problem stringlengths 75 15.2k | answer stringlengths 1 34 | text_logic_form listlengths 1 11 | diagram_logic_form listlengths 0 456 | line_instances listlengths 1 110 | point_positions stringlengths 2 551 | circle_instances listlengths 0 4 |
|---|---|---|---|---|---|---|
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, C, B)), 82)
- Equals(MeasureOf(Angle(C, B, A)), 28)
- Equals(MeasureOf(Angle(B, E, C)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(A, E, D)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(D, A, E)), 68)
- Equals(MeasureOf(Angle(C, D, A)), MeasureOf(angle 3))
- PointLiesO... | 70 | [
"Find(MeasureOf(Angle(1)))"
] | [
"Equals(MeasureOf(Angle(E, C, B)), 82)",
"Equals(MeasureOf(Angle(C, B, A)), 28)",
"Equals(MeasureOf(Angle(B, E, C)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(A, E, D)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(D, A, E)), 68)",
"Equals(MeasureOf(Angle(C, D, A)), MeasureOf(angle 3))",
"PointLies... | [
"AB",
"AD",
"AE",
"BC",
"BE",
"DC",
"DE",
"EC"
] | {"A": [409.0, 162.0], "B": [1.0, 98.0], "C": [276.0, 0.0], "D": [334.0, 288.0], "E": [305.0, 146.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 6.4)
- Equals(LengthOf(Line(C, B)), 13)
- Equals(LengthOf(Line(D, E)), x)
- PointLiesOnLine(E, Line(C, B))
- Perpendicular(Line(D, E), Line(E, C))
Find $x$. $A = 78$ cm$^2$. | 8.0 | [
"Equals(AreaOf(Shape(A)),78)",
"Find(x)"
] | [
"Equals(LengthOf(Line(A, D)), 6.4)",
"Equals(LengthOf(Line(C, B)), 13)",
"Equals(LengthOf(Line(D, E)), x)",
"PointLiesOnLine(E, Line(C, B))",
"Perpendicular(Line(D, E), Line(E, C))"
] | [
"AC",
"AD",
"CB",
"DB",
"DE",
"BE",
"CE"
] | {"A": [167.0, 2.0], "B": [1.0, 129.0], "C": [223.0, 130.0], "D": [60.0, 1.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, A, C)), 60)
- Equals(LengthOf(Line(A, B)), y)
- Equals(LengthOf(Line(A, C)), 5)
- Equals(LengthOf(Line(B, C)), x)
- Perpendicular(Line(A, C), Line(B, C))
Find x. | 5 \sqrt { 3 } | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(B, A, C)), 60)",
"Equals(LengthOf(Line(A, B)), y)",
"Equals(LengthOf(Line(A, C)), 5)",
"Equals(LengthOf(Line(B, C)), x)",
"Perpendicular(Line(A, C), Line(B, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [0.6675650470152448, 0.5310112340323485], "B": [257.98010271232806, 151.98823195437302], "C": [0.006622010544276691, 150.000076407814]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, B)), 2x+9)
- Equals(MeasureOf(Angle(D, B, C)), 106)
- Equals(MeasureOf(Angle(C, A, D)), 3y+19)
- Equals(LengthOf(Line(A, C)), x+11)
Find $x$ so that the quadrilateral is a parallelogram | 2 | [
"Parallelogram($)",
"Find(x)"
] | [
"Equals(LengthOf(Line(D, B)), 2x+9)",
"Equals(MeasureOf(Angle(D, B, C)), 106)",
"Equals(MeasureOf(Angle(C, A, D)), 3y+19)",
"Equals(LengthOf(Line(A, C)), x+11)"
] | [
"AC",
"AD",
"CB",
"DB"
] | {"A": [325.0, 165.0], "B": [42.0, 2.0], "C": [2.0, 165.0], "D": [366.0, 2.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(C, Line(D, G))
- PointLiesOnLine(C, Line(E, H))
- PointLiesOnCircle(D, Circle(C, radius_0_0))
- PointLiesOnCircle(G, Circle(C, radius_0_0))
- PointLiesOnCircle(F, Circle(C, radius_0_0))
- PointLiesOnCircle(E, Circle(C, radius_0_0))
- PointLiesOnCircle(H, Circle(C, radius_0_0))
- Pe... | 142 | [
"Circle(C)",
"Equals(MeasureOf(Angle(H,C,G)),2x)",
"Equals(MeasureOf(Angle(H,C,D)),6x+28)",
"Find(MeasureOf(Arc(H,D)))"
] | [
"PointLiesOnLine(C, Line(D, G))",
"PointLiesOnLine(C, Line(E, H))",
"PointLiesOnCircle(D, Circle(C, radius_0_0))",
"PointLiesOnCircle(G, Circle(C, radius_0_0))",
"PointLiesOnCircle(F, Circle(C, radius_0_0))",
"PointLiesOnCircle(E, Circle(C, radius_0_0))",
"PointLiesOnCircle(H, Circle(C, radius_0_0))",
... | [
"",
"",
"",
"CD",
"CE",
"CF",
"CG",
"CH",
"DG",
"EH"
] | {"C": [134.0, 135.0], "D": [275.0, 139.0], "E": [255.0, 195.0], "F": [140.0, 271.0], "G": [0.0, 136.0], "H": [24.0, 83.0]} | [
"C"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(H, E)), 9)
- PointLiesOnLine(B, Line(H, E))
- PointLiesOnLine(A, Line(H, G))
- PointLiesOnLine(C, Line(E, F))
- PointLiesOnLine(D, Line(G, F))
In the figure, the vertices of quadrilateral ABCD intersect square EFGH and divide its sides into segments with measures that have a ... | 45 | [
"Quadrilateral(A,B,C,D)",
"Square(E,F,G,H)",
"Find(AreaOf(Quadrilateral(A,B,C,D)))"
] | [
"Equals(LengthOf(Line(H, E)), 9)",
"PointLiesOnLine(B, Line(H, E))",
"PointLiesOnLine(A, Line(H, G))",
"PointLiesOnLine(C, Line(E, F))",
"PointLiesOnLine(D, Line(G, F))"
] | [
"AD",
"BA",
"BC",
"CF",
"DC",
"DF",
"EB",
"EC",
"EF",
"GA",
"GD",
"GF",
"HA",
"HB",
"HE",
"HG"
] | {"A": [64.0, 184.0], "B": [1.0, 64.0], "C": [123.0, 2.0], "D": [185.0, 122.0], "E": [1.0, 0.0], "F": [184.0, 1.0], "G": [186.0, 186.0], "H": [1.0, 184.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(T, R)), 14)
- PointLiesOnLine(X, Line(T, R))
- Perpendicular(Line(R, X), Line(S, X))
- Equals(LengthOf(Line(R, S)), LengthOf(Line(T, S)))
Find the measure of $XT$. | 7 | [
"Find(LengthOf(Line(X,T)))"
] | [
"Equals(LengthOf(Line(T, R)), 14)",
"PointLiesOnLine(X, Line(T, R))",
"Perpendicular(Line(R, X), Line(S, X))",
"Equals(LengthOf(Line(R, S)), LengthOf(Line(T, S)))"
] | [
"RS",
"RX",
"SX",
"TR",
"TS",
"TX"
] | {"R": [231.0, 20.0], "S": [44.0, 159.0], "T": [278.0, 165.0], "X": [252.0, 92.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, A, D)), 42)
- PointLiesOnLine(A, Line(B, D))
- PointLiesOnLine(A, Line(E, C))
- PointLiesOnCircle(B, Circle(A, radius_3_0))
- PointLiesOnCircle(E, Circle(A, radius_3_0))
- PointLiesOnCircle(D, Circle(A, radius_3_0))
- PointLiesOnCircle(C, Circle(A, radius_3_0))
In $\odot... | 222 | [
"Circle(A)",
"Equals(MeasureOf(Angle(E,A,D)),42)",
"Find(MeasureOf(Arc(E,D,B)))"
] | [
"Equals(MeasureOf(Angle(E, A, D)), 42)",
"PointLiesOnLine(A, Line(B, D))",
"PointLiesOnLine(A, Line(E, C))",
"PointLiesOnCircle(B, Circle(A, radius_3_0))",
"PointLiesOnCircle(E, Circle(A, radius_3_0))",
"PointLiesOnCircle(D, Circle(A, radius_3_0))",
"PointLiesOnCircle(C, Circle(A, radius_3_0))"
] | [
"BD",
"BA",
"DE",
"DA",
"AE",
"AC",
"EC"
] | {"B": [28.656490264952964, 24.741438483668503], "E": [170.10799469013062, 92.01022434936148], "D": [144.29229174629, 146.30728106661257], "A": [86.23865979381443, 85.22525773195876], "C": [3.1088217723741565, 76.19965176543187]} | [
"A"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(H, G, A)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(F, H, G)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(A, J, H)), MeasureOf(angle 3))
- PointLiesOnLine(A, Line(J, G))
- PointLiesOnLine(B, Line(J, G))
- PointLiesOnLine(A, Line(J, B))
- PointLiesOnLine(B, Line(H, F))
... | 33 | [
"Equals(MeasureOf(Arc(J,H)),114)",
"Find(MeasureOf(Angle(3)))"
] | [
"Equals(MeasureOf(Angle(H, G, A)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(F, H, G)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(A, J, H)), MeasureOf(angle 3))",
"PointLiesOnLine(A, Line(J, G))",
"PointLiesOnLine(B, Line(J, G))",
"PointLiesOnLine(A, Line(J, B))",
"PointLiesOnLine(B, Line(H, F))... | [
"AB",
"BF",
"GA",
"GB",
"HB",
"HF",
"HG",
"JA",
"JB",
"JG",
"JH"
] | {"A": [105.0, 106.0], "B": [102.0, 82.0], "F": [4.0, 80.0], "G": [100.0, 2.0], "H": [202.0, 83.0], "J": [103.0, 205.0]} | [
"A"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), 36)
- Equals(LengthOf(Line(B, D)), w+4)
- Equals(LengthOf(Line(A, D)), 6)
- Equals(LengthOf(Line(C, D)), 24)
- PointLiesOnLine(D, Line(A, C))
- Perpendicular(Line(B, C), Line(A, B))
- Perpendicular(Line(B, D), Line(C, D))
Find the value of the variable w. | 8 | [
"Find(w)"
] | [
"Equals(LengthOf(Line(B, C)), 36)",
"Equals(LengthOf(Line(B, D)), w+4)",
"Equals(LengthOf(Line(A, D)), 6)",
"Equals(LengthOf(Line(C, D)), 24)",
"PointLiesOnLine(D, Line(A, C))",
"Perpendicular(Line(B, C), Line(A, B))",
"Perpendicular(Line(B, D), Line(C, D))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [397.0, 192.0], "B": [237.0, 1.0], "C": [0.0, 194.0], "D": [238.0, 193.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), y)
- Equals(MeasureOf(Angle(C, A, B)), 45)
- Equals(LengthOf(Line(B, C)), x)
- Equals(LengthOf(Line(A, C)), 7\sqrt{2})
- Perpendicular(Line(B, C), Line(A, C))
Find y. | 14 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(A, B)), y)",
"Equals(MeasureOf(Angle(C, A, B)), 45)",
"Equals(LengthOf(Line(B, C)), x)",
"Equals(LengthOf(Line(A, C)), 7\\sqrt{2})",
"Perpendicular(Line(B, C), Line(A, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [252.0, 31.0], "B": [1.0, 1.0], "C": [115.0, 142.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(J, E, K)), MeasureOf(Angle(1)))
- Equals(MeasureOf(Angle(A, L, E)), 133)
- Equals(MeasureOf(Angle(G, K, I)), 126)
- PointLiesOnLine(L, Line(B, A))
- PointLiesOnLine(E, Line(L, C))
- PointLiesOnLine(J, Line(L, C))
- PointLiesOnLine(J, Line(L, E))
- PointLiesOnLine(E, Line(C, ... | 79 | [
"Parallel(Line(a),Line(b))",
"Find(MeasureOf(Angle(1)))"
] | [
"Equals(MeasureOf(Angle(J, E, K)), MeasureOf(Angle(1)))",
"Equals(MeasureOf(Angle(A, L, E)), 133)",
"Equals(MeasureOf(Angle(G, K, I)), 126)",
"PointLiesOnLine(L, Line(B, A))",
"PointLiesOnLine(E, Line(L, C))",
"PointLiesOnLine(J, Line(L, C))",
"PointLiesOnLine(J, Line(L, E))",
"PointLiesOnLine(E, Line... | [
"BA",
"BL",
"CD",
"CE",
"CJ",
"DE",
"DJ",
"EG",
"EH",
"EJ",
"EK",
"FI",
"GH",
"GK",
"HK",
"JF",
"JI",
"JK",
"KF",
"KI",
"LA",
"LC",
"LD",
"LE",
"LJ"
] | {"A": [60.0, 1.0], "B": [60.0, 329.0], "C": [398.0, 422.0], "D": [0.0, 51.0], "E": [317.0, 346.0], "F": [246.0, 65.0], "G": [462.0, 240.0], "H": [119.0, 489.0], "I": [247.0, 489.0], "J": [247.0, 280.0], "K": [247.0, 396.0], "L": [60.0, 107.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, C, A)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(F, C, D)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(G, C, F)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(E, C, G)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(B, C, E)), MeasureOf(angle 5))
- Equals(MeasureOf(A... | 18 | [
"Isosceles(Triangle(A,B,C))",
"Equilateral(Triangle(D,C,E))",
"Isosceles(Triangle(F,C,G))",
"Equals(Angle(5),Angle(C))",
"Find(MeasureOf(Angle(5)))"
] | [
"Equals(MeasureOf(Angle(D, C, A)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(F, C, D)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(G, C, F)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(E, C, G)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(B, C, E)), MeasureOf(angle 5))",
"Equals(MeasureOf(Ang... | [
"AB",
"AC",
"AD",
"AE",
"AF",
"AG",
"BD",
"BG",
"CB",
"CD",
"CE",
"CF",
"CG",
"DG",
"EB",
"ED",
"EF",
"EG",
"FB",
"FD",
"FG"
] | {"A": [0.0, 233.0], "B": [518.0, 233.0], "C": [259.0, 1.0], "D": [103.0, 233.0], "E": [413.0, 233.0], "F": [208.0, 233.0], "G": [311.0, 233.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(A, Line(M, H))
- PointLiesOnLine(N, Line(H, G))
- PointLiesOnLine(P, Line(H, J))
- PointLiesOnLine(M, Line(G, J))
- PointLiesOnLine(B, Line(G, P))
- PointLiesOnLine(B, Line(J, N))
In $\Delta G H J$, $H P=5 x-16$, $P J=3 x+8$, $m \angle G J N=6 y-3$, $m \angle N J H=4 y+23$ and $m ... | 150 | [
"Triangle(G,H,J)",
"Equals(LengthOf(Line(H,P)),5x-16)",
"Equals(LengthOf(Line(P,J)),3x+8)",
"Equals(MeasureOf(Angle(G,J,N)),6y-3)",
"Equals(MeasureOf(Angle(N,J,H)),4y+23)",
"Equals(MeasureOf(Angle(H,M,G)),4z+14)",
"BisectsAngle(Line(J,N),Angle($))",
"Find(MeasureOf(Angle(G,J,H)))"
] | [
"PointLiesOnLine(A, Line(M, H))",
"PointLiesOnLine(N, Line(H, G))",
"PointLiesOnLine(P, Line(H, J))",
"PointLiesOnLine(M, Line(G, J))",
"PointLiesOnLine(B, Line(G, P))",
"PointLiesOnLine(B, Line(J, N))"
] | [
"AB",
"AN",
"AP",
"BN",
"BP",
"GA",
"GB",
"GJ",
"GN",
"GP",
"HA",
"HB",
"HG",
"HJ",
"HN",
"HP",
"JA",
"JB",
"JN",
"JP",
"MA",
"MB",
"MG",
"MH",
"MJ"
] | {"A": [181.0, 82.0], "B": [168.0, 74.0], "G": [3.0, 52.0], "H": [218.0, 2.0], "J": [231.0, 161.0], "M": [160.0, 128.0], "N": [132.0, 22.0], "P": [225.0, 81.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(P, K)), x+1)
- Equals(LengthOf(Line(K, J)), x+10)
- Equals(LengthOf(Line(M, K)), x+8)
- Equals(LengthOf(Line(L, K)), x)
- PointLiesOnLine(K, Line(P, M))
- PointLiesOnLine(K, Line(J, L))
- PointLiesOnCircle(P, Circle(O, radius_4_0))
- PointLiesOnCircle(M, Circle(O, radius_4_0))... | 8 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(P, K)), x+1)",
"Equals(LengthOf(Line(K, J)), x+10)",
"Equals(LengthOf(Line(M, K)), x+8)",
"Equals(LengthOf(Line(L, K)), x)",
"PointLiesOnLine(K, Line(P, M))",
"PointLiesOnLine(K, Line(J, L))",
"PointLiesOnCircle(P, Circle(O, radius_4_0))",
"PointLiesOnCircle(M, Circle(O, radius_4... | [
"KJ",
"KL",
"JL",
"MK",
"PK",
"PM"
] | {"K": [231.0, 131.0], "J": [2.0, 193.0], "O": [165.0, 168.0], "L": [321.0, 107.0], "M": [244.0, 315.0], "P": [222.0, 13.0]} | [
"O"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, G, C)), 60)
- PointLiesOnLine(G, Line(E, C))
- PointLiesOnLine(G, Line(A, B))
- PointLiesOnCircle(E, Circle(G, radius_0_0))
- PointLiesOnCircle(C, Circle(G, radius_0_0))
- PointLiesOnCircle(A, Circle(G, radius_0_0))
- PointLiesOnCircle(D, Circle(G, radius_0_0))
- PointLie... | 90 | [
"Find(MeasureOf(Angle(A,G,D)))"
] | [
"Equals(MeasureOf(Angle(A, G, C)), 60)",
"PointLiesOnLine(G, Line(E, C))",
"PointLiesOnLine(G, Line(A, B))",
"PointLiesOnCircle(E, Circle(G, radius_0_0))",
"PointLiesOnCircle(C, Circle(G, radius_0_0))",
"PointLiesOnCircle(A, Circle(G, radius_0_0))",
"PointLiesOnCircle(D, Circle(G, radius_0_0))",
"Poin... | [
"AB",
"EC",
"GA",
"GB",
"GC",
"GD",
"GE"
] | {"A": [1.0, 82.0], "B": [169.0, 86.0], "C": [44.0, 12.0], "D": [85.0, 159.0], "E": [126.0, 158.0], "G": [86.0, 85.0]} | [
"G"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(R, T)), 7\sqrt{2})
- Equals(LengthOf(Line(T, S)), 3\sqrt{2})
- Perpendicular(Line(T, S), Line(R, S))
Find the measure of $∠T$ to the nearest tenth. | 64.6 | [
"Find(MeasureOf(Angle(T)))"
] | [
"Equals(LengthOf(Line(R, T)), 7\\sqrt{2})",
"Equals(LengthOf(Line(T, S)), 3\\sqrt{2})",
"Perpendicular(Line(T, S), Line(R, S))"
] | [
"RS",
"RT",
"TS"
] | {"R": [0.0, 186.0], "S": [152.0, 216.0], "T": [196.0, 0.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 20)
- Equals(LengthOf(Line(B, M)), 30)
- Equals(LengthOf(Line(C, M)), 12)
- PointLiesOnLine(M, Line(C, B))
- Perpendicular(Line(A, M), Line(M, C))
Find the perimeter of the triangle. Round to the nearest tenth if necessary. | 80 | [
"Find(PerimeterOf(Triangle($)))"
] | [
"Equals(LengthOf(Line(A, C)), 20)",
"Equals(LengthOf(Line(B, M)), 30)",
"Equals(LengthOf(Line(C, M)), 12)",
"PointLiesOnLine(M, Line(C, B))",
"Perpendicular(Line(A, M), Line(M, C))"
] | [
"AB",
"AM",
"BM",
"AC",
"CM",
"BC"
] | {"A": [37.0, 1.0], "B": [223.0, 105.0], "M": [36.0, 102.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, A, E)), 30)
- Equals(LengthOf(Line(A, E)), 4\sqrt{3})
- Perpendicular(Line(A, D), Line(C, D))
- Perpendicular(Line(A, B), Line(B, C))
In the figure, below, square $A B C D$ is attached to $\triangle A D E$ as shown. If $m \angle E A D$ is $30^{\circ}$ and $A E$ is equal ... | 64 | [
"Square(A,B,C,D)",
"Triangle(A,D,E)",
"Equals(MeasureOf(Angle(E,A,D)),30)",
"Equals(LengthOf(Line(A,E)),4\\sqrt{3})",
"Find(AreaOf(Square(A,B,C,D)))"
] | [
"Equals(MeasureOf(Angle(D, A, E)), 30)",
"Equals(LengthOf(Line(A, E)), 4\\sqrt{3})",
"Perpendicular(Line(A, D), Line(C, D))",
"Perpendicular(Line(A, B), Line(B, C))"
] | [
"AD",
"AE",
"BA",
"BC",
"CD",
"ED"
] | {"A": [1.0, 92.0], "B": [161.0, 0.0], "C": [254.0, 160.0], "D": [94.0, 252.0], "E": [2.0, 253.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, H)), 4)
- Equals(LengthOf(Line(B, C)), 6)
- Equals(LengthOf(Line(H, C)), LengthOf(Line(B, H)))
- PointLiesOnLine(H, Line(C, B))
- Perpendicular(Line(A,H), Line(B,C))
Find the area of the figure. Round to the nearest tenth. | 12 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(A, H)), 4)",
"Equals(LengthOf(Line(B, C)), 6)",
"Equals(LengthOf(Line(H, C)), LengthOf(Line(B, H)))",
"PointLiesOnLine(H, Line(C, B))",
"Perpendicular(Line(A,H), Line(B,C))"
] | [
"AB",
"AC",
"AH",
"BC",
"BH",
"CH"
] | {"A": [92.0, 2.0], "B": [187.0, 124.0], "C": [1.0, 124.0], "H": [92.0, 124.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(R, Q, S)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(P, R, Q)), 33)
- Equals(MeasureOf(Angle(S, Q, P)), 51)
- Equals(MeasureOf(Angle(Q, S, R)), MeasureOf(angle 1))
- PointLiesOnLine(S, Line(R, P))
- Perpendicular(Line(Q, R), Line(Q, P))
Find $m \angle 2$. | 39 | [
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(R, Q, S)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(P, R, Q)), 33)",
"Equals(MeasureOf(Angle(S, Q, P)), 51)",
"Equals(MeasureOf(Angle(Q, S, R)), MeasureOf(angle 1))",
"PointLiesOnLine(S, Line(R, P))",
"Perpendicular(Line(Q, R), Line(Q, P))"
] | [
"QR",
"QP",
"QS",
"RP",
"RS",
"PS"
] | {"Q": [1.573872437334387, 0.8606283267274648], "R": [485.81635375591, 0.6684126890706779], "P": [2.6584867075664818, 314.1411042944785], "S": [216.43816430794527, 175.54007868929472]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 17)
- Equals(MeasureOf(Angle(A, C, D)), 45)
- Equals(LengthOf(Line(C, E)), 9)
- PointLiesOnLine(E, Line(C, D))
- Perpendicular(Line(A, E), Line(E, D))
Find the area of the parallelogram. Round to the nearest tenth if necessary. | 153 | [
"Find(AreaOf(Parallelogram($)))"
] | [
"Equals(LengthOf(Line(A, B)), 17)",
"Equals(MeasureOf(Angle(A, C, D)), 45)",
"Equals(LengthOf(Line(C, E)), 9)",
"PointLiesOnLine(E, Line(C, D))",
"Perpendicular(Line(A, E), Line(E, D))"
] | [
"AB",
"AC",
"BD",
"CD"
] | {"A": [113.0, 2.0], "B": [321.0, 5.0], "C": [0.0, 114.0], "D": [214.0, 107.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, Y, X)), 2x)
- Equals(MeasureOf(Angle(Y, X, W)), x)
- Equals(MeasureOf(Angle(X, W, A)), 3x)
- Equals(MeasureOf(Angle(W, A, Y)), 4x)
Find $m\angle X$ | 36 | [
"Find(MeasureOf(Angle(X)))"
] | [
"Equals(MeasureOf(Angle(A, Y, X)), 2x)",
"Equals(MeasureOf(Angle(Y, X, W)), x)",
"Equals(MeasureOf(Angle(X, W, A)), 3x)",
"Equals(MeasureOf(Angle(W, A, Y)), 4x)"
] | [
"XY",
"XW",
"YA",
"WA"
] | {"X": [0.0, 0.0], "A": [246.72685185185185, 214.0], "Y": [330.33333333333337, 0.0], "W": [81.74263565891472, 213.66666666666669]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, A, F)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(A, F, B)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(C, A, D)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(D, F, A)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(C, F, D)), MeasureOf(angle 6))
- Equals(MeasureOf(A... | 8 | [
"Rhombus(A,B,C,D)",
"Equals(MeasureOf(Angle(1)),2x+20)",
"Equals(MeasureOf(Angle(2)),5x-4)",
"Equals(LengthOf(Line(A,C)),15)",
"Equals(MeasureOf(Angle(3)),y^{2}+26)",
"Find(x)"
] | [
"Equals(MeasureOf(Angle(B, A, F)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(A, F, B)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(C, A, D)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(D, F, A)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(C, F, D)), MeasureOf(angle 6))",
"Equals(MeasureOf(Ang... | [
"AB",
"AC",
"AD",
"AF",
"BF",
"CB",
"CD",
"CF",
"DB",
"DF"
] | {"A": [1.0, 43.0], "B": [102.0, 1.0], "C": [102.0, 111.0], "D": [0.0, 154.0], "F": [51.0, 76.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(E, H)), 10)
- Equals(LengthOf(Line(K, H)), 5)
- Equals(LengthOf(Line(I, E)), 5)
- Equals(LengthOf(Line(B, I)), 7)
- Equals(LengthOf(Line(A, K)), 7)
- Equals(LengthOf(Line(B, L)), 5)
- Equals(LengthOf(Line(A, G)), 5)
- Equals(LengthOf(Line(L, F)), 7)
- Equals(LengthOf(Line(G, D... | 150 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(E, H)), 10)",
"Equals(LengthOf(Line(K, H)), 5)",
"Equals(LengthOf(Line(I, E)), 5)",
"Equals(LengthOf(Line(B, I)), 7)",
"Equals(LengthOf(Line(A, K)), 7)",
"Equals(LengthOf(Line(B, L)), 5)",
"Equals(LengthOf(Line(A, G)), 5)",
"Equals(LengthOf(Line(L, F)), 7)",
"Equals(LengthOf(Li... | [
"AB",
"AG",
"AI",
"AK",
"BI",
"BL",
"CE",
"CF",
"CJ",
"DH",
"EF",
"EH",
"FD",
"GD",
"GF",
"GL",
"IC",
"IE",
"IK",
"JD",
"JH",
"KH",
"KJ",
"LF"
] | {"A": [222.0, 67.0], "B": [92.0, 67.0], "C": [1.0, 196.0], "D": [132.0, 133.0], "E": [0.0, 0.0], "F": [1.0, 131.0], "G": [223.0, 131.0], "H": [131.0, 1.0], "I": [2.0, 65.0], "J": [130.0, 197.0], "K": [132.0, 65.0], "L": [93.0, 132.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(G, F)), 4.1)
- PointLiesOnLine(F, Line(A, B))
- PointLiesOnLine(J, Line(B, D))
- PointLiesOnLine(A, Line(B, G))
- PointLiesOnLine(F, Line(B, G))
- PointLiesOnLine(L, Line(B, H))
- PointLiesOnLine(A, Line(F, G))
- PointLiesOnLine(K, Line(G, C))
- PointLiesOnCircle(E, Circle(F, ... | 4.1 | [
"Regular(Polygon($))",
"Find(AreaOf(Shaded(Shape($))))"
] | [
"Equals(LengthOf(Line(G, F)), 4.1)",
"PointLiesOnLine(F, Line(A, B))",
"PointLiesOnLine(J, Line(B, D))",
"PointLiesOnLine(A, Line(B, G))",
"PointLiesOnLine(F, Line(B, G))",
"PointLiesOnLine(L, Line(B, H))",
"PointLiesOnLine(A, Line(F, G))",
"PointLiesOnLine(K, Line(G, C))",
"PointLiesOnCircle(E, Cir... | [
"AB",
"AF",
"AG",
"AK",
"BD",
"BG",
"BH",
"BJ",
"BL",
"DC",
"DJ",
"EI",
"FG",
"GC",
"GI",
"GK",
"HE",
"HI",
"HL",
"JL",
"KC",
"KI"
] | {"A": [32.0, 73.0], "B": [170.0, 96.0], "C": [55.0, 1.0], "D": [139.0, 14.0], "E": [75.0, 153.0], "F": [89.0, 84.0], "G": [5.0, 68.0], "H": [120.0, 152.0], "I": [31.0, 147.0], "J": [155.0, 56.0], "K": [26.0, 38.0], "L": [151.0, 115.0]} | [
"F"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(I, D, W)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(W, D, L)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(D, U, A)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(A, U, L)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(H, D, I)), MeasureOf(angle 5))
- Equals(MeasureOf(A... | 116 | [
"Equals(MeasureOf(Angle(12)),64)",
"Find(MeasureOf(Angle(3)))"
] | [
"Equals(MeasureOf(Angle(I, D, W)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(W, D, L)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(D, U, A)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(A, U, L)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(H, D, I)), MeasureOf(angle 5))",
"Equals(MeasureOf(Ang... | [
"AE",
"AG",
"AK",
"AQ",
"AU",
"BH",
"BN",
"DI",
"DJ",
"DL",
"DW",
"EB",
"EG",
"EH",
"EK",
"EN",
"EU",
"GK",
"GQ",
"GU",
"HD",
"HJ",
"HN",
"HW",
"IL",
"KU",
"QD",
"QI",
"QL",
"QU",
"UD",
"UI",
"UL",
"WJ"
] | {"A": [378.0, 3.0], "B": [7.0, 171.0], "D": [176.0, 72.0], "E": [277.0, 171.0], "G": [353.0, 43.0], "H": [118.0, 170.0], "I": [27.0, 71.0], "J": [72.0, 249.0], "K": [231.0, 249.0], "L": [518.0, 73.0], "N": [492.0, 172.0], "Q": [353.0, 73.0], "S": [503.0, 72.0], "T": [460.0, 73.0], "U": [334.0, 73.0], "W": [218.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(F, E)), 8)
- Equals(LengthOf(Line(A, B)), x+1)
- Equals(LengthOf(Line(C, D)), x-1)
- Equals(LengthOf(Line(H, G)), 5)
- Equals(MeasureOf(Angle(B, A, D)), MeasureOf(Angle(E, H, G)))
- Equals(MeasureOf(Angle(A, D, C)), MeasureOf(Angle(H, G, F)))
- Equals(MeasureOf(Angle(B, C, D))... | \frac { 16 } { 3 } | [
"Similar(Polygon($1),Polygon($2))",
"Find(LengthOf(Line(A,B)))"
] | [
"Equals(LengthOf(Line(F, E)), 8)",
"Equals(LengthOf(Line(A, B)), x+1)",
"Equals(LengthOf(Line(C, D)), x-1)",
"Equals(LengthOf(Line(H, G)), 5)",
"Equals(MeasureOf(Angle(B, A, D)), MeasureOf(Angle(E, H, G)))",
"Equals(MeasureOf(Angle(A, D, C)), MeasureOf(Angle(H, G, F)))",
"Equals(MeasureOf(Angle(B, C, D)... | [
"AB",
"AD",
"BC",
"CD",
"EF",
"FG",
"HE",
"HG"
] | {"E": [0.0, 17.0], "F": [145.0, 1.0], "G": [90.0, 149.0], "H": [2.0, 168.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, G)), 20-3x)
- Equals(LengthOf(Line(A, F)), \frac{1}{2}y+20)
- Equals(LengthOf(Line(C, F)), 3y)
- Equals(LengthOf(Line(H, G)), 2x-5)
- Equals(LengthOf(Line(F, C)), LengthOf(Line(A, F)))
- Parallel(Line(F, G), Line(A, H))
Find $y$. | 8 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(C, G)), 20-3x)",
"Equals(LengthOf(Line(A, F)), \\frac{1}{2}y+20)",
"Equals(LengthOf(Line(C, F)), 3y)",
"Equals(LengthOf(Line(H, G)), 2x-5)",
"Equals(LengthOf(Line(F, C)), LengthOf(Line(A, F)))",
"Parallel(Line(F, G), Line(A, H))"
] | [
"AC",
"AF",
"AH",
"CG",
"CH",
"FC",
"FG",
"GH"
] | {"A": [0.0, 212.0], "C": [258.0, 1.0], "F": [115.0, 117.0], "G": [304.0, 185.0], "H": [339.0, 328.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(F, Line(A, C))
- PointLiesOnLine(B, Line(A, C))
- PointLiesOnLine(F, Line(A, G))
- PointLiesOnLine(C, Line(A, G))
- PointLiesOnLine(B, Line(A, G))
- PointLiesOnLine(F, Line(A, B))
- PointLiesOnLine(B, Line(F, C))
- PointLiesOnLine(B, Line(F, G))
- PointLiesOnCircle(A, Circle(B, rad... | 5 | [
"Equals(DiameterOf(Circle(A)),8)",
"Equals(DiameterOf(Circle(B)),18)",
"Equals(DiameterOf(Circle(C)),11)",
"Find(LengthOf(Line(F,B)))"
] | [
"PointLiesOnLine(F, Line(A, C))",
"PointLiesOnLine(B, Line(A, C))",
"PointLiesOnLine(F, Line(A, G))",
"PointLiesOnLine(C, Line(A, G))",
"PointLiesOnLine(B, Line(A, G))",
"PointLiesOnLine(F, Line(A, B))",
"PointLiesOnLine(B, Line(F, C))",
"PointLiesOnLine(B, Line(F, G))",
"PointLiesOnCircle(A, Circle... | [
"AB",
"AC",
"AF",
"AG",
"CB",
"CG",
"FB",
"FC",
"FG",
"GB"
] | {"A": [85.0, 294.0], "B": [243.0, 221.0], "C": [447.0, 120.0], "F": [151.0, 262.0], "G": [463.0, 115.0]} | [
"A",
"G",
"B"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, Y, F)), 4y+10)
- PointLiesOnLine(Y, Line(B, F))
- PointLiesOnLine(H, Line(Y, J))
- PointLiesOnLine(H, Line(D, J))
- PointLiesOnLine(Y, Line(D, J))
- PointLiesOnLine(Y, Line(D, H))
- PointLiesOnLine(H, Line(E, A))
Find y so that $e || f$. | 20 | [
"Parallel(Line(e),Line(f))",
"Find(y)"
] | [
"Equals(MeasureOf(Angle(D, Y, F)), 4y+10)",
"PointLiesOnLine(Y, Line(B, F))",
"PointLiesOnLine(H, Line(Y, J))",
"PointLiesOnLine(H, Line(D, J))",
"PointLiesOnLine(Y, Line(D, J))",
"PointLiesOnLine(Y, Line(D, H))",
"PointLiesOnLine(H, Line(E, A))"
] | [
"BF",
"BY",
"DH",
"DJ",
"EA",
"FY",
"HA",
"HE",
"JH",
"YD",
"YH",
"YJ"
] | {"A": [310.0, 68.0], "B": [0.0, 79.0], "D": [139.0, 177.0], "E": [1.0, 40.0], "F": [308.0, 107.0], "H": [150.0, 53.0], "J": [154.0, 1.0], "Y": [146.0, 92.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(G, Line(D, A))
- PointLiesOnLine(G, Line(B, F))
- PointLiesOnCircle(D, Circle(G, radius_0_0))
- PointLiesOnCircle(A, Circle(G, radius_0_0))
- PointLiesOnCircle(C, Circle(G, radius_0_0))
- PointLiesOnCircle(B, Circle(G, radius_0_0))
- PointLiesOnCircle(F, Circle(G, radius_0_0))
- Pe... | 150 | [
"Circle(G)",
"Equals(MeasureOf(Angle(A,G,B)),30)",
"Perpendicular(Line(C,G),Line(G,D))",
"Find(MeasureOf(Arc(B,C,D)))"
] | [
"PointLiesOnLine(G, Line(D, A))",
"PointLiesOnLine(G, Line(B, F))",
"PointLiesOnCircle(D, Circle(G, radius_0_0))",
"PointLiesOnCircle(A, Circle(G, radius_0_0))",
"PointLiesOnCircle(C, Circle(G, radius_0_0))",
"PointLiesOnCircle(B, Circle(G, radius_0_0))",
"PointLiesOnCircle(F, Circle(G, radius_0_0))",
... | [
"BF",
"DA",
"GA",
"GB",
"GC",
"GD",
"GF"
] | {"A": [4.0, 62.0], "B": [34.0, 21.0], "C": [121.0, 7.0], "D": [176.0, 123.0], "F": [149.0, 161.0], "G": [90.0, 91.0]} | [
"G"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(G, K, F)), MeasureOf(angle 16))
- Equals(MeasureOf(Angle(F, K, A)), MeasureOf(angle 15))
- Equals(MeasureOf(Angle(G, A, J)), MeasureOf(angle 14))
- Equals(MeasureOf(Angle(H, K, G)), MeasureOf(angle 9))
- Equals(MeasureOf(Angle(J, A, M)), MeasureOf(angle 13))
- Equals(Measure... | 123 | [
"Equals(MeasureOf(Angle(1)),123)",
"Find(MeasureOf(Angle(11)))"
] | [
"Equals(MeasureOf(Angle(G, K, F)), MeasureOf(angle 16))",
"Equals(MeasureOf(Angle(F, K, A)), MeasureOf(angle 15))",
"Equals(MeasureOf(Angle(G, A, J)), MeasureOf(angle 14))",
"Equals(MeasureOf(Angle(H, K, G)), MeasureOf(angle 9))",
"Equals(MeasureOf(Angle(J, A, M)), MeasureOf(angle 13))",
"Equals(MeasureOf... | [
"AD",
"AG",
"AI",
"AJ",
"AK",
"AM",
"AO",
"AP",
"AQ",
"AS",
"AV",
"AW",
"BF",
"BH",
"BL",
"BT",
"BU",
"CE",
"CN",
"CR",
"DG",
"DK",
"DM",
"DO",
"DP",
"DV",
"DW",
"EN",
"ER",
"FH",
"FT",
"FU",
"GK",
"GM",
"GO",
"GP",
"GV",
"GW",
"HT",
"HU"... | {"A": [233.0, 125.0], "B": [87.0, 140.0], "C": [186.0, 219.0], "D": [152.0, 109.0], "E": [329.0, 259.0], "F": [86.0, 0.0], "G": [2.0, 64.0], "H": [85.0, 295.0], "I": [234.0, 307.0], "J": [233.0, 15.0], "K": [84.0, 87.0], "L": [118.0, 197.0], "M": [331.0, 158.0], "N": [0.0, 165.0], "O": [181.0, 116.0], "P": [136.0, 101.... | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(P, Line(Q, M))
- PointLiesOnLine(P, Line(N, R))
MNQR is a rectangle. If $N R=2 x+10$ and $N P=2 x-30$
find $M P$ | 40 | [
"Rectangle(M,N,Q,R)",
"Equals(LengthOf(Line(N,R)),2x+10)",
"Equals(LengthOf(Line(N,P)),2x-30)",
"Find(LengthOf(Line(M,P)))"
] | [
"PointLiesOnLine(P, Line(Q, M))",
"PointLiesOnLine(P, Line(N, R))"
] | [
"QN",
"QM",
"QR",
"QP",
"NM",
"NR",
"NP",
"MR",
"MP",
"RP"
] | {"Q": [243.7343669598904, 1.4978226799990892], "N": [0.0, 0.0], "M": [2.2714008937304158, 152.20072974912947], "R": [241.9054888680542, 153.28370572690017], "P": [122.14524780951108, 77.40892248010167]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, B, C)), 68)
- Equals(LengthOf(Line(B, C)), x)
- Equals(MeasureOf(Angle(C, A, B)), 50)
- Equals(LengthOf(Line(A, C)), 5)
Find x. Round side measures to the nearest tenth. | 4.1 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(A, B, C)), 68)",
"Equals(LengthOf(Line(B, C)), x)",
"Equals(MeasureOf(Angle(C, A, B)), 50)",
"Equals(LengthOf(Line(A, C)), 5)"
] | [
"AB",
"AC",
"BC"
] | {"A": [251.09995858671726, 181.66854116262343], "B": [96.64774722059684, 0.7021650087770723], "C": [0.6638004905002504, 183.005377773838]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(V, W)), 2)
- Equals(LengthOf(Line(T, V)), 13)
- PointLiesOnLine(W, Line(T, V))
- Perpendicular(Line(T, W), Line(U, W))
- Perpendicular(Line(U, W), Line(T, U))
Find the measure of the altitude drawn to the hypotenuse. | \sqrt { 26 } | [
"Equals(Line($1,$3),HypotenuseOf(Triangle($1,$2,$3)))",
"Find(LengthOf(AltitudeOf(Triangle($1,$2,$3))))"
] | [
"Equals(LengthOf(Line(V, W)), 2)",
"Equals(LengthOf(Line(T, V)), 13)",
"PointLiesOnLine(W, Line(T, V))",
"Perpendicular(Line(T, W), Line(U, W))",
"Perpendicular(Line(U, W), Line(T, U))"
] | [
"VW",
"TV",
"TU",
"TW",
"UV",
"UW"
] | {"V": [0.0, 0.0], "T": [255.0, 100.0], "U": [1.0, 100.0], "W": [36.0, 14.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, B, D)), 55)
- Equals(MeasureOf(Angle(G, B, F)), 35)
- PointLiesOnLine(B, Line(A, D))
- PointLiesOnLine(B, Line(C, G))
- PointLiesOnCircle(F, Circle(B, radius_6_0))
- PointLiesOnCircle(D, Circle(B, radius_6_0))
- PointLiesOnCircle(A, Circle(B, radius_6_0))
- PointLiesOnCir... | 270 | [
"IsDiameterOf(Line(A,D),Circle(B))",
"IsDiameterOf(Line(C,G),Circle(B))",
"Find(MeasureOf(Arc(A,C,F)))"
] | [
"Equals(MeasureOf(Angle(C, B, D)), 55)",
"Equals(MeasureOf(Angle(G, B, F)), 35)",
"PointLiesOnLine(B, Line(A, D))",
"PointLiesOnLine(B, Line(C, G))",
"PointLiesOnCircle(F, Circle(B, radius_6_0))",
"PointLiesOnCircle(D, Circle(B, radius_6_0))",
"PointLiesOnCircle(A, Circle(B, radius_6_0))",
"PointLiesO... | [
"AB",
"AD",
"BD",
"CB",
"CG",
"FB",
"GB"
] | {"A": [34.0, 274.0], "B": [181.0, 172.0], "C": [173.0, 1.0], "D": [316.0, 74.0], "F": [272.0, 318.0], "G": [173.0, 347.0]} | [
"B"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, D, B)), 92)
- PointLiesOnLine(C, Line(B, D))
- Equals(LengthOf(Line(A, C)), LengthOf(Line(B, C)))
- Equals(LengthOf(Line(C, D)), LengthOf(Line(A, D)))
Find $m \angle ACB$. | 136 | [
"Find(MeasureOf(Angle(A,C,B)))"
] | [
"Equals(MeasureOf(Angle(A, D, B)), 92)",
"PointLiesOnLine(C, Line(B, D))",
"Equals(LengthOf(Line(A, C)), LengthOf(Line(B, C)))",
"Equals(LengthOf(Line(C, D)), LengthOf(Line(A, D)))"
] | [
"AC",
"AD",
"BA",
"BC",
"BD",
"DC"
] | {"A": [15.0, 1.0], "B": [524.0, 273.0], "C": [208.0, 273.0], "D": [22.0, 272.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, D)), 4)
- Equals(LengthOf(Line(B, D)), 9)
- Equals(LengthOf(Line(A, C)), x)
- Equals(LengthOf(Line(A, D)), z)
- Equals(LengthOf(Line(A, B)), y)
- PointLiesOnLine(D, Line(B, C))
- Perpendicular(Line(B, D), Line(A, D))
- Perpendicular(Line(A, C), Line(A, B))
Find y. | 3 \sqrt { 13 } | [
"Find(y)"
] | [
"Equals(LengthOf(Line(C, D)), 4)",
"Equals(LengthOf(Line(B, D)), 9)",
"Equals(LengthOf(Line(A, C)), x)",
"Equals(LengthOf(Line(A, D)), z)",
"Equals(LengthOf(Line(A, B)), y)",
"PointLiesOnLine(D, Line(B, C))",
"Perpendicular(Line(B, D), Line(A, D))",
"Perpendicular(Line(A, C), Line(A, B))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [2.0, 139.0], "B": [287.0, 140.0], "C": [1.0, 1.0], "D": [57.0, 28.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, I)), 3.5)
- Equals(LengthOf(Line(I, F)), 3)
- Equals(LengthOf(Line(N, G)), 5.5)
- PointLiesOnLine(G, Line(J, D))
- PointLiesOnLine(G, Line(N, F))
- PointLiesOnCircle(F, Circle(G))
- PointLiesOnCircle(J, Circle(G))
- Perpendicular(Line(F, I), Line(I, D))
- Perpendicular(Line... | 39.4 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(D, I)), 3.5)",
"Equals(LengthOf(Line(I, F)), 3)",
"Equals(LengthOf(Line(N, G)), 5.5)",
"PointLiesOnLine(G, Line(J, D))",
"PointLiesOnLine(G, Line(N, F))",
"PointLiesOnCircle(F, Circle(G))",
"PointLiesOnCircle(J, Circle(G))",
"Perpendicular(Line(F, I), Line(I, D))",
"Perpendicul... | [
"ID",
"DG",
"GN",
"NE",
"JE",
"GJ",
"FG",
"IF"
] | {"D": [75.0, 1.0], "E": [195.0, 140.0], "F": [1.0, 63.0], "G": [76.0, 65.0], "I": [1.0, 0.0], "J": [78.0, 140.0], "N": [196.0, 71.0]} | [
"G"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, C, A)), 40)
- Equals(MeasureOf(Angle(E, C, B)), 35)
- Equals(MeasureOf(Angle(6)), MeasureOf(Angle(D, C, B)))
- PointLiesOnCircle(A, Circle(C, radius_2_0))
- PointLiesOnCircle(B, Circle(C, radius_2_0))
- PointLiesOnCircle(D, Circle(C, radius_2_0))
- PointLiesOnCircle(E, Ci... | 140 | [
"Find(MeasureOf(Angle(6)))"
] | [
"Equals(MeasureOf(Angle(D, C, A)), 40)",
"Equals(MeasureOf(Angle(E, C, B)), 35)",
"Equals(MeasureOf(Angle(6)), MeasureOf(Angle(D, C, B)))",
"PointLiesOnCircle(A, Circle(C, radius_2_0))",
"PointLiesOnCircle(B, Circle(C, radius_2_0))",
"PointLiesOnCircle(D, Circle(C, radius_2_0))",
"PointLiesOnCircle(E, C... | [
"AC",
"BC",
"CD",
"CE"
] | {"A": [18.0, 29.0], "B": [138.0, 127.0], "C": [80.0, 80.0], "D": [0.0, 79.0], "E": [145.0, 84.0]} | [
"C"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, X, A)), 3x)
- Equals(MeasureOf(Angle(A, X, B)), 7x+10)
- Equals(MeasureOf(Angle(B, X, C)), 90)
- PointLiesOnCircle(A, Circle(X, radius_0_0))
- PointLiesOnCircle(B, Circle(X, radius_0_0))
- PointLiesOnCircle(C, Circle(X, radius_0_0))
What is the value of x in the figure? | 26 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(C, X, A)), 3x)",
"Equals(MeasureOf(Angle(A, X, B)), 7x+10)",
"Equals(MeasureOf(Angle(B, X, C)), 90)",
"PointLiesOnCircle(A, Circle(X, radius_0_0))",
"PointLiesOnCircle(B, Circle(X, radius_0_0))",
"PointLiesOnCircle(C, Circle(X, radius_0_0))"
] | [
"XA",
"XB",
"XC"
] | {"A": [103.0, 7.0], "B": [146.0, 288.0], "C": [1.0, 142.0], "X": [145.0, 148.0]} | [
"X"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 5.3)
- PointLiesOnLine(D, Line(C, A))
- Perpendicular(Line(C, D), Line(B, D))
- Perpendicular(Line(B, A), Line(B, C))
Refer to the figure at the right. The orthocenter of $\triangle A B C$ is located 6.4 units from point $D$. Find $B C$. | 10.03 | [
"Triangle(A,B,C)",
"IsOrthocenterOf(Point($1), Triangle(A,B,C))",
"Equals(LengthOf(Line($1, D)), 6.4)",
"Find(LengthOf(Line(B,C)))"
] | [
"Equals(LengthOf(Line(A, D)), 5.3)",
"PointLiesOnLine(D, Line(C, A))",
"Perpendicular(Line(C, D), Line(B, D))",
"Perpendicular(Line(B, A), Line(B, C))"
] | [
"AD",
"BA",
"BC",
"BD",
"CA",
"CD"
] | {"A": [0.0, 0.0], "B": [2.0, 207.0], "C": [254.0, 208.0], "D": [104.0, 84.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(N, Line(F, D))
- PointLiesOnCircle(E, Circle(N, radius_6_0))
- PointLiesOnCircle(F, Circle(N, radius_6_0))
- PointLiesOnCircle(C, Circle(N, radius_6_0))
- PointLiesOnCircle(D, Circle(N, radius_6_0))
If $EN=13$, what is the diameter of the circle? | 26 | [
"Equals(LengthOf(Line(E,N)),13)",
"Find(DiameterOf(Circle($)))"
] | [
"PointLiesOnLine(N, Line(F, D))",
"PointLiesOnCircle(E, Circle(N, radius_6_0))",
"PointLiesOnCircle(F, Circle(N, radius_6_0))",
"PointLiesOnCircle(C, Circle(N, radius_6_0))",
"PointLiesOnCircle(D, Circle(N, radius_6_0))"
] | [
"CN",
"EF",
"FD",
"ND",
"NE",
"NF"
] | {"C": [24.0, 254.0], "D": [80.0, 26.0], "E": [210.0, 7.0], "F": [255.0, 309.0], "N": [168.0, 172.0]} | [
"N"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(I, D, W)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(W, D, L)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(D, U, A)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(A, U, L)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(H, D, I)), MeasureOf(angle 5))
- Equals(MeasureOf(A... | 116 | [
"Equals(MeasureOf(Angle(12)),64)",
"Find(MeasureOf(Angle(3)))"
] | [
"Equals(MeasureOf(Angle(I, D, W)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(W, D, L)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(D, U, A)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(A, U, L)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(H, D, I)), MeasureOf(angle 5))",
"Equals(MeasureOf(Ang... | [
"AE",
"AG",
"AK",
"AQ",
"AU",
"BH",
"BN",
"DI",
"DJ",
"DL",
"DW",
"EB",
"EG",
"EH",
"EK",
"EN",
"EU",
"GK",
"GQ",
"GU",
"HD",
"HJ",
"HN",
"HW",
"IL",
"KU",
"QD",
"QI",
"QL",
"QU",
"UD",
"UI",
"UL",
"WJ"
] | {"A": [378.0, 3.0], "B": [7.0, 171.0], "D": [176.0, 72.0], "E": [277.0, 171.0], "G": [353.0, 43.0], "H": [118.0, 170.0], "I": [27.0, 71.0], "J": [72.0, 249.0], "K": [231.0, 249.0], "L": [518.0, 73.0], "N": [492.0, 172.0], "Q": [353.0, 73.0], "S": [503.0, 72.0], "T": [460.0, 73.0], "U": [334.0, 73.0], "W": [218.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 10)
- Equals(LengthOf(Line(A, E)), 17)
- Equals(LengthOf(Line(B, C)), 22)
- PointLiesOnLine(E, Line(C, B))
- Perpendicular(Line(A, E), Line(E, B))
Find the area of the trapezoid. | 272 | [
"Find(AreaOf(Trapezoid($)))"
] | [
"Equals(LengthOf(Line(A, D)), 10)",
"Equals(LengthOf(Line(A, E)), 17)",
"Equals(LengthOf(Line(B, C)), 22)",
"PointLiesOnLine(E, Line(C, B))",
"Perpendicular(Line(A, E), Line(E, B))"
] | [
"AC",
"AD",
"CB",
"DB"
] | {"A": [45.0, 123.0], "B": [162.0, 1.0], "C": [0.0, 0.0], "D": [118.0, 125.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 35)
- Equals(LengthOf(Line(B, C)), 22)
In right triangle $ABC$ shown below, what is the measure of $∠ A$ to the nearest tenth of a degree? | 38.9 | [
"Right(Triangle(A,B,C))",
"Find(MeasureOf(Angle(A)))"
] | [
"Equals(LengthOf(Line(A, B)), 35)",
"Equals(LengthOf(Line(B, C)), 22)"
] | [
"AB",
"AC",
"BC"
] | {"A": [1.0, 1.0], "B": [248.0, 198.0], "C": [0.0, 196.0], "D": [0.0, 173.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Arc(G, I)), 5x)
- Equals(MeasureOf(Angle(E, B, D)), 60)
- Equals(MeasureOf(Arc(F, J)), 105)
- PointLiesOnLine(E, Line(A, B))
- PointLiesOnLine(G, Line(A, B))
- PointLiesOnLine(J, Line(A, B))
- PointLiesOnLine(J, Line(A, E))
- PointLiesOnLine(E, Line(A, G))
- PointLiesOnLine(J, Lin... | 9 | [
"Tangent(Line($),Circle($))",
"Find(x)"
] | [
"Equals(MeasureOf(Arc(G, I)), 5x)",
"Equals(MeasureOf(Angle(E, B, D)), 60)",
"Equals(MeasureOf(Arc(F, J)), 105)",
"PointLiesOnLine(E, Line(A, B))",
"PointLiesOnLine(G, Line(A, B))",
"PointLiesOnLine(J, Line(A, B))",
"PointLiesOnLine(J, Line(A, E))",
"PointLiesOnLine(E, Line(A, G))",
"PointLiesOnLine... | [
"AB",
"AE",
"AG",
"AH",
"AJ",
"BD",
"BE",
"BF",
"BG",
"BI",
"BJ",
"EC",
"ED",
"EF",
"EG",
"EH",
"EJ",
"FC",
"FI",
"GH",
"GJ",
"HD",
"HJ"
] | {"A": [205.0, 119.0], "B": [0.0, 0.0], "C": [151.0, 54.0], "D": [1.0, 87.0], "E": [154.0, 90.0], "F": [153.0, 1.0], "G": [96.0, 56.0], "H": [109.0, 89.0], "I": [127.0, 4.0], "J": [176.0, 102.0]} | [
"C"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(W, Y, Z)), 53)
- PointLiesOnLine(V, Line(X, Z))
- PointLiesOnLine(V, Line(W, Y))
Use rhombus XYZW with $m \angle W Y Z=53, V W=3$, $X V=2 a-2,$ and $Z V=\frac{5 a+1}{4}$
Find XW | 5 | [
"Rhombus(X,Y,Z,W)",
"Equals(MeasureOf(Angle(W,Y,Z)),53)",
"Equals(LengthOf(Line(V,W)),3)",
"Equals(LengthOf(Line(X,V)),2a-2)",
"Equals(LengthOf(Line(Z,V)),\\frac{5a+1}{4})",
"Find(LengthOf(Line(X,W)))"
] | [
"Equals(MeasureOf(Angle(W, Y, Z)), 53)",
"PointLiesOnLine(V, Line(X, Z))",
"PointLiesOnLine(V, Line(W, Y))"
] | [
"VY",
"WV",
"WY",
"XV",
"XW",
"XY",
"XZ",
"ZV",
"ZW",
"ZY"
] | {"V": [87.0, 48.0], "W": [68.0, 95.0], "X": [0.0, 0.0], "Y": [106.0, 1.0], "Z": [175.0, 96.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(G, Line(D, A))
- PointLiesOnLine(G, Line(B, F))
- PointLiesOnCircle(D, Circle(G, radius_0_0))
- PointLiesOnCircle(A, Circle(G, radius_0_0))
- PointLiesOnCircle(C, Circle(G, radius_0_0))
- PointLiesOnCircle(B, Circle(G, radius_0_0))
- PointLiesOnCircle(F, Circle(G, radius_0_0))
- Pe... | 30 | [
"Circle(G)",
"Equals(MeasureOf(Angle(A,G,B)),30)",
"Perpendicular(Line(C,G),Line(G,D))",
"Find(MeasureOf(Arc(F,D)))"
] | [
"PointLiesOnLine(G, Line(D, A))",
"PointLiesOnLine(G, Line(B, F))",
"PointLiesOnCircle(D, Circle(G, radius_0_0))",
"PointLiesOnCircle(A, Circle(G, radius_0_0))",
"PointLiesOnCircle(C, Circle(G, radius_0_0))",
"PointLiesOnCircle(B, Circle(G, radius_0_0))",
"PointLiesOnCircle(F, Circle(G, radius_0_0))",
... | [
"BF",
"DA",
"GA",
"GB",
"GC",
"GD",
"GF"
] | {"A": [4.0, 62.0], "B": [34.0, 21.0], "C": [121.0, 7.0], "D": [176.0, 123.0], "F": [149.0, 161.0], "G": [90.0, 91.0]} | [
"G"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(N, R)), 3)
- Equals(LengthOf(Line(R, M)), 6)
- Equals(LengthOf(Line(Q, R)), 10)
- Equals(LengthOf(Line(P, R)), x)
- PointLiesOnLine(R, Line(Q, N))
- PointLiesOnLine(R, Line(P, M))
- PointLiesOnCircle(Q, Circle(A, radius_4_0))
- PointLiesOnCircle(N, Circle(A, radius_4_0))
- Poi... | 5 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(N, R)), 3)",
"Equals(LengthOf(Line(R, M)), 6)",
"Equals(LengthOf(Line(Q, R)), 10)",
"Equals(LengthOf(Line(P, R)), x)",
"PointLiesOnLine(R, Line(Q, N))",
"PointLiesOnLine(R, Line(P, M))",
"PointLiesOnCircle(Q, Circle(A, radius_4_0))",
"PointLiesOnCircle(N, Circle(A, radius_4_0))",... | [
"RM",
"RP",
"NR",
"NP",
"PM",
"QR",
"QN"
] | {"A": [97.0, 97.0], "R": [94.0, 44.0], "M": [10.0, 56.0], "N": [110.0, 2.0], "P": [169.0, 34.0], "Q": [45.0, 177.0]} | [
"A"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 10)
- Equals(LengthOf(Line(A, D)), x)
- Equals(LengthOf(Line(C, D)), 4)
- Equals(LengthOf(Line(B, D)), y)
- PointLiesOnLine(D, Line(B, C))
- Perpendicular(Line(A, B), Line(A, C))
- Perpendicular(Line(A, D), Line(B, D))
Find z | 25 | [
"Find(z)"
] | [
"Equals(LengthOf(Line(A, C)), 10)",
"Equals(LengthOf(Line(A, D)), x)",
"Equals(LengthOf(Line(C, D)), 4)",
"Equals(LengthOf(Line(B, D)), y)",
"PointLiesOnLine(D, Line(B, C))",
"Perpendicular(Line(A, B), Line(A, C))",
"Perpendicular(Line(A, D), Line(B, D))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [143.88225871619943, 0.9123764477109972], "B": [0.7610619469026574, 112.33333333333334], "C": [227.0, 112.0], "D": [144.99557522123894, 112.5]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, H)), 6)
- PointLiesOnLine(H, Line(B, F))
- Perpendicular(Line(D, H), Line(H, B))
- Equals(LengthOf(Line(E, F)), 6)
- Equals(LengthOf(Line(A, E)), 6)
- PointLiesOnLine(C, Line(E, F))
- Perpendicular(Line(B, F), Line(A, B))
- Perpendicular(Line(E, F), Line(A, E))
Find the ar... | 54 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(D, H)), 6)",
"PointLiesOnLine(H, Line(B, F))",
"Perpendicular(Line(D, H), Line(H, B))",
"Equals(LengthOf(Line(E, F)), 6)",
"Equals(LengthOf(Line(A, E)), 6)",
"PointLiesOnLine(C, Line(E, F))",
"Perpendicular(Line(B, F), Line(A, B))",
"Perpendicular(Line(E, F), Line(A, E))"
] | [
"AB",
"AE",
"BD",
"BF",
"DF",
"EF"
] | {"A": [89.0, 176.0], "B": [89.0, 92.0], "D": [46.0, 1.0], "E": [0.0, 176.0], "F": [1.0, 90.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, E)), 5y)
- Equals(LengthOf(Line(E, B)), \frac{7}{3}y+8)
- Equals(LengthOf(Line(A, D)), \frac{1}{3}x+2)
- Equals(LengthOf(Line(A, C)), \frac{2}{3}x-4)
- PointLiesOnLine(A, Line(C, D))
- PointLiesOnLine(E, Line(D, B))
- Equals(LengthOf(Line(A, D)), LengthOf(Line(A, C)))
- Equ... | 18 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(D, E)), 5y)",
"Equals(LengthOf(Line(E, B)), \\frac{7}{3}y+8)",
"Equals(LengthOf(Line(A, D)), \\frac{1}{3}x+2)",
"Equals(LengthOf(Line(A, C)), \\frac{2}{3}x-4)",
"PointLiesOnLine(A, Line(C, D))",
"PointLiesOnLine(E, Line(D, B))",
"Equals(LengthOf(Line(A, D)), LengthOf(Line(A, C)))",... | [
"AC",
"AD",
"AE",
"CB",
"CD",
"DB",
"DE",
"EB"
] | {"A": [32.0, 94.0], "B": [189.0, 62.0], "C": [66.0, 188.0], "D": [0.0, 0.0], "E": [95.0, 31.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, D)), 8)
- Equals(LengthOf(Line(A, C)), 2x)
- Equals(LengthOf(Line(F, H)), LengthOf(Line(A, B)))
- PointLiesOnLine(D, Line(A, X))
- Equals(LengthOf(Line(E, F)), 9)
- Equals(LengthOf(Line(F, G)), x)
- Equals(LengthOf(Line(H, G)), LengthOf(Line(G, E)))
- PointLiesOnLine(G, Li... | 6 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(C, D)), 8)",
"Equals(LengthOf(Line(A, C)), 2x)",
"Equals(LengthOf(Line(F, H)), LengthOf(Line(A, B)))",
"PointLiesOnLine(D, Line(A, X))",
"Equals(LengthOf(Line(E, F)), 9) ",
"Equals(LengthOf(Line(F, G)), x)",
"Equals(LengthOf(Line(H, G)), LengthOf(Line(G, E)))",
"PointLiesOnLine(G... | [
"AC",
"AD",
"AX",
"CD",
"CX",
"FE",
"FG",
"FH",
"GE",
"HE",
"HG",
"XD"
] | {"A": [153.0, 7.0], "C": [44.0, 106.0], "D": [75.0, 13.0], "X": [2.0, 22.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(P, Line(D, B))
- PointLiesOnLine(P, Line(C, A))
- Perpendicular(Line(A, P), Line(D, P))
Quadrilateral $ABCD$ is a rhombus. If $m\angle DPC = 3x – 15$, find $x$. | 35 | [
"Rhombus(A,B,C,D)",
"Equals(MeasureOf(Angle(D,P,C)),3x-15)",
"Find(x)"
] | [
"PointLiesOnLine(P, Line(D, B))",
"PointLiesOnLine(P, Line(C, A))",
"Perpendicular(Line(A, P), Line(D, P))"
] | [
"DB",
"DC",
"DA",
"DP",
"BC",
"BA",
"BP",
"CA",
"CP",
"AP"
] | {"D": [0.0, 163.0], "B": [220.5954165289054, 1.662674650698591], "C": [166.77464155029716, 161.84853144795147], "A": [54.84151329243353, 1.5], "P": [111.0, 81.5]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, A, B)), MeasureOf(angle 6))
- Equals(MeasureOf(Angle(B, A, D)), MeasureOf(angle 7))
- Equals(MeasureOf(Angle(D, A, C)), MeasureOf(angle 8))
- PointLiesOnLine(A, Line(C, E))
$∠6$ and $∠8$ are complementary, $m∠8 = 47$. Find the measure of $\angle 6$. | 43 | [
"Equals(SumOf(MeasureOf(Angle(6)),MeasureOf(Angle(6))),90)",
"Equals(MeasureOf(Angle(8)),47)",
"Find(MeasureOf(Angle(6)))"
] | [
"Equals(MeasureOf(Angle(E, A, B)), MeasureOf(angle 6))",
"Equals(MeasureOf(Angle(B, A, D)), MeasureOf(angle 7))",
"Equals(MeasureOf(Angle(D, A, C)), MeasureOf(angle 8))",
"PointLiesOnLine(A, Line(C, E))"
] | [
"AB",
"AC",
"AD",
"AE",
"CE",
""
] | {"A": [130.0, 5.0], "B": [17.0, 101.0], "C": [251.0, 6.0], "D": [241.0, 138.0], "E": [0.0, 6.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(K, J, M)), 59)
- Equals(MeasureOf(Angle(M, L, K)), 67)
- Equals(LengthOf(Line(J, M)), LengthOf(Line(J, K)))
- Equals(LengthOf(Line(M, L)), LengthOf(Line(L, K)))
Find $m \angle K$. | 117 | [
"Find(MeasureOf(Angle(K)))"
] | [
"Equals(MeasureOf(Angle(K, J, M)), 59)",
"Equals(MeasureOf(Angle(M, L, K)), 67)",
"Equals(LengthOf(Line(J, M)), LengthOf(Line(J, K)))",
"Equals(LengthOf(Line(M, L)), LengthOf(Line(L, K)))"
] | [
"JK",
"LK",
"MJ",
"ML"
] | {"J": [102.0, 1.0], "K": [202.0, 181.0], "L": [103.0, 334.0], "M": [2.0, 181.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(K, M, P)), MeasureOf(angle 7))
- Equals(MeasureOf(Angle(K, M, H)), MeasureOf(angle 5))
- Equals(MeasureOf(Angle(D, M, P)), MeasureOf(angle 8))
- Equals(MeasureOf(Angle(G, H, M)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(D, M, H)), MeasureOf(angle 6))
- Equals(MeasureOf(A... | 38 | [
"Equals(MeasureOf(Angle(5)),68)",
"Equals(MeasureOf(Angle(3)),3y-2)",
"Find(y)"
] | [
"Equals(MeasureOf(Angle(K, M, P)), MeasureOf(angle 7))",
"Equals(MeasureOf(Angle(K, M, H)), MeasureOf(angle 5))",
"Equals(MeasureOf(Angle(D, M, P)), MeasureOf(angle 8))",
"Equals(MeasureOf(Angle(G, H, M)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(D, M, H)), MeasureOf(angle 6))",
"Equals(MeasureOf(Ang... | [
"EH",
"EM",
"EP",
"GF",
"GH",
"HF",
"HM",
"HP",
"KD",
"KM",
"MD",
"MP"
] | {"D": [330.0, 219.0], "E": [22.0, 225.0], "F": [206.0, 270.0], "G": [25.0, 71.0], "H": [119.0, 178.0], "K": [136.0, 3.0], "M": [244.0, 118.0], "P": [316.0, 83.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(G, Line(F, H))
- PointLiesOnLine(J, Line(H, K))
Find x so that $GJ \parallel FK$. GF = 12, HG = 6, HJ = 8, JK = x - 4. | 20 | [
"Parallel(Line(G,J),Line(F,K))",
"Equals(LengthOf(Line(G,F)),12)",
"Equals(LengthOf(Line(H,G)),6)",
"Equals(LengthOf(Line(H,J)),8)",
"Equals(LengthOf(Line(J,K)),x-4)",
"Find(x)"
] | [
"PointLiesOnLine(G, Line(F, H))",
"PointLiesOnLine(J, Line(H, K))"
] | [
"FG",
"FH",
"FK",
"GJ",
"HG",
"HJ",
"HK",
"KJ"
] | {"F": [0.0, 204.0], "G": [85.0, 123.0], "H": [213.0, 1.0], "J": [288.0, 123.0], "K": [338.0, 204.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(A, Line(D, B))
- PointLiesOnLine(C, Line(D, G))
- PointLiesOnLine(C, Line(D, E))
- PointLiesOnLine(G, Line(B, F))
- PointLiesOnLine(G, Line(D, E))
- PointLiesOnLine(G, Line(C, E))
- PointLiesOnCircle(A, Circle(O, radius_4_0))
- PointLiesOnCircle(C, Circle(O, radius_4_0))
- PointLie... | 15 | [
"Equals(MeasureOf(Arc(F,E)),118)",
"Equals(MeasureOf(Arc(A,B)),108)",
"Equals(MeasureOf(Angle(E,G,B)),52)",
"Equals(MeasureOf(Angle(E,F,B)),30)",
"Find(MeasureOf(Arc(E,D,B)))"
] | [
"PointLiesOnLine(A, Line(D, B))",
"PointLiesOnLine(C, Line(D, G))",
"PointLiesOnLine(C, Line(D, E))",
"PointLiesOnLine(G, Line(B, F))",
"PointLiesOnLine(G, Line(D, E))",
"PointLiesOnLine(G, Line(C, E))",
"PointLiesOnCircle(A, Circle(O, radius_4_0))",
"PointLiesOnCircle(C, Circle(O, radius_4_0))",
"P... | [
"AD",
"BD",
"CE",
"CG",
"DB",
"DC",
"DE",
"DG",
"EF",
"GE"
] | {"A": [149.0, 30.0], "B": [265.0, 32.0], "C": [137.0, 65.0], "D": [0.0, 28.0], "E": [269.0, 100.0], "F": [153.0, 115.0], "G": [197.0, 82.0], "O": [205.0, 78.0]} | [
"O"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(X, P, Q)), 4x)
- Equals(MeasureOf(Angle(R, Q, P)), 2x)
- Equals(MeasureOf(Angle(R, X, P)), x)
- Equals(MeasureOf(Angle(X, R, Q)), 5x)
Find $m\angle R$ | 150 | [
"Find(MeasureOf(Angle(R)))"
] | [
"Equals(MeasureOf(Angle(X, P, Q)), 4x)",
"Equals(MeasureOf(Angle(R, Q, P)), 2x)",
"Equals(MeasureOf(Angle(R, X, P)), x)",
"Equals(MeasureOf(Angle(X, R, Q)), 5x)"
] | [
"PQ",
"RQ",
"XP",
"XR"
] | {"P": [228.0, 1.0], "Q": [265.0, 64.0], "R": [112.0, 64.0], "X": [0.0, 0.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(J, K)), 10)
- PointLiesOnLine(P, Line(M, N))
- PointLiesOnLine(K, Line(P, J))
- PointLiesOnLine(P, Line(L, J))
- PointLiesOnLine(K, Line(L, J))
- PointLiesOnLine(P, Line(L, K))
- PointLiesOnCircle(M, Circle(K, radius_7_0))
- PointLiesOnCircle(J, Circle(K, radius_7_0))
- PointL... | 131.00 | [
"Circle(K)",
"Equals(LengthOf(Line(M,N)),16)",
"Equals(MeasureOf(Arc(M,N)),98)",
"Find(MeasureOf(Arc(N,J)))"
] | [
"Equals(LengthOf(Line(J, K)), 10)",
"PointLiesOnLine(P, Line(M, N))",
"PointLiesOnLine(K, Line(P, J))",
"PointLiesOnLine(P, Line(L, J))",
"PointLiesOnLine(K, Line(L, J))",
"PointLiesOnLine(P, Line(L, K))",
"PointLiesOnCircle(M, Circle(K, radius_7_0))",
"PointLiesOnCircle(J, Circle(K, radius_7_0))",
... | [
"JK",
"LJ",
"LK",
"ML",
"MN",
"MP",
"NL",
"PJ",
"PK",
"PL",
"PN"
] | {"J": [160.0, 24.0], "K": [93.0, 97.0], "L": [33.0, 166.0], "M": [1.0, 96.0], "N": [98.0, 186.0], "P": [52.0, 144.0]} | [
"K"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(H, F)), 10)
- Equals(LengthOf(Line(C, H)), 7)
- Equals(LengthOf(Line(E, H)), 6)
- Equals(LengthOf(Line(E, F)), 11)
- PointLiesOnLine(C, Line(B, D))
- PointLiesOnLine(H, Line(B, E))
- PointLiesOnLine(B, Line(D, A))
- PointLiesOnLine(C, Line(D, A))
- PointLiesOnLine(F, Line(E, G... | 18.9 | [
"Similar(Triangle(C,B,H),Triangle(F,E,H))",
"Parallelogram(A,D,E,G)",
"Equals(LengthOf(Line(C,H)),7)",
"Equals(LengthOf(Line(F,H)),10)",
"Equals(LengthOf(Line(F,E)),11)",
"Equals(LengthOf(Line(E,H)),6)",
"Find(PerimeterOf(Triangle(C,B,H)))"
] | [
"Equals(LengthOf(Line(H, F)), 10)",
"Equals(LengthOf(Line(C, H)), 7)",
"Equals(LengthOf(Line(E, H)), 6)",
"Equals(LengthOf(Line(E, F)), 11)",
"PointLiesOnLine(C, Line(B, D))",
"PointLiesOnLine(H, Line(B, E))",
"PointLiesOnLine(B, Line(D, A))",
"PointLiesOnLine(C, Line(D, A))",
"PointLiesOnLine(F, Li... | [
"BD",
"BE",
"BC",
"BA",
"BH",
"DE",
"DC",
"DA",
"EG",
"EF",
"EH",
"CF",
"CA",
"CH",
"AG",
"HF",
"GF"
] | {"B": [179.02158306488724, 21.44707777266452], "D": [0.0, 120.0], "G": [392.5, 46.5], "E": [183.49198305616568, 165.58393473486038], "F": [321.7828727227661, 89.93016482835543], "C": [79.58838805416434, 76.03375997032092], "A": [218.11381316598025, 0.12028502320715972], "H": [181.94030950626382, 81.90641120117907]} | [] |
Diagram Logic Form:
- 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_4_0))
- PointLiesOnCircle(F, Circle(E, radius_4_0))
Find x. Assume that segments that appear to be tangent are tangent. | 9 | [
"Tangent(Line($),Circle($))",
"Find(x)"
] | [
"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_4_0))",
"PointLiesOnCircle(F, Circle(E, radius_4_0))"
] | [
"BF",
"CB",
"CE",
"EB",
"EF"
] | {"B": [1.0, 87.0], "C": [125.0, 13.0], "E": [169.0, 86.0], "F": [84.0, 88.0]} | [
"E"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(H, G, A)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(F, H, G)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(A, J, H)), MeasureOf(angle 3))
- PointLiesOnLine(A, Line(J, G))
- PointLiesOnLine(B, Line(J, G))
- PointLiesOnLine(A, Line(J, B))
- PointLiesOnLine(B, Line(H, F))
... | 30 | [
"Equals(MeasureOf(Angle(2)),2x)",
"Equals(MeasureOf(Angle(3)),x)",
"Find(MeasureOf(Angle(1)))"
] | [
"Equals(MeasureOf(Angle(H, G, A)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(F, H, G)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(A, J, H)), MeasureOf(angle 3))",
"PointLiesOnLine(A, Line(J, G))",
"PointLiesOnLine(B, Line(J, G))",
"PointLiesOnLine(A, Line(J, B))",
"PointLiesOnLine(B, Line(H, F))... | [
"AB",
"BF",
"GA",
"GB",
"HB",
"HF",
"HG",
"JA",
"JB",
"JG",
"JH"
] | {"A": [105.0, 106.0], "B": [102.0, 82.0], "F": [4.0, 80.0], "G": [100.0, 2.0], "H": [202.0, 83.0], "J": [103.0, 205.0]} | [
"A"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(E, F)), 3y)
- Equals(LengthOf(Line(E, B)), 3y-6)
- Equals(LengthOf(Line(B, F)), 2y+4)
- Equals(LengthOf(Line(F, G)), \frac{1}{2}x+12)
- Equals(LengthOf(Line(D, G)), \frac{3}{2}x+8)
- PointLiesOnLine(G, Line(D, F))
- PointLiesOnLine(B, Line(E, F))
-
If $\overline{PR} \| \over... | 20 | [
"Parallel(Line(P,R),Line(K,L))",
"Equals(LengthOf(Line(K,N)),9)",
"Equals(LengthOf(Line(L,N)),16)",
"Equals(LengthOf(Line(P,M)),Mul(Line(K,P),2))",
"Find(LengthOf(Line(M,L)))"
] | [
"Equals(LengthOf(Line(E, F)), 3y)",
"Equals(LengthOf(Line(E, B)), 3y-6)",
"Equals(LengthOf(Line(B, F)), 2y+4)",
"Equals(LengthOf(Line(F, G)), \\frac{1}{2}x+12)",
"Equals(LengthOf(Line(D, G)), \\frac{3}{2}x+8)",
"PointLiesOnLine(G, Line(D, F))",
"PointLiesOnLine(B, Line(E, F))",
""
] | [
"BF",
"BG",
"DE",
"DF",
"DG",
"EB",
"EF",
"FG"
] | {"B": [133.0, 99.0], "D": [296.0, 328.0], "E": [261.0, 1.0], "F": [0.0, 196.0], "G": [153.0, 264.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(T, W)), 4x-4)
- Equals(LengthOf(Line(S, T)), 2x+2)
- PointLiesOnLine(T, Line(S, W))
- PointLiesOnLine(R, Line(T, C))
- Perpendicular(Line(T, W), Line(T, R))
- Equals(LengthOf(Line(R, W)), LengthOf(Line(S, R)))
Find $SW$. | 16 | [
"Find(LengthOf(Line(S,W)))"
] | [
"Equals(LengthOf(Line(T, W)), 4x-4)",
"Equals(LengthOf(Line(S, T)), 2x+2)",
"PointLiesOnLine(T, Line(S, W))",
"PointLiesOnLine(R, Line(T, C))",
"Perpendicular(Line(T, W), Line(T, R))",
"Equals(LengthOf(Line(R, W)), LengthOf(Line(S, R)))"
] | [
"CR",
"RW",
"SR",
"ST",
"SW",
"TC",
"TR",
"TW"
] | {"C": [5.0, 103.0], "R": [66.0, 102.0], "S": [219.0, 200.0], "T": [219.0, 102.0], "W": [220.0, 1.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(G, K, H)), 122)
-
- PointLiesOnLine(K, Line(G, J))
-
- PointLiesOnCircle(L, Circle(K, radius_0_0))
- PointLiesOnCircle(H, Circle(K, radius_0_0))
- PointLiesOnCircle(J, Circle(K, radius_0_0))
- PointLiesOnCircle(G, Circle(K, radius_0_0))
$\overline{GJ}$ is a diameter of $\... | 238 | [
"IsDiameterOf(Line(G,J),Circle(K))",
"Find(MeasureOf(Arc(G,L,H)))"
] | [
"Equals(MeasureOf(Angle(G, K, H)), 122)",
"",
"PointLiesOnLine(K, Line(G, J))",
"",
"PointLiesOnCircle(L, Circle(K, radius_0_0))",
"PointLiesOnCircle(H, Circle(K, radius_0_0))",
"PointLiesOnCircle(J, Circle(K, radius_0_0))",
"PointLiesOnCircle(G, Circle(K, radius_0_0))"
] | [
"GJ",
"KG",
"KH",
"KJ"
] | {"G": [0.0, 176.0], "H": [268.0, 28.0], "J": [349.0, 175.0], "K": [170.0, 175.0]} | [
"K"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, A, D)), 120)
- Equals(MeasureOf(Angle(A, D, C)), 85)
- Equals(LengthOf(Line(C, D)), LengthOf(Line(B, C)))
- Equals(LengthOf(Line(A, D)), LengthOf(Line(B, A)))
If $ABCD$ is a kite, Find $m \angle C$ | 70 | [
"Kite(A,B,C,D)",
"Find(MeasureOf(Angle(C)))"
] | [
"Equals(MeasureOf(Angle(B, A, D)), 120)",
"Equals(MeasureOf(Angle(A, D, C)), 85)",
"Equals(LengthOf(Line(C, D)), LengthOf(Line(B, C)))",
"Equals(LengthOf(Line(A, D)), LengthOf(Line(B, A)))"
] | [
"AD",
"BA",
"BC",
"CD"
] | {"A": [105.0, 1.0], "B": [198.0, 68.0], "C": [107.0, 187.0], "D": [1.0, 68.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 3.6)
- Equals(LengthOf(Line(D, C)), 2)
- Equals(LengthOf(Line(A, B)), 6)
- PointLiesOnLine(D, Line(A, B))
- Perpendicular(Line(C, D), Line(B, D))
Find the perimeter of the triangle. Round to the nearest tenth if necessary. | 13.2 | [
"Find(PerimeterOf(Triangle($)))"
] | [
"Equals(LengthOf(Line(A, C)), 3.6)",
"Equals(LengthOf(Line(D, C)), 2)",
"Equals(LengthOf(Line(A, B)), 6)",
"PointLiesOnLine(D, Line(A, B))",
"Perpendicular(Line(C, D), Line(B, D))"
] | [
"AB",
"AC",
"BC"
] | {"A": [214.0, 114.0], "B": [0.0, 115.0], "C": [108.0, 1.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(R, B)), 5)
- Equals(LengthOf(Line(B, S)), x-1)
- Equals(LengthOf(Line(S, D)), x-1)
- Equals(LengthOf(Line(T, D)), 10)
- Equals(LengthOf(Line(T, C)), 3x-2)
- Equals(LengthOf(Line(R, C)), x+1)
- PointLiesOnLine(C, Line(T, R))
- PointLiesOnLine(D, Line(T, S))
- PointLiesOnLine(B,... | 36 | [
"CircumscribedTo(Triangle(R,S,T),Circle($))",
"Find(PerimeterOf(Triangle($)))"
] | [
"Equals(LengthOf(Line(R, B)), 5)",
"Equals(LengthOf(Line(B, S)), x-1)",
"Equals(LengthOf(Line(S, D)), x-1)",
"Equals(LengthOf(Line(T, D)), 10)",
"Equals(LengthOf(Line(T, C)), 3x-2)",
"Equals(LengthOf(Line(R, C)), x+1)",
"PointLiesOnLine(C, Line(T, R))",
"PointLiesOnLine(D, Line(T, S))",
"PointLiesOn... | [
"RB",
"RC",
"RS",
"SB",
"SD",
"TC",
"TD",
"TR",
"TS"
] | {"A": [90.0, 172.0], "B": [0.0, 171.0], "C": [141.0, 98.0], "D": [89.0, 265.0], "R": [1.0, 1.0], "S": [0.0, 262.0], "T": [385.0, 267.0]} | [
"A"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(Q, S, R)), 48)
- PointLiesOnLine(R, Line(Q, A))
- PointLiesOnLine(P, Line(Q, B))
- Perpendicular(Line(Q, P), Line(S, P))
- Perpendicular(Line(Q, R), Line(S, R))
- Equals(LengthOf(Line(S, P)), LengthOf(Line(S, R)))
- Equals(MeasureOf(Angle(P, Q, S)), MeasureOf(Angle(R, Q, S))... | 42 | [
"Find(MeasureOf(Angle(P,Q,S)))"
] | [
"Equals(MeasureOf(Angle(Q, S, R)), 48)",
"PointLiesOnLine(R, Line(Q, A))",
"PointLiesOnLine(P, Line(Q, B))",
"Perpendicular(Line(Q, P), Line(S, P))",
"Perpendicular(Line(Q, R), Line(S, R))",
"Equals(LengthOf(Line(S, P)), LengthOf(Line(S, R)))",
"Equals(MeasureOf(Angle(P, Q, S)), MeasureOf(Angle(R, Q, S)... | [
"PB",
"QA",
"QB",
"QP",
"QR",
"QS",
"QY",
"RA",
"SP",
"SR",
"SY"
] | {"A": [391.0, 225.0], "B": [1.0, 229.0], "P": [66.0, 152.0], "Q": [196.0, 2.0], "R": [328.0, 152.0], "S": [197.0, 267.0], "Y": [194.0, 336.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, D)), x)
- Equals(LengthOf(Line(D, C)), 6)
- Equals(LengthOf(Line(D, E)), 3)
- Equals(LengthOf(Line(A, D)), 9)
- PointLiesOnLine(D, Line(A, B))
- PointLiesOnLine(D, Line(C, E))
- PointLiesOnCircle(A, Circle(F, radius_5_0))
- PointLiesOnCircle(B, Circle(F, radius_5_0))
- Poin... | 2 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(B, D)), x)",
"Equals(LengthOf(Line(D, C)), 6)",
"Equals(LengthOf(Line(D, E)), 3)",
"Equals(LengthOf(Line(A, D)), 9)",
"PointLiesOnLine(D, Line(A, B))",
"PointLiesOnLine(D, Line(C, E))",
"PointLiesOnCircle(A, Circle(F, radius_5_0))",
"PointLiesOnCircle(B, Circle(F, radius_5_0))",
... | [
"AB",
"AD",
"BD",
"DC",
"DE",
"CE"
] | {"A": [119.98236519907263, 211.92911501588017], "B": [69.30677117882367, 8.233099836448048], "C": [194.58246685528718, 48.02123049888371], "D": [80.64655453951666, 53.81458197256695], "E": [16.625556067348924, 57.06988697962633], "F": [107.5, 107.5]} | [
"F"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, F, A)), 3x-15)
- Equals(MeasureOf(Angle(A, C, F)), y^{2})
- Equals(MeasureOf(Angle(F, A, C)), 68)
- Equals(MeasureOf(Angle(B, E, C)), 2x)
- PointLiesOnLine(B, Line(C, F))
- PointLiesOnLine(E, Line(A, C))
- Parallel(Line(F,A), Line(B,E))
Find $x$ in the figure. | 34 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(C, F, A)), 3x-15)",
"Equals(MeasureOf(Angle(A, C, F)), y^{2})",
"Equals(MeasureOf(Angle(F, A, C)), 68)",
"Equals(MeasureOf(Angle(B, E, C)), 2x)",
"PointLiesOnLine(B, Line(C, F))",
"PointLiesOnLine(E, Line(A, C))",
"Parallel(Line(F,A), Line(B,E))"
] | [
"AE",
"AC",
"EC",
"FB",
"BC",
"FC",
"AF",
"EB"
] | {"A": [0.0, 180.0], "B": [235.0, 76.0], "C": [458.0, 179.0], "E": [190.0, 180.0], "F": [73.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 2x+9)
- Equals(LengthOf(Line(B, D)), 4x-5)
- Equals(MeasureOf(Angle(C, A, E)), 42)
- Equals(MeasureOf(Angle(E, B, D)), 83)
- Equals(MeasureOf(Angle(E, A, B)), 23)
- Equals(MeasureOf(Angle(D, C, E)), 4y)
- PointLiesOnLine(E, Line(A, D))
- PointLiesOnLine(E, Line(B, C))
... | 8 | [
"Parallelogram($)",
"Find(y)"
] | [
"Equals(LengthOf(Line(A, C)), 2x+9)",
"Equals(LengthOf(Line(B, D)), 4x-5)",
"Equals(MeasureOf(Angle(C, A, E)), 42)",
"Equals(MeasureOf(Angle(E, B, D)), 83)",
"Equals(MeasureOf(Angle(E, A, B)), 23)",
"Equals(MeasureOf(Angle(D, C, E)), 4y)",
"PointLiesOnLine(E, Line(A, D))",
"PointLiesOnLine(E, Line(B, ... | [
"AB",
"AC",
"AD",
"AE",
"BC",
"BD",
"BE",
"CD",
"CE",
"DE"
] | {"A": [0.0, 228.0], "B": [463.0, 226.0], "C": [107.0, 2.0], "D": [568.0, 2.0], "E": [286.0, 114.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, E)), 6)
- Equals(LengthOf(Line(A, G)), b)
- Equals(LengthOf(Line(A, D)), 8)
- Equals(LengthOf(Line(A, F)), a)
- Equals(LengthOf(Line(B, G)), 10)
- Equals(LengthOf(Line(B, F)), 4)
- PointLiesOnLine(F, Line(A, B))
- PointLiesOnLine(A, Line(B, E))
- PointLiesOnLine(F, Line(B, ... | 11.3 | [
"Tangent(Line($),Circle($))",
"Find(b)"
] | [
"Equals(LengthOf(Line(A, E)), 6)",
"Equals(LengthOf(Line(A, G)), b)",
"Equals(LengthOf(Line(A, D)), 8)",
"Equals(LengthOf(Line(A, F)), a)",
"Equals(LengthOf(Line(B, G)), 10)",
"Equals(LengthOf(Line(B, F)), 4)",
"PointLiesOnLine(F, Line(A, B))",
"PointLiesOnLine(A, Line(B, E))",
"PointLiesOnLine(F, L... | [
"AB",
"AD",
"AE",
"AF",
"AG",
"AH",
"BE",
"BF",
"BG",
"DG",
"EF"
] | {"A": [94.0, 74.0], "B": [0.0, 204.0], "D": [190.0, 74.0], "E": [139.0, 11.0], "F": [29.0, 165.0], "G": [2.0, 74.0], "H": [97.0, 98.0]} | [
"H"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, B)), \frac{5}{3}x+11)
- Equals(LengthOf(Line(D, B)), 3y-9)
- Equals(LengthOf(Line(A, D)), x+2)
- Equals(LengthOf(Line(Y, D)), 2y+6)
- PointLiesOnLine(D, Line(Y, B))
- PointLiesOnLine(A, Line(Y, C))
- Equals(LengthOf(Line(D, B)), LengthOf(Line(Y, D)))
- Equals(LengthOf(Line(... | 15 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(C, B)), \\frac{5}{3}x+11)",
"Equals(LengthOf(Line(D, B)), 3y-9)",
"Equals(LengthOf(Line(A, D)), x+2)",
"Equals(LengthOf(Line(Y, D)), 2y+6)",
"PointLiesOnLine(D, Line(Y, B))",
"PointLiesOnLine(A, Line(Y, C))",
"Equals(LengthOf(Line(D, B)), LengthOf(Line(Y, D)))",
"Equals(LengthOf(... | [
"AC",
"AD",
"AY",
"CB",
"DB",
"YB",
"YC",
"YD"
] | {"A": [65.0, 172.0], "B": [133.0, 2.0], "C": [1.0, 90.0], "D": [134.0, 129.0], "Y": [134.0, 258.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), y)
- Equals(MeasureOf(Angle(B, C, A)), 60)
- Equals(LengthOf(Line(A, C)), x)
- Equals(LengthOf(Line(A, B)), 12)
- Perpendicular(Line(A, C), Line(A, B))
Find x. | 4 \sqrt { 3 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(B, C)), y)",
"Equals(MeasureOf(Angle(B, C, A)), 60)",
"Equals(LengthOf(Line(A, C)), x)",
"Equals(LengthOf(Line(A, B)), 12)",
"Perpendicular(Line(A, C), Line(A, B))"
] | [
"AB",
"AC",
"BC"
] | {"A": [78.39695228578566, 138.2877008909984], "B": [268.1804767789431, 1.682066394161204], "C": [0.22136486726680005, 28.644364982277846]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, B, C)), 18)
- Equals(LengthOf(Line(D, B)), 12)
Find the area of the triangle. Round to the nearest hundredth. | 23.39 | [
"Find(AreaOf(Triangle($)))"
] | [
"Equals(MeasureOf(Angle(D, B, C)), 18)",
"Equals(LengthOf(Line(D, B)), 12)"
] | [
"BC",
"DB",
"DC"
] | {"B": [252.0, 2.0], "C": [1.0, 47.0], "D": [38.0, 119.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, C)), 4)
- Equals(LengthOf(Line(D, A)), 10)
- Equals(LengthOf(Line(D, E)), 5)
- PointLiesOnLine(E, Line(C, B))
- Perpendicular(Line(D, E), Line(B, E))
Find the perimeter of $▱ ABCD$. | 28 | [
"Find(PerimeterOf(Parallelogram(A,B,C,D)))"
] | [
"Equals(LengthOf(Line(D, C)), 4)",
"Equals(LengthOf(Line(D, A)), 10)",
"Equals(LengthOf(Line(D, E)), 5)",
"PointLiesOnLine(E, Line(C, B))",
"Perpendicular(Line(D, E), Line(B, E))"
] | [
"AB",
"AD",
"BC",
"CD",
"DE",
"BE",
"CE"
] | {"A": [3.0, 1.0], "B": [115.0, 1.0], "D": [136.0, 255.0], "E": [207.0, 216.0], "C": [251.0, 255.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, D, B)), 133)
- Equals(MeasureOf(Angle(A, D, C)), 133)
- Equals(LengthOf(Line(A, C)), 4x-2)
- Equals(LengthOf(Line(E, B)), 6x-10)
- PointLiesOnCircle(A, Circle(D, radius_3_0))
- PointLiesOnCircle(B, Circle(D, radius_3_0))
- PointLiesOnCircle(C, Circle(D, radius_3_0))
- Poi... | 4 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(E, D, B)), 133)",
"Equals(MeasureOf(Angle(A, D, C)), 133)",
"Equals(LengthOf(Line(A, C)), 4x-2)",
"Equals(LengthOf(Line(E, B)), 6x-10)",
"PointLiesOnCircle(A, Circle(D, radius_3_0))",
"PointLiesOnCircle(B, Circle(D, radius_3_0))",
"PointLiesOnCircle(C, Circle(D, radius_3_0))",
... | [
"AC",
"AE",
"EB"
] | {"A": [3.0, 100.0], "B": [219.0, 177.0], "C": [220.0, 61.0], "D": [120.0, 120.0], "E": [3.0, 138.0]} | [
"D"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(K, A, J)), MeasureOf(angle 13))
- Equals(MeasureOf(Angle(E, A, K)), MeasureOf(angle 14))
- Equals(MeasureOf(Angle(D, H, F)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(C, I, B)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(D, I, C)), MeasureOf(angle 1))
- Equals(MeasureOf... | 55 | [
"Equals(MeasureOf(Angle(3)),110)",
"Equals(MeasureOf(Angle(12)),55)",
"Find(MeasureOf(Angle(15)))"
] | [
"Equals(MeasureOf(Angle(K, A, J)), MeasureOf(angle 13))",
"Equals(MeasureOf(Angle(E, A, K)), MeasureOf(angle 14))",
"Equals(MeasureOf(Angle(D, H, F)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(C, I, B)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(D, I, C)), MeasureOf(angle 1))",
"Equals(MeasureOf(A... | [
"AC",
"AE",
"AI",
"AJ",
"AK",
"AL",
"BD",
"BH",
"CI",
"CK",
"DH",
"EF",
"EG",
"EH",
"EJ",
"EL",
"FG",
"HF",
"HG",
"IB",
"ID",
"IH",
"IK",
"JL"
] | {"A": [86.0, 246.0], "B": [407.0, 114.0], "C": [153.0, 1.0], "D": [0.0, 83.0], "E": [245.0, 212.0], "F": [302.0, 1.0], "G": [214.0, 325.0], "H": [274.0, 104.0], "I": [128.0, 93.0], "J": [0.0, 265.0], "K": [65.0, 325.0], "L": [406.0, 177.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, A, E)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(E, B, A)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(D, B, E)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(A, E, B)), MeasureOf(angle 6))
- Equals(MeasureOf(Angle(B, E, C)), MeasureOf(angle 5))
- Equals(MeasureOf(A... | 58 | [
"Equals(MeasureOf(Angle(1)),58)",
"Equals(MeasureOf(Angle(2)),47)",
"Equals(MeasureOf(Angle(3)),26)",
"Find(MeasureOf(Angle(7)))"
] | [
"Equals(MeasureOf(Angle(B, A, E)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(E, B, A)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(D, B, E)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(A, E, B)), MeasureOf(angle 6))",
"Equals(MeasureOf(Angle(B, E, C)), MeasureOf(angle 5))",
"Equals(MeasureOf(Ang... | [
"BA",
"BC",
"BE",
"DA",
"DB",
"DC",
"DE",
"EA",
"EC"
] | {"A": [1.0, 8.0], "B": [198.0, 8.0], "C": [160.0, 132.0], "D": [133.0, 216.0], "E": [81.0, 131.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(P, Line(Q, T))
- PointLiesOnLine(M, Line(R, S))
For trapezoid QRST, M and P are midpoints of the legs. If TS = 2x + 2, QR = 5x + 3, and PM = 13, find TS. | 8 | [
"Trapezoid(Q,R,S,T)",
"IsMidpointOf(Point(M),LegOf(Trapezoid(Q,R,S,T)))",
"IsMidpointOf(Point(P),LegOf(Trapezoid(Q,R,S,T)))",
"Equals(LengthOf(Line(T,S)),2x+2)",
"Equals(LengthOf(Line(Q,R)),5x+3)",
"Equals(LengthOf(Line(P,M)),13)",
"Find(LengthOf(Line(T,S)))"
] | [
"PointLiesOnLine(P, Line(Q, T))",
"PointLiesOnLine(M, Line(R, S))"
] | [
"MS",
"PM",
"QP",
"QR",
"QT",
"RM",
"RS",
"TP",
"TS"
] | {"M": [172.0, 68.0], "P": [25.0, 70.0], "Q": [0.0, 0.0], "R": [197.0, 1.0], "S": [145.0, 140.0], "T": [50.0, 139.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(P, Q, R)), 2x-16)
- Equals(MeasureOf(Angle(S, R, Q)), 2x)
- Equals(MeasureOf(Angle(P, S, R)), x+10)
- Equals(MeasureOf(Angle(Q, P, S)), x)
Find the measure of $\angle R$ | 122 | [
"Find(MeasureOf(Angle(R)))"
] | [
"Equals(MeasureOf(Angle(P, Q, R)), 2x-16)",
"Equals(MeasureOf(Angle(S, R, Q)), 2x)",
"Equals(MeasureOf(Angle(P, S, R)), x+10)",
"Equals(MeasureOf(Angle(Q, P, S)), x)"
] | [
"PS",
"QP",
"QR",
"RS"
] | {"P": [6.0, 184.0], "Q": [111.0, 0.0], "R": [314.0, 24.0], "S": [370.0, 191.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Arc(R,S,T)), 7.94)
- Equals(MeasureOf(Angle(N, S, T)), 70)
- PointLiesOnCircle(R, Circle(S, radius_0_0))
- PointLiesOnCircle(T, Circle(S, radius_0_0))
Find the circumference of $\odot S$. Round to the nearest hundredth. | 40.83 | [
"Find(CircumferenceOf(Circle(S)))"
] | [
"Equals(LengthOf(Arc(R,S,T)), 7.94)",
"Equals(MeasureOf(Angle(N, S, T)), 70)",
"PointLiesOnCircle(R, Circle(S, radius_0_0))",
"PointLiesOnCircle(T, Circle(S, radius_0_0))"
] | [
"SR",
"ST"
] | {"T": [276.0, 140.0], "S": [141.0, 142.0], "R": [184.0, 268.0]} | [
"S"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, D)), 8)
- PointLiesOnLine(H, Line(A, B))
- PointLiesOnLine(G, Line(A, C))
- PointLiesOnLine(H, Line(A, J))
- PointLiesOnLine(F, Line(B, C))
- PointLiesOnLine(I, Line(B, C))
- PointLiesOnLine(J, Line(B, C))
- PointLiesOnLine(E, Line(B, D))
- PointLiesOnLine(J, Line(B, D))
- ... | 168.2 | [
"Regular(Polygon($))",
"Find(AreaOf(Shaded(Shape($))))"
] | [
"Equals(LengthOf(Line(B, D)), 8)",
"PointLiesOnLine(H, Line(A, B))",
"PointLiesOnLine(G, Line(A, C))",
"PointLiesOnLine(H, Line(A, J))",
"PointLiesOnLine(F, Line(B, C))",
"PointLiesOnLine(I, Line(B, C))",
"PointLiesOnLine(J, Line(B, C))",
"PointLiesOnLine(E, Line(B, D))",
"PointLiesOnLine(J, Line(B,... | [
"AB",
"AC",
"AD",
"AE",
"AG",
"AH",
"AJ",
"BC",
"BD",
"BE",
"BF",
"BG",
"BH",
"BI",
"BJ",
"CD",
"CE",
"CF",
"CG",
"CH",
"CI",
"CJ",
"DE",
"DF",
"DG",
"DH",
"DI",
"DJ",
"EF",
"EG",
"EH",
"EI",
"EJ",
"FI",
"GF",
"GJ",
"HI",
"HJ",
"JF",
"JI"... | {"A": [60.0, 4.0], "B": [161.0, 100.0], "C": [26.0, 141.0], "D": [79.0, 82.0], "E": [120.0, 90.0], "F": [77.0, 123.0], "G": [44.0, 76.0], "H": [110.0, 56.0], "I": [106.0, 115.0], "J": [156.0, 100.0]} | [
"D"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, B, D)), 55)
- Equals(MeasureOf(Angle(G, B, F)), 35)
- PointLiesOnLine(B, Line(A, D))
- PointLiesOnLine(B, Line(C, G))
- PointLiesOnCircle(F, Circle(B, radius_6_0))
- PointLiesOnCircle(D, Circle(B, radius_6_0))
- PointLiesOnCircle(A, Circle(B, radius_6_0))
- PointLiesOnCir... | 325 | [
"IsDiameterOf(Line(A,D),Circle(B))",
"IsDiameterOf(Line(C,G),Circle(B))",
"Find(MeasureOf(Arc(G,C,F)))"
] | [
"Equals(MeasureOf(Angle(C, B, D)), 55)",
"Equals(MeasureOf(Angle(G, B, F)), 35)",
"PointLiesOnLine(B, Line(A, D))",
"PointLiesOnLine(B, Line(C, G))",
"PointLiesOnCircle(F, Circle(B, radius_6_0))",
"PointLiesOnCircle(D, Circle(B, radius_6_0))",
"PointLiesOnCircle(A, Circle(B, radius_6_0))",
"PointLiesO... | [
"AB",
"AD",
"BD",
"CB",
"CG",
"FB",
"GB"
] | {"A": [34.0, 274.0], "B": [181.0, 172.0], "C": [173.0, 1.0], "D": [316.0, 74.0], "F": [272.0, 318.0], "G": [173.0, 347.0]} | [
"B"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, C, A)), 55)
- Equals(MeasureOf(Angle(B, D, E)), 47)
- Equals(MeasureOf(Angle(E, A, D)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(C, A, B)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(D, E, C)), 57)
- Equals(MeasureOf(Angle(A, B, C)), MeasureOf(angle 3))
- PointLiesO... | 49 | [
"Find(MeasureOf(Angle(3)))"
] | [
"Equals(MeasureOf(Angle(B, C, A)), 55)",
"Equals(MeasureOf(Angle(B, D, E)), 47)",
"Equals(MeasureOf(Angle(E, A, D)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(C, A, B)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(D, E, C)), 57)",
"Equals(MeasureOf(Angle(A, B, C)), MeasureOf(angle 3))",
"PointLies... | [
"AB",
"AC",
"AD",
"AE",
"BC",
"BD",
"CE",
"DE"
] | {"A": [109.0, 112.0], "B": [264.0, 239.0], "C": [259.0, 1.0], "D": [0.0, 22.0], "E": [11.0, 183.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(L, K)), 4x)
- Equals(LengthOf(Line(J, K)), 3x+6)
- Equals(LengthOf(Line(J, L)), 5x-6)
- Equals(LengthOf(Line(J, K)), LengthOf(Line(L, K)))
- Equals(LengthOf(Line(L, K)), LengthOf(Line(J, L)))
Find $JK$. | 24 | [
"Find(LengthOf(Line(J,K)))"
] | [
"Equals(LengthOf(Line(L, K)), 4x)",
"Equals(LengthOf(Line(J, K)), 3x+6)",
"Equals(LengthOf(Line(J, L)), 5x-6)",
"Equals(LengthOf(Line(J, K)), LengthOf(Line(L, K)))",
"Equals(LengthOf(Line(L, K)), LengthOf(Line(J, L)))"
] | [
"JL",
"JK",
"LK"
] | {"J": [1.1529790660225387, 206.66666666666669], "L": [300.0, 206.0], "K": [150.50242718446603, 1.6821031312287005]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, I, C)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(L, I, B)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(L, D, A)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(A, D, I)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(O, D, L)), MeasureOf(angle 5))
- Equals(MeasureOf(A... | 76 | [
"Equals(MeasureOf(Angle(4)),104)",
"Equals(MeasureOf(Angle(14)),118)",
"Find(MeasureOf(Angle(7)))"
] | [
"Equals(MeasureOf(Angle(B, I, C)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(L, I, B)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(L, D, A)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(A, D, I)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(O, D, L)), MeasureOf(angle 5))",
"Equals(MeasureOf(Ang... | [
"AO",
"BK",
"BN",
"CI",
"CL",
"DA",
"DC",
"DE",
"DI",
"DL",
"DO",
"EA",
"EO",
"FB",
"FH",
"FJ",
"FK",
"HJ",
"IB",
"IF",
"IK",
"IL",
"OF",
"OH",
"OJ"
] | {"A": [82.0, 1.0], "B": [247.0, 1.0], "C": [325.0, 66.0], "D": [83.0, 68.0], "E": [83.0, 240.0], "F": [247.0, 150.0], "H": [0.0, 182.0], "I": [245.0, 66.0], "J": [329.0, 140.0], "K": [246.0, 247.0], "L": [0.0, 67.0], "N": [246.0, 108.0], "O": [83.0, 171.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 5)
- Equals(LengthOf(Line(E, C)), 4.5)
- Equals(LengthOf(Line(C, A)), 7.5)
- Equals(LengthOf(Line(B, D)), x)
- PointLiesOnLine(C, Line(E, A))
- PointLiesOnLine(B, Line(A, D))
- PointLiesOnCircle(E, Circle(X, radius_4_0))
- PointLiesOnCircle(C, Circle(X, radius_4_0))
- ... | 13 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), 5)",
"Equals(LengthOf(Line(E, C)), 4.5)",
"Equals(LengthOf(Line(C, A)), 7.5)",
"Equals(LengthOf(Line(B, D)), x)",
"PointLiesOnLine(C, Line(E, A))",
"PointLiesOnLine(B, Line(A, D))",
"PointLiesOnCircle(E, Circle(X, radius_4_0))",
"PointLiesOnCircle(C, Circle(X, radius_4_0)... | [
"AB",
"AD",
"AX",
"BD",
"CA",
"CB",
"EA",
"EC"
] | {"A": [3.0, 188.0], "B": [59.0, 154.0], "C": [100.0, 185.0], "D": [222.0, 60.0], "E": [176.0, 182.0], "X": [134.0, 97.0]} | [
"X"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, E, D)), 75)
- Equals(MeasureOf(Angle(B, I, D)), x)
- Equals(MeasureOf(Angle(A, E, B)), 143)
- PointLiesOnLine(I, Line(A, D))
- PointLiesOnLine(I, Line(B, C))
- PointLiesOnCircle(B, Circle(E, radius_7_0))
- PointLiesOnCircle(A, Circle(E, radius_7_0))
- PointLiesOnCircle(D,... | 71 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(C, E, D)), 75)",
"Equals(MeasureOf(Angle(B, I, D)), x)",
"Equals(MeasureOf(Angle(A, E, B)), 143)",
"PointLiesOnLine(I, Line(A, D))",
"PointLiesOnLine(I, Line(B, C))",
"PointLiesOnCircle(B, Circle(E, radius_7_0))",
"PointLiesOnCircle(A, Circle(E, radius_7_0))",
"PointLiesOnCircl... | [
"AD",
"BC",
"IA",
"IB",
"IC",
"ID"
] | {"A": [100.0, 100.0], "B": [244.0, 307.0], "C": [276.0, 64.0], "D": [342.0, 170.0], "E": [209.0, 179.0], "I": [265.0, 148.0]} | [
"E"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), y)
- Equals(LengthOf(Line(A, B)), 15)
- Equals(MeasureOf(Angle(A, B, C)), 30)
- Equals(LengthOf(Line(B, C)), x)
- Perpendicular(Line(A, C), Line(B, C))
Find x. | \frac { 15 } { 2 } \sqrt { 3 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, C)), y)",
"Equals(LengthOf(Line(A, B)), 15)",
"Equals(MeasureOf(Angle(A, B, C)), 30)",
"Equals(LengthOf(Line(B, C)), x)",
"Perpendicular(Line(A, C), Line(B, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [107.0866319532211, 0.43782754495052245], "B": [0.8102121861655291, 280.62082315604073], "C": [204.63232485676951, 117.69397259356049]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(T, V, S)), 75)
- Equals(MeasureOf(Angle(P, V, T)), 72)
- PointLiesOnLine(V, Line(S, Q))
- PointLiesOnCircle(S, Circle(V, radius_1_0))
- PointLiesOnCircle(P, Circle(V, radius_1_0))
- PointLiesOnCircle(R, Circle(V, radius_1_0))
- PointLiesOnCircle(T, Circle(V, radius_1_0))
- P... | 255 | [
"IsDiameterOf(Line(Q,S),Circle(V))",
"Find(MeasureOf(Arc(Q,R,T)))"
] | [
"Equals(MeasureOf(Angle(T, V, S)), 75)",
"Equals(MeasureOf(Angle(P, V, T)), 72)",
"PointLiesOnLine(V, Line(S, Q))",
"PointLiesOnCircle(S, Circle(V, radius_1_0))",
"PointLiesOnCircle(P, Circle(V, radius_1_0))",
"PointLiesOnCircle(R, Circle(V, radius_1_0))",
"PointLiesOnCircle(T, Circle(V, radius_1_0))",
... | [
"QP",
"SQ",
"SV",
"VP",
"VQ",
"VR",
"VT"
] | {"P": [25.0, 235.0], "Q": [1.0, 150.0], "R": [151.0, 0.0], "S": [304.0, 153.0], "T": [191.0, 292.0], "V": [156.0, 149.0]} | [
"V"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, D)), 10)
- Equals(LengthOf(Line(C, B)), 2x+4)
- Equals(LengthOf(Line(D, B)), x+2)
- Equals(LengthOf(Line(B, C)), LengthOf(Line(C, D)))
Find $BC$. | 10 | [
"Find(LengthOf(Line(B,C)))"
] | [
"Equals(LengthOf(Line(C, D)), 10)",
"Equals(LengthOf(Line(C, B)), 2x+4)",
"Equals(LengthOf(Line(D, B)), x+2)",
"Equals(LengthOf(Line(B, C)), LengthOf(Line(C, D)))"
] | [
"CB",
"CD",
"DB"
] | {"B": [2.0, 135.0], "C": [269.0, 0.0], "D": [536.0, 136.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 24)
- Equals(LengthOf(Line(A, X)), x)
- Equals(LengthOf(Line(B, C)), 7)
- PointLiesOnLine(X, Line(A, C))
- PointLiesOnCircle(B, Circle(C, radius_2_0))
- PointLiesOnCircle(X, Circle(C, radius_2_0))
Find x. Assume that segments that appear to be tangent are tangent. | 18 | [
"Tangent(Line($),Circle($))",
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), 24)",
"Equals(LengthOf(Line(A, X)), x)",
"Equals(LengthOf(Line(B, C)), 7)",
"PointLiesOnLine(X, Line(A, C))",
"PointLiesOnCircle(B, Circle(C, radius_2_0))",
"PointLiesOnCircle(X, Circle(C, radius_2_0))"
] | [
"AB",
"AC",
"AX",
"BC",
"CX"
] | {"A": [292.0, 60.0], "B": [132.0, 161.0], "C": [88.0, 87.0], "X": [176.0, 76.0]} | [
"C"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, A, D)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(A, D, G)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(F, G, B)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(G, C, B)), MeasureOf(angle 3))
- PointLiesOnLine(B, Line(G, A))
- PointLiesOnLine(F, Line(A, D))
- Perpendi... | 37 | [
"Equals(MeasureOf(Angle(D,G,F)),53)",
"Equals(MeasureOf(Angle(A,G,C)),40)",
"Find(MeasureOf(Angle(1)))"
] | [
"Equals(MeasureOf(Angle(B, A, D)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(A, D, G)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(F, G, B)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(G, C, B)), MeasureOf(angle 3))",
"PointLiesOnLine(B, Line(G, A))",
"PointLiesOnLine(F, Line(A, D))",
"Perpend... | [
"AB",
"AC",
"AD",
"AF",
"CB",
"DF",
"GA",
"GB",
"GC",
"GD",
"GF"
] | {"A": [532.0, 1.0], "B": [426.0, 88.0], "C": [532.0, 212.0], "D": [0.0, 0.0], "F": [280.0, 0.0], "G": [282.0, 210.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(K, L)), 11x-8)
- Equals(LengthOf(Line(L, J)), x+12)
- Equals(LengthOf(Line(K, J)), 7x)
- Equals(LengthOf(Line(K, L)), LengthOf(Line(K, J)))
- Equals(LengthOf(Line(K, J)), LengthOf(Line(L, J)))
Find $KL$. | 14 | [
"Find(LengthOf(Line(K,L)))"
] | [
"Equals(LengthOf(Line(K, L)), 11x-8)",
"Equals(LengthOf(Line(L, J)), x+12)",
"Equals(LengthOf(Line(K, J)), 7x)",
"Equals(LengthOf(Line(K, L)), LengthOf(Line(K, J)))",
"Equals(LengthOf(Line(K, J)), LengthOf(Line(L, J)))"
] | [
"JK",
"LJ",
"LK"
] | {"J": [2.0, 182.0], "K": [124.0, 2.0], "L": [274.0, 184.0]} | [
""
] |
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