), 12y-10); PointLiesOnLine(F, Line(A, D)); PointLiesOnLine(F, Line(B, E)); "
}
] |
geometry3k/train/373/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, B)), 48); Equals(LengthOf(Line(A, C)), 20); Equals(LengthOf(Line(B, C)), x); Perpendicular(Line(A, B), Line(A, C)); "
}
] |
geometry3k/train/374/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, B)), 18); Equals(LengthOf(Line(B, C)), x); Equals(MeasureOf(Angle(B, A, C)), 45); Perpendicular(Line(B, C), Line(A, C)); "
}
] |
geometry3k/train/375/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(J, L, M)), 6x+8); Equals(MeasureOf(Angle(K, L, M)), 9x-4); Perpendicular(Line(J, M), Line(J, L)); Perpendicular(Line(K, M), Line(K, L)); Equals(LengthOf(Line(M, J)), LengthOf(Line(M, K))); "
}
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.