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(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_4_0))
- PointLiesOnCircle(B, Circle(X, radius_4_0))
- Poin... | 10 | [
"Tangent(Line($),Circle($))",
"Find(x)"
] | [
"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_4_0))",
"PointLiesOnCircle(B, Circle(X, radius_4_0))",
... | [
"AB",
"AD",
"AE",
"BE",
"DC",
"DE",
"EC"
] | {"A": [33.0, 20.0], "B": [116.0, 164.0], "C": [129.0, 14.0], "D": [2.0, 79.0], "E": [52.0, 53.0], "X": [86.0, 86.0]} | [
"X"
] |
Diagram Logic Form:
- PointLiesOnLine(B, Line(E, A))
- PointLiesOnLine(C, Line(A, D))
- Parallel(Line(C, B), Line(E, D))
Find $AC$ if $AC=x-3$, $BE=20, AB=16,$ and $CD=x+5$ | 32 | [
"Equals(LengthOf(Line(A,C)),x-3)",
"Equals(LengthOf(Line(B,E)),20)",
"Equals(LengthOf(Line(A,B)),16)",
"Equals(LengthOf(Line(C,D)),x+5)",
"Find(LengthOf(Line(A,C)))"
] | [
"PointLiesOnLine(B, Line(E, A))",
"PointLiesOnLine(C, Line(A, D))",
"Parallel(Line(C, B), Line(E, D))"
] | [
"AB",
"AC",
"AD",
"BC",
"DC",
"EA",
"EB",
"ED"
] | {"A": [1.0, 82.0], "B": [90.0, 124.0], "C": [87.0, 43.0], "D": [180.0, 1.0], "E": [181.0, 165.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(J, Q, R)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(R, Q, C)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(H, R, Q)), MeasureOf(angle 5))
- Equals(MeasureOf(Angle(Q, T, S)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(Q, R, S)), MeasureOf(angle 6))
- Equals(MeasureOf(A... | 131 | [
"Parallel(Line(Q,R),Line(T,S))",
"Parallel(Line(Q,T),Line(R,S))",
"Equals(MeasureOf(Angle(1)),131)",
"Find(MeasureOf(Angle(6)))"
] | [
"Equals(MeasureOf(Angle(J, Q, R)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(R, Q, C)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(H, R, Q)), MeasureOf(angle 5))",
"Equals(MeasureOf(Angle(Q, T, S)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(Q, R, S)), MeasureOf(angle 6))",
"Equals(MeasureOf(Ang... | [
"AB",
"AH",
"AL",
"AM",
"AO",
"AR",
"BH",
"BL",
"BM",
"BO",
"BR",
"CF",
"CJ",
"CK",
"CN",
"CP",
"CQ",
"EG",
"EP",
"FJ",
"FK",
"FN",
"FP",
"FQ",
"GA",
"GB",
"GH",
"GL",
"GM",
"GO",
"GP",
"GR",
"HL",
"HM",
"HO",
"IS",
"JK",
"JN",
"JP",
"JQ"... | {"A": [147.0, 69.0], "B": [148.0, 263.0], "C": [8.0, 266.0], "E": [76.0, 173.0], "F": [13.0, 208.0], "G": [146.0, 215.0], "H": [147.0, 1.0], "I": [78.0, 97.0], "J": [9.0, 1.0], "K": [10.0, 186.0], "L": [148.0, 44.0], "M": [146.0, 114.0], "N": [8.0, 224.0], "O": [145.0, 88.0], "P": [22.0, 143.0], "Q": [6.0, 55.0], "R": ... | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(B, Line(M, E))
- PointLiesOnLine(B, Line(N, P))
- PointLiesOnLine(P, Line(N, G))
- PointLiesOnLine(B, Line(N, G))
- PointLiesOnLine(P, Line(G, B))
- PointLiesOnCircle(M, Circle(P, radius_4_0))
- PointLiesOnCircle(E, Circle(P, radius_4_0))
- PointLiesOnCircle(N, Circle(P, radius_4_0... | 44.5 | [
"Circle(P)",
"Equals(MeasureOf(Arc(E,N)),66)",
"Equals(MeasureOf(Angle(G,P,M)),89)",
"Find(MeasureOf(Angle(G,N,M)))"
] | [
"PointLiesOnLine(B, Line(M, E))",
"PointLiesOnLine(B, Line(N, P))",
"PointLiesOnLine(P, Line(N, G))",
"PointLiesOnLine(B, Line(N, G))",
"PointLiesOnLine(P, Line(G, B))",
"PointLiesOnCircle(M, Circle(P, radius_4_0))",
"PointLiesOnCircle(E, Circle(P, radius_4_0))",
"PointLiesOnCircle(N, Circle(P, radius... | [
"EB",
"EG",
"EN",
"GB",
"MB",
"ME",
"MG",
"MN",
"MP",
"NB",
"NG",
"NP",
"PB",
"PG"
] | {"B": [117.0, 110.0], "E": [186.0, 45.0], "G": [18.0, 46.0], "M": [41.0, 183.0], "N": [186.0, 155.0], "P": [103.0, 100.0]} | [
"P"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(F, B, G)), 60)
- Equals(MeasureOf(Angle(B, G, H)), 60)
- Equals(LengthOf(Line(H, G)), 12)
- PointLiesOnLine(A, Line(F, H))
Find $FH$. | 12 | [
"Find(LengthOf(Line(F,H)))"
] | [
"Equals(MeasureOf(Angle(F, B, G)), 60)",
"Equals(MeasureOf(Angle(B, G, H)), 60)",
"Equals(LengthOf(Line(H, G)), 12)",
"PointLiesOnLine(A, Line(F, H))"
] | [
"AF",
"AH",
"FG",
"FH",
"FB",
"HG",
"GB"
] | {"A": [255.44525547445255, 189.84671532846716], "F": [144.48604292737986, 0.9764238638173026], "G": [0.0, 253.0], "H": [288.7431117827655, 250.20632371234927], "B": [116.0, 57.0]} | [] |
Diagram Logic Form:
- PointLiesOnLine(P, Line(W, Y))
- PointLiesOnLine(P, Line(Z, X))
- Perpendicular(Line(W, X), Line(W, Z))
If $m\angle ZXW = x - 11$ and $m \angle WZX = x - 9$, find $m\angle ZXY$. | 46 | [
"Equals(MeasureOf(Angle(Z,X,W)),x-11)",
"Equals(MeasureOf(Angle(W,Z,X)),x-9)",
"Find(MeasureOf(Angle(Z,X,Y)))"
] | [
"PointLiesOnLine(P, Line(W, Y))",
"PointLiesOnLine(P, Line(Z, X))",
"Perpendicular(Line(W, X), Line(W, Z))"
] | [
"WP",
"WX",
"WY",
"WZ",
"XP",
"YP",
"YX",
"YZ",
"ZP",
"ZX"
] | {"P": [140.0, 69.0], "W": [1.0, 137.0], "X": [276.0, 137.0], "Y": [277.0, 2.0], "Z": [2.0, 0.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, F, G)), x+20)
- Equals(MeasureOf(Angle(F, E, J)), x)
- Equals(MeasureOf(Angle(J, H, G)), x-5)
- Equals(MeasureOf(Angle(E, J, H)), x+10)
- Equals(MeasureOf(Angle(F, G, H)), x+5)
Find $m\angle F$ | 122 | [
"Find(MeasureOf(Angle(F)))"
] | [
"Equals(MeasureOf(Angle(E, F, G)), x+20)",
"Equals(MeasureOf(Angle(F, E, J)), x)",
"Equals(MeasureOf(Angle(J, H, G)), x-5)",
"Equals(MeasureOf(Angle(E, J, H)), x+10)",
"Equals(MeasureOf(Angle(F, G, H)), x+5)"
] | [
"EJ",
"FE",
"GF",
"GH",
"HJ"
] | {"E": [2.0, 54.0], "F": [31.0, 0.0], "G": [203.0, 2.0], "H": [233.0, 109.0], "J": [134.0, 166.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(L, J)), 13)
- Equals(LengthOf(Line(J, K)), 5)
- Equals(LengthOf(Line(L, K)), 12)
- Perpendicular(Line(J, K), Line(L, K))
Express the ratio of $\cos L$ as a decimal to the nearest hundredth. | 0.92 | [
"Find(RatioOf(CosOf(Angle(L))))"
] | [
"Equals(LengthOf(Line(L, J)), 13)",
"Equals(LengthOf(Line(J, K)), 5)",
"Equals(LengthOf(Line(L, K)), 12)",
"Perpendicular(Line(J, K), Line(L, K))"
] | [
"LJ",
"LK",
"JK"
] | {"L": [1.865591397849471, 123.66666666666666], "J": [222.0133808136398, 1.5486133592316804], "K": [223.9918699186992, 123.33333333333334]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(F, D, E)), 42)
- Equals(MeasureOf(Angle(D, F, E)), 4x+11)
- Equals(LengthOf(Line(F, E)), 2x-3)
- Equals(LengthOf(Line(D, E)), LengthOf(Line(D, F)))
What is the length of $\overline{EF}$? | 26 | [
"Find(LengthOf(Line(E,F)))"
] | [
"Equals(MeasureOf(Angle(F, D, E)), 42)",
"Equals(MeasureOf(Angle(D, F, E)), 4x+11)",
"Equals(LengthOf(Line(F, E)), 2x-3)",
"Equals(LengthOf(Line(D, E)), LengthOf(Line(D, F)))"
] | [
"DE",
"EF",
"DF"
] | {"D": [65.0, 1.0], "E": [0.0, 167.0], "F": [130.0, 166.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(T, B, S)), 126)
- Equals(MeasureOf(Angle(R, O, Q)), 108)
- Equals(LengthOf(Line(S, B)), 5)
- PointLiesOnLine(B, Line(Q, S))
- PointLiesOnLine(B, Line(R, T))
- PointLiesOnCircle(Q, Circle(O, radius_4_0))
- PointLiesOnCircle(R, Circle(O, radius_4_0))
- PointLiesOnCircle(T, Cir... | 144 | [
"Find(MeasureOf(Arc(T,S)))"
] | [
"Equals(MeasureOf(Angle(T, B, S)), 126)",
"Equals(MeasureOf(Angle(R, O, Q)), 108)",
"Equals(LengthOf(Line(S, B)), 5)",
"PointLiesOnLine(B, Line(Q, S))",
"PointLiesOnLine(B, Line(R, T))",
"PointLiesOnCircle(Q, Circle(O, radius_4_0))",
"PointLiesOnCircle(R, Circle(O, radius_4_0))",
"PointLiesOnCircle(T,... | [
"SB",
"BR",
"BT",
"QS",
"QB",
"RT"
] | {"S": [245.0, 238.0], "B": [143.0, 141.0], "Q": [38.0, 47.0], "R": [126.0, 280.0], "T": [157.0, 1.0], "O": [143.0, 140.0]} | [
"O"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(E, B)), 3)
- Equals(MeasureOf(Angle(E, B, C)), 32)
Find the area of the sector. Round to the nearest tenth. | 2.5 | [
"Find(AreaOf(Sector($)))"
] | [
"Equals(LengthOf(Line(E, B)), 3)",
"Equals(MeasureOf(Angle(E, B, C)), 32)"
] | [
"CB",
"CE",
"EB"
] | {"B": [101.0, 93.0], "C": [18.0, 117.0], "E": [19.0, 67.0]} | [
""
] |
Diagram Logic Form:
-
In quadrilateral $P Q R S, P Q=721, Q R=547$, $R S=593, P S=756,$ and $m \angle P=58 .$
Find $m\angle R$ | 77.8 | [
"Quadrilateral(P,Q,R,S)",
"Equals(LengthOf(Line(P,Q)),721)",
"Equals(LengthOf(Line(Q,R)),547)",
"Equals(LengthOf(Line(R,S)),593)",
"Equals(LengthOf(Line(P,S)),756)",
"Equals(MeasureOf(Angle(P)),58)",
"Find(MeasureOf(Angle(R)))"
] | [
""
] | [
"AP",
"AQ",
"QP",
"RA",
"RQ"
] | {"A": [64.0, 188.0], "P": [0.0, 0.0], "Q": [189.0, 9.0], "R": [213.0, 150.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, Q, B)), x+24)
- Equals(MeasureOf(Angle(A, C, D)), 3x)
- PointLiesOnLine(G, Line(C, A))
- PointLiesOnLine(G, Line(D, B))
- PointLiesOnCircle(D, Circle(Q, radius_16_0))
- PointLiesOnCircle(A, Circle(Q, radius_16_0))
- PointLiesOnCircle(B, Circle(Q, radius_16_0))
- PointLies... | 36 | [
"Find(MeasureOf(Angle(B)))"
] | [
"Equals(MeasureOf(Angle(A, Q, B)), x+24)",
"Equals(MeasureOf(Angle(A, C, D)), 3x)",
"PointLiesOnLine(G, Line(C, A))",
"PointLiesOnLine(G, Line(D, B))",
"PointLiesOnCircle(D, Circle(Q, radius_16_0))",
"PointLiesOnCircle(A, Circle(Q, radius_16_0))",
"PointLiesOnCircle(B, Circle(Q, radius_16_0))",
"Point... | [
"BA",
"CA",
"CD",
"CG",
"DB",
"DG",
"GA",
"GB"
] | {"A": [30.0, 250.0], "B": [135.0, 4.0], "C": [303.0, 102.0], "D": [202.0, 311.0], "G": [172.0, 173.0], "Q": [157.0, 160.0]} | [
"Q"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, A)), 7)
- Equals(LengthOf(Line(C, A)), 3)
- Equals(LengthOf(Line(B, C)), 6)
- Equals(LengthOf(Line(E, F)), 9)
Find the perimeter of $\triangle D E F$ if $\triangle D E F \sim \triangle A B C$ | 24 | [
"Similar(Triangle(D,E,F),Triangle(A,B,C))",
"Find(PerimeterOf(Triangle(D,E,F)))"
] | [
"Equals(LengthOf(Line(B, A)), 7)",
"Equals(LengthOf(Line(C, A)), 3)",
"Equals(LengthOf(Line(B, C)), 6)",
"Equals(LengthOf(Line(E, F)), 9)"
] | [
"ED",
"FD",
"FE"
] | {"D": [28.0, 1.0], "E": [223.0, 130.0], "F": [0.0, 113.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(G, D, F)), 8x+4)
- Equals(MeasureOf(Angle(I, H, E)), 9x-11)
- PointLiesOnLine(H, Line(A, E))
- PointLiesOnLine(D, Line(H, G))
- PointLiesOnLine(D, Line(B, F))
- PointLiesOnLine(H, Line(D, I))
- PointLiesOnLine(D, Line(F, J))
- PointLiesOnLine(D, Line(C, G))
- PointLiesOnLine... | 15 | [
"Parallel(Line(m),Line(n))",
"Find(x)"
] | [
"Equals(MeasureOf(Angle(G, D, F)), 8x+4)",
"Equals(MeasureOf(Angle(I, H, E)), 9x-11)",
"PointLiesOnLine(H, Line(A, E))",
"PointLiesOnLine(D, Line(H, G))",
"PointLiesOnLine(D, Line(B, F))",
"PointLiesOnLine(H, Line(D, I))",
"PointLiesOnLine(D, Line(F, J))",
"PointLiesOnLine(D, Line(C, G))",
"PointLie... | [
"AE",
"AH",
"BD",
"BF",
"BJ",
"CG",
"CI",
"DC",
"DF",
"DG",
"DI",
"DJ",
"EH",
"FJ",
"GI",
"HC",
"HD",
"HG",
"HI"
] | {"A": [253.0, 1.0], "B": [20.0, 201.0], "C": [273.0, 107.0], "D": [88.0, 100.0], "E": [118.0, 201.0], "F": [155.0, 1.0], "G": [0.0, 100.0], "H": [186.0, 100.0], "I": [293.0, 100.0], "J": [36.0, 187.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, D)), 7)
- Equals(LengthOf(Line(A, B)), 16)
- Equals(LengthOf(Line(A, E)), 6)
- PointLiesOnLine(B, Line(A, F))
- PointLiesOnLine(A, Line(B, C))
- PointLiesOnLine(A, Line(C, F))
- PointLiesOnLine(B, Line(C, F))
- Perpendicular(Line(B, D), Line(B, F))
Find the area of the qua... | 104 | [
"Find(AreaOf(Quadrilateral($)))"
] | [
"Equals(LengthOf(Line(B, D)), 7)",
"Equals(LengthOf(Line(A, B)), 16)",
"Equals(LengthOf(Line(A, E)), 6)",
"PointLiesOnLine(B, Line(A, F))",
"PointLiesOnLine(A, Line(B, C))",
"PointLiesOnLine(A, Line(C, F))",
"PointLiesOnLine(B, Line(C, F))",
"Perpendicular(Line(B, D), Line(B, F))"
] | [
"AB",
"AC",
"AE",
"AF",
"BC",
"BD",
"BF",
"CD",
"CE",
"CF",
"EF",
"FD"
] | {"A": [177.0, 121.0], "B": [41.0, 132.0], "C": [309.0, 110.0], "D": [31.0, 0.0], "E": [186.0, 237.0], "F": [1.0, 135.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(F, T)), 12)
- PointLiesOnLine(T, Line(D, A))
- PointLiesOnLine(C, Line(D, F))
- PointLiesOnLine(Q, Line(D, E))
- PointLiesOnLine(T, Line(F, Q))
- PointLiesOnLine(A, Line(F, E))
- PointLiesOnLine(T, Line(C, E))
- Equals(LengthOf(Line(A, F)), LengthOf(Line(A, E)))
- Equals(Lengt... | 6 | [
"Triangle(E,D,F)",
"IsCentroidOf(Point(T),Triangle(E,D,F))",
"Equals(LengthOf(Line(F,T)),12)",
"Find(LengthOf(Line(T,Q)))"
] | [
"Equals(LengthOf(Line(F, T)), 12)",
"PointLiesOnLine(T, Line(D, A))",
"PointLiesOnLine(C, Line(D, F))",
"PointLiesOnLine(Q, Line(D, E))",
"PointLiesOnLine(T, Line(F, Q))",
"PointLiesOnLine(A, Line(F, E))",
"PointLiesOnLine(T, Line(C, E))",
"Equals(LengthOf(Line(A, F)), LengthOf(Line(A, E)))",
"Equal... | [
"AE",
"AF",
"AT",
"CE",
"DA",
"DC",
"DE",
"DF",
"DQ",
"DT",
"FC",
"FE",
"FQ",
"FT",
"QE",
"TC",
"TE",
"TQ"
] | {"A": [170.0, 155.0], "C": [414.0, 165.0], "D": [489.0, 322.0], "E": [0.0, 313.0], "F": [336.0, 1.0], "Q": [254.0, 318.0], "T": [281.0, 213.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(O, N)), 6)
- Equals(LengthOf(Line(P, N)), x)
- Equals(LengthOf(Line(P, O)), 10)
- PointLiesOnLine(A, Line(P, O))
- PointLiesOnCircle(N, Circle(O, radius_1_0))
- PointLiesOnCircle(A, Circle(O, radius_1_0))
Find x. Assume that segments that appear to be tangent are tangent. | 8 | [
"Tangent(Line($),Circle($))",
"Find(x)"
] | [
"Equals(LengthOf(Line(O, N)), 6)",
"Equals(LengthOf(Line(P, N)), x)",
"Equals(LengthOf(Line(P, O)), 10)",
"PointLiesOnLine(A, Line(P, O))",
"PointLiesOnCircle(N, Circle(O, radius_1_0))",
"PointLiesOnCircle(A, Circle(O, radius_1_0))"
] | [
"OA",
"ON",
"PA",
"PN",
"PO"
] | {"A": [179.0, 84.0], "N": [139.0, 15.0], "O": [86.0, 90.0], "P": [235.0, 82.0]} | [
"O"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(J, K)), 12)
- Equals(LengthOf(Line(P, Q)), 15)
If $\triangle J K L \sim \triangle P Q R$ and the area of $\triangle J K L$ is
30 square inches, find the area of $\triangle P Q R$。 | 46.9 | [
"Similar(Triangle(J,K,L),Triangle(P,Q,R))",
"Equals(AreaOf(Triangle(J,K,L)),30)",
"Find(AreaOf(Triangle(P,Q,R)))"
] | [
"Equals(LengthOf(Line(J, K)), 12)",
"Equals(LengthOf(Line(P, Q)), 15)"
] | [
"PQ",
"PR",
"RQ",
"JK",
"KL",
"JL"
] | {"P": [1.0, 128.0], "Q": [235.0, 129.0], "R": [234.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(R, S)), 6x+2)
- Equals(LengthOf(Line(R, T)), 4x+3)
- Equals(LengthOf(Line(R, W)), 12)
- Equals(LengthOf(Line(W, S)), 16)
- Equals(LengthOf(Line(W, T)), 9)
- PointLiesOnLine(W, Line(S, T))
- Perpendicular(Line(R, W), Line(W, T))
Find $RT$. | 15 | [
"Find(LengthOf(Line(R,T)))"
] | [
"Equals(LengthOf(Line(R, S)), 6x+2)",
"Equals(LengthOf(Line(R, T)), 4x+3)",
"Equals(LengthOf(Line(R, W)), 12)",
"Equals(LengthOf(Line(W, S)), 16)",
"Equals(LengthOf(Line(W, T)), 9)",
"PointLiesOnLine(W, Line(S, T))",
"Perpendicular(Line(R, W), Line(W, T))"
] | [
"RW",
"RS",
"RT",
"WS",
"WT",
"ST"
] | {"R": [256.19770407104005, 1.7512475828501408], "W": [255.00840336134453, 237.0], "S": [0.3629943502824631, 236.33333333333331], "T": [434.07909604519773, 236.33333333333331]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, C, B)), 82)
- Equals(MeasureOf(Angle(C, B, D)), 28)
- Equals(MeasureOf(Angle(B, E, C)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(D, E, A)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(A, D, E)), 68)
- Equals(MeasureOf(Angle(C, A, D)), MeasureOf(angle 3))
- PointLiesO... | 42 | [
"Find(MeasureOf(Angle(3)))"
] | [
"Equals(MeasureOf(Angle(E, C, B)), 82)",
"Equals(MeasureOf(Angle(C, B, D)), 28)",
"Equals(MeasureOf(Angle(B, E, C)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(D, E, A)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(A, D, E)), 68)",
"Equals(MeasureOf(Angle(C, A, D)), MeasureOf(angle 3))",
"PointLies... | [
"AC",
"AD",
"AE",
"CB",
"CE",
"DB",
"DE",
"EB"
] | {"A": [334.0, 288.0], "B": [1.0, 98.0], "C": [276.0, 0.0], "D": [409.0, 162.0], "E": [305.0, 146.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(K, G)), x)
- Equals(LengthOf(Line(J, G)), x)
- Equals(LengthOf(Line(H, K)), 8)
- Equals(LengthOf(Line(H, J)), 12)
- PointLiesOnLine(K, Line(H, G))
- PointLiesOnCircle(K, Circle(G, radius_2_0))
- PointLiesOnCircle(J, Circle(G, radius_2_0))
$\overline{JH}$ is tangent to $\odot ... | 5 | [
"Tangent(Line(J,H),Circle(G)) at J. Find(x)"
] | [
"Equals(LengthOf(Line(K, G)), x)",
"Equals(LengthOf(Line(J, G)), x)",
"Equals(LengthOf(Line(H, K)), 8)",
"Equals(LengthOf(Line(H, J)), 12)",
"PointLiesOnLine(K, Line(H, G))",
"PointLiesOnCircle(K, Circle(G, radius_2_0))",
"PointLiesOnCircle(J, Circle(G, radius_2_0))"
] | [
"",
"HG",
"HJ",
"HK",
"JG",
"KG"
] | {"G": [159.0, 160.0], "H": [485.0, 311.0], "J": [155.0, 311.0], "K": [298.0, 224.0]} | [
"G"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, E)), 13)
- Equals(LengthOf(Line(A, D)), 11)
- Equals(LengthOf(Line(B, E)), x)
- PointLiesOnLine(E, Line(C, D))
- Perpendicular(Line(A, E), Line(B, C))
Find $x$. $A = 177$ cm$^2$. | 16.2 | [
"Equals(AreaOf(Shape(A)),177)",
"Find(x)"
] | [
"Equals(LengthOf(Line(A, E)), 13)",
"Equals(LengthOf(Line(A, D)), 11)",
"Equals(LengthOf(Line(B, E)), x)",
"PointLiesOnLine(E, Line(C, D))",
"Perpendicular(Line(A, E), Line(B, C))"
] | [
"AC",
"AD",
"CB",
"DB",
"BE",
"CE",
"AE"
] | {"A": [157.0, 126.0], "B": [0.0, 0.0], "C": [199.0, 2.0], "D": [42.0, 127.0], "E": [157.0, 1.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(J, Q, R)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(R, Q, C)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(H, R, Q)), MeasureOf(angle 5))
- Equals(MeasureOf(Angle(Q, T, S)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(Q, R, S)), MeasureOf(angle 6))
- Equals(MeasureOf(A... | 49 | [
"Parallel(Line(Q,R),Line(T,S))",
"Parallel(Line(Q,T),Line(R,S))",
"Equals(MeasureOf(Angle(1)),131)",
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(J, Q, R)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(R, Q, C)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(H, R, Q)), MeasureOf(angle 5))",
"Equals(MeasureOf(Angle(Q, T, S)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(Q, R, S)), MeasureOf(angle 6))",
"Equals(MeasureOf(Ang... | [
"AB",
"AH",
"AL",
"AM",
"AO",
"AR",
"BH",
"BL",
"BM",
"BO",
"BR",
"CF",
"CJ",
"CK",
"CN",
"CP",
"CQ",
"EG",
"EP",
"FJ",
"FK",
"FN",
"FP",
"FQ",
"GA",
"GB",
"GH",
"GL",
"GM",
"GO",
"GP",
"GR",
"HL",
"HM",
"HO",
"IS",
"JK",
"JN",
"JP",
"JQ"... | {"A": [147.0, 69.0], "B": [148.0, 263.0], "C": [8.0, 266.0], "E": [76.0, 173.0], "F": [13.0, 208.0], "G": [146.0, 215.0], "H": [147.0, 1.0], "I": [78.0, 97.0], "J": [9.0, 1.0], "K": [10.0, 186.0], "L": [148.0, 44.0], "M": [146.0, 114.0], "N": [8.0, 224.0], "O": [145.0, 88.0], "P": [22.0, 143.0], "Q": [6.0, 55.0], "R": ... | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(E, F)), x)
- Equals(LengthOf(Line(B, E)), 3)
- Equals(LengthOf(Line(F, C)), 5)
- Equals(LengthOf(Line(B, D)), 9)
- PointLiesOnLine(F, Line(E, C))
- PointLiesOnLine(B, Line(E, D))
- PointLiesOnCircle(B, Circle(A, radius_0_0))
- PointLiesOnCircle(C, Circle(A, radius_0_0))
- Poin... | 4 | [
"Tangent(Line($),Circle($))",
"Find(x)"
] | [
"Equals(LengthOf(Line(E, F)), x)",
"Equals(LengthOf(Line(B, E)), 3)",
"Equals(LengthOf(Line(F, C)), 5)",
"Equals(LengthOf(Line(B, D)), 9)",
"PointLiesOnLine(F, Line(E, C))",
"PointLiesOnLine(B, Line(E, D))",
"PointLiesOnCircle(B, Circle(A, radius_0_0))",
"PointLiesOnCircle(C, Circle(A, radius_0_0))",
... | [
"BD",
"BE",
"EC",
"ED",
"EF",
"FC"
] | {"A": [80.0, 99.0], "B": [120.0, 35.0], "C": [16.0, 55.0], "D": [23.0, 150.0], "E": [150.0, 1.0], "F": [92.0, 24.0]} | [
"A"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, A)), 3x+4)
- Equals(LengthOf(Line(A, B)), 5x)
- PointLiesOnLine(C, Line(X, Y))
- PointLiesOnCircle(X, Circle(A, radius_3_0))
- PointLiesOnCircle(W, Circle(A, radius_3_0))
- PointLiesOnCircle(Y, Circle(A, radius_3_0))
- Perpendicular(Line(A, B), Line(X, B))
- Perpendicular(L... | 10 | [
"Circle(A)",
"Equals(LengthOf(Line(W,X)),22)",
"Equals(LengthOf(Line(X,Y)),22)",
"Find(LengthOf(Line(A,B)))"
] | [
"Equals(LengthOf(Line(C, A)), 3x+4)",
"Equals(LengthOf(Line(A, B)), 5x)",
"PointLiesOnLine(C, Line(X, Y))",
"PointLiesOnCircle(X, Circle(A, radius_3_0))",
"PointLiesOnCircle(W, Circle(A, radius_3_0))",
"PointLiesOnCircle(Y, Circle(A, radius_3_0))",
"Perpendicular(Line(A, B), Line(X, B))",
"Perpendicul... | [
"AB",
"CA",
"CX",
"CY",
"WB",
"XA",
"XB",
"XW",
"XY"
] | {"A": [179.0, 184.0], "B": [92.0, 290.0], "C": [269.0, 289.0], "W": [3.0, 211.0], "X": [183.0, 358.0], "Y": [356.0, 213.0]} | [
"A"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 10)
- Equals(LengthOf(Line(B, C)), x)
- Equals(MeasureOf(Angle(B, A, C)), 45)
- Equals(LengthOf(Line(A, B)), y)
- Perpendicular(Line(B, C), Line(A, B))
Find y | 5 \sqrt { 2 } | [
"Find(y)"
] | [
"Equals(LengthOf(Line(A, C)), 10)",
"Equals(LengthOf(Line(B, C)), x)",
"Equals(MeasureOf(Angle(B, A, C)), 45)",
"Equals(LengthOf(Line(A, B)), y)",
"Perpendicular(Line(B, C), Line(A, B))"
] | [
"AB",
"AC",
"BC"
] | {"A": [159.67078189300412, 160.33539094650206], "B": [1.3332815775172762, 160.99583365680718], "C": [0.0, 0.0]} | [] |
Diagram Logic Form:
- Equals(LengthOf(PerimeterOf(Cirle(G))), 20)
- Equals(LengthOf(Line(I, N)), 1)
- PointLiesOnLine(G, Line(D, B))
- PointLiesOnLine(G, Line(E, C))
- PointLiesOnLine(G, Line(C, J))
- PointLiesOnCircle(B, Circle(G, radius_6_0))
- PointLiesOnCircle(C, Circle(G, radius_6_0))
- PointLiesOnCircle(D, Circle... | 114.2 | [
"Find(AreaOf(Blue(Shape($))))"
] | [
"Equals(LengthOf(PerimeterOf(Cirle(G))), 20)",
"Equals(LengthOf(Line(I, N)), 1)",
"PointLiesOnLine(G, Line(D, B))",
"PointLiesOnLine(G, Line(E, C))",
"PointLiesOnLine(G, Line(C, J))",
"PointLiesOnCircle(B, Circle(G, radius_6_0))",
"PointLiesOnCircle(C, Circle(G, radius_6_0))",
"PointLiesOnCircle(D, Ci... | [
"EB",
"BC",
"CD",
"ED",
"EC",
"BD",
"GE",
"GB",
"GC",
"GD"
] | {"B": [218.0, 78.0], "C": [146.0, 217.0], "D": [7.0, 148.0], "E": [76.0, 7.0], "G": [112.0, 111.0], "J": [103.0, 88.0]} | [
"G"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), x)
- Equals(LengthOf(Line(A, C)), 23)
- Equals(MeasureOf(Angle(A, B, C)), 21)
- Equals(MeasureOf(Angle(C, A, B)), 128)
Find x. Round the side measure to the nearest tenth. | 50.6 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(B, C)), x)",
"Equals(LengthOf(Line(A, C)), 23)",
"Equals(MeasureOf(Angle(A, B, C)), 21)",
"Equals(MeasureOf(Angle(C, A, B)), 128)"
] | [
"AB",
"AC",
"BC"
] | {"A": [173.0, 206.0], "B": [555.0, 195.0], "C": [1.0, 1.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(R, S)), 8)
- Equals(LengthOf(Line(T, S)), 12)
- Perpendicular(Line(R, S), Line(T, S))
Find the measure of $∠T$ to the nearest tenth. | 33.7 | [
"Find(MeasureOf(Angle(T)))"
] | [
"Equals(LengthOf(Line(R, S)), 8)",
"Equals(LengthOf(Line(T, S)), 12)",
"Perpendicular(Line(R, S), Line(T, S))"
] | [
"RT",
"RS",
"TS"
] | {"R": [156.76637573329518, 0.6651690752134272], "T": [0.0, 223.0], "S": [2.9998850310416145, 0.0064095194297522085]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(J, R)), 5)
- Equals(LengthOf(Line(S, J)), 5)
- PointLiesOnLine(R, Line(H, G))
- PointLiesOnLine(S, Line(L, K))
-
- PointLiesOnCircle(G, Circle(J, radius_9_0))
- PointLiesOnCircle(H, Circle(J, radius_9_0))
- PointLiesOnCircle(L, Circle(J, radius_9_0))
- PointLiesOnCircle(K, Ci... | 2 | [
"Circle(J)",
"Equals(LengthOf(Line(G,H)),9)",
"Equals(LengthOf(Line(K,L)),4x+1)",
"Find(x)"
] | [
"Equals(LengthOf(Line(J, R)), 5)",
"Equals(LengthOf(Line(S, J)), 5)",
"PointLiesOnLine(R, Line(H, G))",
"PointLiesOnLine(S, Line(L, K))",
"",
"PointLiesOnCircle(G, Circle(J, radius_9_0))",
"PointLiesOnCircle(H, Circle(J, radius_9_0))",
"PointLiesOnCircle(L, Circle(J, radius_9_0))",
"PointLiesOnCircl... | [
"HG",
"HR",
"JR",
"LK",
"RG",
"SH",
"SJ",
"SK",
"SL"
] | {"G": [49.0, 244.0], "H": [49.0, 37.0], "J": [144.0, 142.0], "K": [105.0, 283.0], "L": [289.0, 164.0], "R": [51.0, 147.0], "S": [197.0, 222.0]} | [
"J"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(N, E, B)), 2x)
- Equals(MeasureOf(Angle(F, G, C)), 6x-144)
- PointLiesOnLine(I, Line(A, E))
- PointLiesOnLine(E, Line(A, N))
- PointLiesOnLine(I, Line(A, N))
- PointLiesOnLine(H, Line(E, B))
- PointLiesOnLine(G, Line(E, C))
- PointLiesOnLine(E, Line(N, I))
- PointLiesOnLine(... | 36 | [
"Parallel(Line(m),Line(n))",
"Find(x)"
] | [
"Equals(MeasureOf(Angle(N, E, B)), 2x)",
"Equals(MeasureOf(Angle(F, G, C)), 6x-144)",
"PointLiesOnLine(I, Line(A, E))",
"PointLiesOnLine(E, Line(A, N))",
"PointLiesOnLine(I, Line(A, N))",
"PointLiesOnLine(H, Line(E, B))",
"PointLiesOnLine(G, Line(E, C))",
"PointLiesOnLine(E, Line(N, I))",
"PointLies... | [
"AE",
"AI",
"AN",
"BC",
"BH",
"CH",
"DJ",
"EB",
"EC",
"EG",
"EH",
"EI",
"EN",
"FD",
"FG",
"FH",
"FJ",
"FK",
"GB",
"GC",
"GH",
"GK",
"HD",
"HJ",
"ID",
"IF",
"IH",
"IJ",
"NI",
"TF",
"TG",
"TK"
] | {"A": [183.0, 242.0], "B": [314.0, 203.0], "C": [0.0, 76.0], "D": [31.0, 235.0], "E": [192.0, 154.0], "F": [125.0, 213.0], "G": [133.0, 130.0], "H": [261.0, 181.0], "I": [187.0, 199.0], "J": [314.0, 169.0], "K": [122.0, 242.0], "N": [207.0, 1.0], "T": [144.0, 14.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(C, Line(N, E))
- PointLiesOnLine(I, Line(N, E))
- PointLiesOnLine(C, Line(N, I))
- PointLiesOnLine(C, Line(N, J))
- PointLiesOnLine(D, Line(B, P))
- PointLiesOnLine(B, Line(D, O))
- PointLiesOnLine(B, Line(O, L))
- PointLiesOnLine(B, Line(O, P))
- PointLiesOnLine(D, Line(O, P))
- P... | 55.6 | [
"Find(AreaOf(Shape($)))"
] | [
"PointLiesOnLine(C, Line(N, E))",
"PointLiesOnLine(I, Line(N, E))",
"PointLiesOnLine(C, Line(N, I))",
"PointLiesOnLine(C, Line(N, J))",
"PointLiesOnLine(D, Line(B, P))",
"PointLiesOnLine(B, Line(D, O))",
"PointLiesOnLine(B, Line(O, L))",
"PointLiesOnLine(B, Line(O, P))",
"PointLiesOnLine(D, Line(O, ... | [
"AK",
"AN",
"BD",
"BG",
"BO",
"BP",
"DL",
"DO",
"DP",
"EI",
"EJ",
"EM",
"GF",
"IJ",
"JM",
"KP",
"NC",
"NE",
"NI",
"NJ",
"OJ",
"OL",
"OP",
"PL"
] | {"A": [178.0, 177.0], "B": [51.0, 4.0], "C": [32.0, 162.0], "D": [174.0, 3.0], "E": [1.0, 41.0], "F": [72.0, 64.0], "G": [74.0, 23.0], "H": [108.0, 41.0], "I": [19.0, 115.0], "J": [4.0, 21.0], "K": [213.0, 32.0], "L": [157.0, 8.0], "M": [0.0, 70.0], "N": [36.0, 179.0], "O": [20.0, 4.0], "P": [193.0, 4.0]} | [
"H"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), 6)
- Equals(LengthOf(Line(A, B)), x)
- Equals(LengthOf(Line(A, C)), 4)
- Perpendicular(Line(B, C), Line(A, C))
Find x. Round to the nearest hundredth. | 7.21 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(B, C)), 6)",
"Equals(LengthOf(Line(A, B)), x)",
"Equals(LengthOf(Line(A, C)), 4)",
"Perpendicular(Line(B, C), Line(A, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [0.0, 198.0], "B": [115.02361881289792, 0.6262066132676125], "C": [130.61901300379614, 184.7424279137388]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(F, E)), 4y)
- Equals(LengthOf(Line(D, E)), 6x-12)
- Equals(LengthOf(Line(G, F)), 2x+36)
- Equals(LengthOf(Line(G, D)), 6y-42)
Find $x$ so that each quadrilateral is a parallelogram. | 12 | [
"Parallelogram($)",
"Find(x)"
] | [
"Equals(LengthOf(Line(F, E)), 4y)",
"Equals(LengthOf(Line(D, E)), 6x-12)",
"Equals(LengthOf(Line(G, F)), 2x+36)",
"Equals(LengthOf(Line(G, D)), 6y-42)"
] | [
"DE",
"FE",
"GD",
"GF"
] | {"D": [0.0, 119.0], "E": [53.0, 1.0], "F": [233.0, 1.0], "G": [179.0, 119.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), 6)
- Equals(LengthOf(Line(A, C)), 8)
- Equals(LengthOf(Line(S, A)), z)
- Equals(LengthOf(Line(S, B)), x)
- PointLiesOnLine(C, Line(S, B))
- Perpendicular(Line(S, C), Line(A, C))
- Perpendicular(Line(A, B), Line(S, A))
Find x | \frac { 50 } { 3 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(B, C)), 6)",
"Equals(LengthOf(Line(A, C)), 8)",
"Equals(LengthOf(Line(S, A)), z)",
"Equals(LengthOf(Line(S, B)), x)",
"PointLiesOnLine(C, Line(S, B))",
"Perpendicular(Line(S, C), Line(A, C))",
"Perpendicular(Line(A, B), Line(S, A))"
] | [
"AB",
"AC",
"BC",
"SA",
"SB",
"SC"
] | {"A": [0.0, 125.0], "B": [1.0, 1.0], "C": [46.0, 21.0], "S": [284.0, 127.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(B, Line(D, E))
- PointLiesOnLine(X, Line(D, E))
- PointLiesOnLine(Y, Line(D, E))
- PointLiesOnLine(Y, Line(D, B))
- PointLiesOnLine(B, Line(D, F))
- PointLiesOnLine(X, Line(D, F))
- PointLiesOnLine(Y, Line(D, F))
- PointLiesOnLine(Z, Line(D, F))
- PointLiesOnLine(B, Line(D, X))
- P... | 12 | [
"Equals(DiameterOf(Circle(A)),10)",
"Equals(DiameterOf(Circle(B)),30)",
"Equals(DiameterOf(Circle(C)),10)",
"Equals(LengthOf(Line(A,Z)),Line(C,W))",
"Equals(LengthOf(Line(C,W)),2)",
"Find(LengthOf(Line(B,Y)))"
] | [
"PointLiesOnLine(B, Line(D, E))",
"PointLiesOnLine(X, Line(D, E))",
"PointLiesOnLine(Y, Line(D, E))",
"PointLiesOnLine(Y, Line(D, B))",
"PointLiesOnLine(B, Line(D, F))",
"PointLiesOnLine(X, Line(D, F))",
"PointLiesOnLine(Y, Line(D, F))",
"PointLiesOnLine(Z, Line(D, F))",
"PointLiesOnLine(B, Line(D, ... | [
"BA",
"BC",
"BF",
"BG",
"BX",
"BY",
"BZ",
"CA",
"CW",
"CZ",
"DA",
"DB",
"DC",
"DE",
"DF",
"DG",
"DH",
"DX",
"DY",
"DZ",
"EA",
"EB",
"EC",
"EF",
"EG",
"EX",
"EY",
"EZ",
"FA",
"FC",
"FG",
"FX",
"FY",
"FZ",
"GA",
"GC",
"GX",
"GY",
"GZ",
"HC"... | {"A": [54.0, 113.0], "B": [176.0, 112.0], "C": [316.0, 109.0], "D": [284.0, 111.0], "E": [68.0, 113.0], "F": [1.0, 108.0], "G": [366.0, 112.0], "H": [311.0, 126.0], "W": [325.0, 151.0], "X": [104.0, 110.0], "Y": [265.0, 111.0], "Z": [19.0, 109.0]} | [
"B",
"C",
"A"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, F, I)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(A, L, C)), 35)
- Equals(MeasureOf(Angle(C, B, G)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(G, B, E)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(E, K, I)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(H, C, F)), ... | 55 | [
"Find(MeasureOf(Angle(5)))"
] | [
"Equals(MeasureOf(Angle(C, F, I)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(A, L, C)), 35)",
"Equals(MeasureOf(Angle(C, B, G)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(G, B, E)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(E, K, I)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(H, C, F)), Me... | [
"AB",
"AC",
"AF",
"AH",
"AI",
"AJ",
"AK",
"AL",
"BC",
"BD",
"BE",
"BF",
"BG",
"BI",
"BJ",
"BK",
"BL",
"CD",
"CE",
"CF",
"CG",
"CH",
"CK",
"CL",
"DE",
"DG",
"EG",
"FI",
"FK",
"FL",
"ID",
"IJ",
"IK",
"IL",
"JD",
"JK",
"JL",
"KD",
"KE",
"KL"... | {"A": [744.0, 22.0], "B": [413.0, 65.0], "C": [773.0, 255.0], "D": [1.0, 254.0], "E": [255.0, 255.0], "F": [906.0, 2.0], "G": [410.0, 247.0], "H": [761.0, 161.0], "I": [377.0, 80.0], "J": [357.0, 87.0], "K": [399.0, 69.0], "L": [424.0, 60.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Arc(S, T)), 2x)
- Equals(LengthOf(Arc(V, U)), 5x-27)
- Equals(LengthOf(Line(S, T)), LengthOf(Line(U, V)))
- PointLiesOnCircle(V, Circle(N, radius_0_0))
- PointLiesOnCircle(U, Circle(N, radius_0_0))
- PointLiesOnCircle(S, Circle(M, radius_0_0))
- PointLiesOnCircle(T, Circle(M, radiu... | 9 | [
"Congruent(Circle(M),Circle(N))",
"Find(x)"
] | [
"Equals(LengthOf(Arc(S, T)), 2x)",
"Equals(LengthOf(Arc(V, U)), 5x-27)",
"Equals(LengthOf(Line(S, T)), LengthOf(Line(U, V)))",
"PointLiesOnCircle(V, Circle(N, radius_0_0))",
"PointLiesOnCircle(U, Circle(N, radius_0_0))",
"PointLiesOnCircle(S, Circle(M, radius_0_0))",
"PointLiesOnCircle(T, Circle(M, radi... | [
"ST",
"UV"
] | {"N": [109.0, 111.0], "U": [11.0, 87.0], "V": [198.0, 50.0]} | [
"N"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(S, C, R)), 5z+2)
- Equals(MeasureOf(Angle(N, R, P)), x)
- Equals(MeasureOf(Angle(R, P, M)), 68)
- Equals(MeasureOf(Angle(M, P, H)), 4*y)
- PointLiesOnLine(R, Line(A, I))
- PointLiesOnLine(V, Line(A, I))
- PointLiesOnLine(C, Line(A, N))
- PointLiesOnLine(V, Line(A, Q))
- Poin... | 112 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(S, C, R)), 5z+2)",
"Equals(MeasureOf(Angle(N, R, P)), x)",
"Equals(MeasureOf(Angle(R, P, M)), 68)",
"Equals(MeasureOf(Angle(M, P, H)), 4*y)",
"PointLiesOnLine(R, Line(A, I))",
"PointLiesOnLine(V, Line(A, I))",
"PointLiesOnLine(C, Line(A, N))",
"PointLiesOnLine(V, Line(A, Q))",
... | [
"NC",
"NR",
"NI",
"CR",
"CI",
"RI",
"DM",
"DP",
"DL",
"MP",
"ML",
"PL",
"SC",
"SM",
"SE",
"CM",
"CE",
"ME",
"GR",
"GP",
"GH",
"RP",
"RH",
"PH"
] | {"A": [180.0, 48.0], "B": [273.0, 175.0], "C": [147.0, 30.0], "D": [0.0, 50.0], "E": [114.0, 242.0], "F": [179.0, 159.0], "G": [299.0, 3.0], "H": [262.0, 242.0], "I": [324.0, 136.0], "J": [279.0, 141.0], "K": [209.0, 178.0], "L": [322.0, 243.0], "M": [132.0, 129.0], "N": [99.0, 0.0], "O": [142.0, 68.0], "P": [267.0, 21... | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 9)
- Equals(MeasureOf(Angle(D, A, C)), 60)
- Equals(LengthOf(Line(A, C)), 5)
Find the area of the parallelogram. Round to the nearest tenth if necessary. | 39.0 | [
"Find(AreaOf(Parallelogram($)))"
] | [
"Equals(LengthOf(Line(A, D)), 9)",
"Equals(MeasureOf(Angle(D, A, C)), 60)",
"Equals(LengthOf(Line(A, C)), 5)"
] | [
"AC",
"AD",
"CB",
"DB"
] | {"A": [1.0, 154.0], "B": [190.0, 0.0], "C": [100.0, 154.0], "D": [95.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, A)), x+2)
- Equals(LengthOf(Line(D, A)), 8)
- Equals(LengthOf(Line(D, E)), 5)
- Equals(LengthOf(Line(C, B)), 6)
- PointLiesOnLine(E, Line(D, A))
- PointLiesOnLine(B, Line(C, A))
- Parallel(Line(E, B), Line(D, C))
Find AC | 9.6 | [
"Find(LengthOf(Line(A,C)))"
] | [
"Equals(LengthOf(Line(B, A)), x+2)",
"Equals(LengthOf(Line(D, A)), 8)",
"Equals(LengthOf(Line(D, E)), 5)",
"Equals(LengthOf(Line(C, B)), 6)",
"PointLiesOnLine(E, Line(D, A))",
"PointLiesOnLine(B, Line(C, A))",
"Parallel(Line(E, B), Line(D, C))"
] | [
"BA",
"CA",
"CB",
"DA",
"DC",
"DE",
"EA",
"EB"
] | {"A": [79.0, 1.0], "B": [133.0, 75.0], "C": [198.0, 164.0], "D": [0.0, 163.0], "E": [43.0, 74.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, I)), 12)
- Equals(LengthOf(Line(B, D)), 13)
- Equals(LengthOf(Line(I, D)), 5)
- PointLiesOnLine(I, Line(A, B))
- PointLiesOnLine(J, Line(I, F))
- PointLiesOnLine(I, Line(D, F))
- PointLiesOnLine(J, Line(D, F))
- PointLiesOnLine(I, Line(D, J))
- Perpendicular(Line(B, I), Lin... | 368 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(B, I)), 12)",
"Equals(LengthOf(Line(B, D)), 13)",
"Equals(LengthOf(Line(I, D)), 5)",
"PointLiesOnLine(I, Line(A, B))",
"PointLiesOnLine(J, Line(I, F))",
"PointLiesOnLine(I, Line(D, F))",
"PointLiesOnLine(J, Line(D, F))",
"PointLiesOnLine(I, Line(D, J))",
"Perpendicular(Line(B, ... | [
"AB",
"AH",
"AI",
"BD",
"BE",
"BG",
"BI",
"DC",
"DF",
"DJ",
"EF",
"FJ",
"GC",
"HD",
"ID",
"IF",
"IJ"
] | {"A": [157.0, 338.0], "B": [155.0, 88.0], "C": [400.0, 156.0], "D": [244.0, 246.0], "E": [1.0, 88.0], "F": [1.0, 246.0], "G": [312.0, 1.0], "H": [243.0, 337.0], "I": [157.0, 246.0], "J": [90.0, 246.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, B)), 9)
- PointLiesOnLine(H, Line(A, C))
- PointLiesOnLine(G, Line(A, D))
- PointLiesOnLine(F, Line(C, B))
- PointLiesOnLine(E, Line(D, B))
- PointLiesOnCircle(E, Circle(P, radius_2_0))
- PointLiesOnCircle(F, Circle(P, radius_2_0))
- PointLiesOnCircle(G, Circle(P, radius_2_... | 9 \pi | [
"Find(CircumferenceOf(Circle($)))"
] | [
"Equals(LengthOf(Line(C, B)), 9)",
"PointLiesOnLine(H, Line(A, C))",
"PointLiesOnLine(G, Line(A, D))",
"PointLiesOnLine(F, Line(C, B))",
"PointLiesOnLine(E, Line(D, B))",
"PointLiesOnCircle(E, Circle(P, radius_2_0))",
"PointLiesOnCircle(F, Circle(P, radius_2_0))",
"PointLiesOnCircle(G, Circle(P, radiu... | [
"AC",
"AD",
"AG",
"AH",
"BE",
"BF",
"CB",
"CF",
"CH",
"DB",
"DE",
"DG"
] | {"A": [1.0, 178.0], "B": [178.0, 2.0], "C": [1.0, 0.0], "D": [180.0, 180.0], "E": [179.0, 90.0], "F": [90.0, 2.0], "G": [87.0, 178.0], "H": [1.0, 92.0], "P": [89.0, 92.0]} | [
"P"
] |
Diagram Logic Form:
- PointLiesOnLine(Y, Line(X, Z))
- PointLiesOnLine(W, Line(D, Y))
- PointLiesOnLine(W, Line(D, T))
- PointLiesOnLine(Y, Line(D, T))
- PointLiesOnLine(Y, Line(W, T))
- Perpendicular(Line(X, Y), Line(Y, W))
- Equals(LengthOf(Line(X, Y)), LengthOf(Line(Y, Z)))
$m$ is the perpendicular bisector of $XZ$... | 21 | [
"IsPerpendicularBisectorOf(Line(m),Line(X,Z))",
"Equals(LengthOf(Line(W,Z)),4a-15)",
"Equals(LengthOf(Line(W,Z)),a+12)",
"Find(LengthOf(Line(W,X)))"
] | [
"PointLiesOnLine(Y, Line(X, Z))",
"PointLiesOnLine(W, Line(D, Y))",
"PointLiesOnLine(W, Line(D, T))",
"PointLiesOnLine(Y, Line(D, T))",
"PointLiesOnLine(Y, Line(W, T))",
"Perpendicular(Line(X, Y), Line(Y, W))",
"Equals(LengthOf(Line(X, Y)), LengthOf(Line(Y, Z)))"
] | [
"DT",
"DW",
"DY",
"WT",
"WX",
"WY",
"WZ",
"XY",
"XZ",
"YT",
"YZ"
] | {"D": [0.0, 182.0], "T": [291.0, 182.0], "W": [100.0, 171.0], "X": [226.0, 0.0], "Y": [226.0, 182.0], "Z": [226.0, 361.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, C)), 15)
- Equals(LengthOf(Line(B, A)), 16)
- Equals(LengthOf(Line(D, A)), 9)
- PointLiesOnLine(A, Line(B, D))
- Perpendicular(Line(C, A), Line(A, D))
Find the area of the triangle. Round to the nearest tenth if necessary. | 96 | [
"Find(AreaOf(Triangle($)))"
] | [
"Equals(LengthOf(Line(D, C)), 15)",
"Equals(LengthOf(Line(B, A)), 16)",
"Equals(LengthOf(Line(D, A)), 9)",
"PointLiesOnLine(A, Line(B, D))",
"Perpendicular(Line(C, A), Line(A, D))"
] | [
"",
"AB",
"AC",
"AD",
"BC",
"BD"
] | {"A": [192.0, 132.0], "B": [0.0, 131.0], "C": [190.0, 1.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, A)), 10)
- PointLiesOnLine(F, Line(A, C))
- PointLiesOnLine(C, Line(A, E))
- PointLiesOnLine(F, Line(A, E))
- PointLiesOnLine(F, Line(A, G))
- PointLiesOnLine(G, Line(B, E))
- PointLiesOnLine(C, Line(E, F))
- PointLiesOnCircle(A, Circle(C, radius_2_0))
- PointLiesOnCircle(B... | 114.2 | [
"Regular(Polygon($))",
"Find(AreaOf(Shaded(Shape($))))"
] | [
"Equals(LengthOf(Line(C, A)), 10)",
"PointLiesOnLine(F, Line(A, C))",
"PointLiesOnLine(C, Line(A, E))",
"PointLiesOnLine(F, Line(A, E))",
"PointLiesOnLine(F, Line(A, G))",
"PointLiesOnLine(G, Line(B, E))",
"PointLiesOnLine(C, Line(E, F))",
"PointLiesOnCircle(A, Circle(C, radius_2_0))",
"PointLiesOnC... | [
"AB",
"AC",
"AD",
"AE",
"AF",
"AG",
"BE",
"BG",
"CF",
"DE",
"DF",
"EF",
"EG",
"FG"
] | {"A": [138.0, 139.0], "B": [138.0, 26.0], "C": [80.0, 78.0], "D": [29.0, 138.0], "E": [25.0, 25.0], "F": [126.0, 126.0], "G": [39.0, 24.0]} | [
"C"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, A, D)), 42)
- PointLiesOnLine(A, Line(C, E))
- PointLiesOnLine(A, Line(D, B))
- PointLiesOnCircle(C, Circle(A, radius_2_0))
- PointLiesOnCircle(E, Circle(A, radius_2_0))
- PointLiesOnCircle(D, Circle(A, radius_2_0))
- PointLiesOnCircle(B, Circle(A, radius_2_0))
In $\odot... | 42 | [
"Circle(A)",
"Equals(MeasureOf(Angle(E,A,D)),42)",
"Find(MeasureOf(Arc(B,C)))"
] | [
"Equals(MeasureOf(Angle(E, A, D)), 42)",
"PointLiesOnLine(A, Line(C, E))",
"PointLiesOnLine(A, Line(D, B))",
"PointLiesOnCircle(C, Circle(A, radius_2_0))",
"PointLiesOnCircle(E, Circle(A, radius_2_0))",
"PointLiesOnCircle(D, Circle(A, radius_2_0))",
"PointLiesOnCircle(B, Circle(A, radius_2_0))"
] | [
"CE",
"CA",
"EA",
"ED",
"AD",
"AB",
"DB"
] | {"C": [3.1088217723741565, 76.19965176543187], "E": [170.10799469013062, 92.01022434936148], "A": [86.23865979381443, 85.22525773195876], "D": [144.29229174629, 146.30728106661257], "B": [28.656490264952964, 24.741438483668503]} | [
"A"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(U, V)), 15x)
- Equals(LengthOf(Line(S, T)), 11x-2)
- Equals(LengthOf(Line(T, U)), 8x+4)
- PointLiesOnLine(D, Line(S, T))
- PointLiesOnLine(T, Line(S, C))
- PointLiesOnLine(D, Line(S, C))
- PointLiesOnLine(T, Line(S, U))
- PointLiesOnLine(C, Line(S, U))
- PointLiesOnLine(D, Lin... | 2 | [
"Congruent(Triangle(R,S,T),Triangle(V,U,T))",
"Find(x)"
] | [
"Equals(LengthOf(Line(U, V)), 15x)",
"Equals(LengthOf(Line(S, T)), 11x-2)",
"Equals(LengthOf(Line(T, U)), 8x+4)",
"PointLiesOnLine(D, Line(S, T))",
"PointLiesOnLine(T, Line(S, C))",
"PointLiesOnLine(D, Line(S, C))",
"PointLiesOnLine(T, Line(S, U))",
"PointLiesOnLine(C, Line(S, U))",
"PointLiesOnLine... | [
"AE",
"CD",
"CU",
"EV",
"SC",
"SD",
"SR",
"ST",
"SU",
"TB",
"TC",
"TD",
"TR",
"TU",
"TV",
"UA",
"UD",
"UE",
"UV",
"VB"
] | {"A": [618.0, 264.0], "B": [590.0, 57.0], "C": [397.0, 295.0], "D": [56.0, 293.0], "E": [651.0, 262.0], "R": [1.0, 1.0], "S": [2.0, 292.0], "T": [325.0, 293.0], "U": [651.0, 293.0], "V": [649.0, 0.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(Z, Line(Y, W))
- PointLiesOnLine(V, Line(U, S))
- PointLiesOnLine(Z, Line(R, X))
- PointLiesOnLine(V, Line(R, T))
- PointLiesOnCircle(Y, Circle(R, radius_5_0))
- PointLiesOnCircle(U, Circle(R, radius_5_0))
- PointLiesOnCircle(S, Circle(R, radius_5_0))
- PointLiesOnCircle(W, Circle(... | 90 | [
"Circle(R)",
"Equals(LengthOf(Line(S,U)),20)",
"Equals(LengthOf(Line(Y,W)),20)",
"Equals(MeasureOf(Arc(Y,X)),45)",
"Find(MeasureOf(Arc(S,U)))"
] | [
"PointLiesOnLine(Z, Line(Y, W))",
"PointLiesOnLine(V, Line(U, S))",
"PointLiesOnLine(Z, Line(R, X))",
"PointLiesOnLine(V, Line(R, T))",
"PointLiesOnCircle(Y, Circle(R, radius_5_0))",
"PointLiesOnCircle(U, Circle(R, radius_5_0))",
"PointLiesOnCircle(S, Circle(R, radius_5_0))",
"PointLiesOnCircle(W, Cir... | [
"RT",
"RX",
"US",
"VR",
"VS",
"VT",
"VU",
"YW",
"YZ",
"ZR",
"ZW",
"ZX"
] | {"R": [100.0, 97.0], "S": [106.0, 0.0], "T": [178.0, 39.0], "U": [195.0, 121.0], "V": [150.0, 60.0], "W": [141.0, 186.0], "X": [61.0, 188.0], "Y": [7.0, 128.0], "Z": [74.0, 157.0]} | [
"R"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, C)), 15)
- Equals(LengthOf(Line(A, D)), 6)
- Equals(LengthOf(Line(A, B)), 17)
- Perpendicular(Line(D, C), Line(A, D))
- Perpendicular(Line(A, D), Line(A, B))
Find the area of the trapezoid. | 96 | [
"Find(AreaOf(Trapezoid($)))"
] | [
"Equals(LengthOf(Line(D, C)), 15)",
"Equals(LengthOf(Line(A, D)), 6)",
"Equals(LengthOf(Line(A, B)), 17)",
"Perpendicular(Line(D, C), Line(A, D))",
"Perpendicular(Line(A, D), Line(A, B))"
] | [
"AB",
"AD",
"BC",
"DC"
] | {"A": [1.0, 113.0], "B": [331.0, 115.0], "C": [249.0, 2.0], "D": [0.0, 0.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, O, C)), 2x+41)
- Equals(MeasureOf(Angle(E, D, C)), 115)
- Equals(LengthOf(Line(D, C)), 3y+13)
- Equals(LengthOf(Line(E, O)), 2y+19)
Find y in the parallelogram | 6 | [
"Parallelogram($)",
"Find(y)"
] | [
"Equals(MeasureOf(Angle(E, O, C)), 2x+41)",
"Equals(MeasureOf(Angle(E, D, C)), 115)",
"Equals(LengthOf(Line(D, C)), 3y+13)",
"Equals(LengthOf(Line(E, O)), 2y+19)"
] | [
"CD",
"CO",
"ED",
"EO"
] | {"C": [526.0, 223.0], "D": [66.0, 223.0], "E": [2.0, 3.0], "O": [462.0, 2.0]} | [
""
] |
Diagram Logic Form:
- 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))
-
Find $x$. | 4 | [
"Find(x)"
] | [
"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(A, B)), 18)
- Equals(LengthOf(Line(A, D)), 9)
- Equals(LengthOf(Line(D, C)), 6)
- PointLiesOnLine(F, Line(B, A))
- PointLiesOnLine(D, Line(A, C))
- Perpendicular(Line(D, F), Line(A, D))
- Perpendicular(Line(B, C), Line(D, C))
Find $AF$. | 10.8 | [
"Find(LengthOf(Line(A,F)))"
] | [
"Equals(LengthOf(Line(A, B)), 18)",
"Equals(LengthOf(Line(A, D)), 9)",
"Equals(LengthOf(Line(D, C)), 6)",
"PointLiesOnLine(F, Line(B, A))",
"PointLiesOnLine(D, Line(A, C))",
"Perpendicular(Line(D, F), Line(A, D))",
"Perpendicular(Line(B, C), Line(D, C))"
] | [
"AC",
"AD",
"AF",
"BA",
"BC",
"BF",
"DC",
"DF"
] | {"A": [53.0, 302.0], "B": [468.0, 99.0], "C": [468.0, 303.0], "D": [317.0, 303.0], "F": [317.0, 170.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(R, S)), 10)
- Equals(LengthOf(Line(R, Q)), 12)
- Equals(LengthOf(Line(R, Z)), x)
- Equals(LengthOf(Line(A, Z)), y)
- Equals(LengthOf(Line(Q, Z)), z)
- Equals(MeasureOf(Angle(S, P, A)), 45)
- Equals(MeasureOf(Angle(A, Q, R)), 30)
- PointLiesOnLine(A, Line(P, Z))
- PointLiesOnLi... | 10 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(R, S)), 10)",
"Equals(LengthOf(Line(R, Q)), 12)",
"Equals(LengthOf(Line(R, Z)), x)",
"Equals(LengthOf(Line(A, Z)), y)",
"Equals(LengthOf(Line(Q, Z)), z)",
"Equals(MeasureOf(Angle(S, P, A)), 45)",
"Equals(MeasureOf(Angle(A, Q, R)), 30)",
"PointLiesOnLine(A, Line(P, Z))",
"PointL... | [
"AQ",
"AZ",
"PA",
"PQ",
"PZ",
"RQ",
"RZ",
"SA",
"SP",
"SR",
"ZQ"
] | {"A": [160.0, 184.0], "P": [1.0, 185.0], "Q": [730.0, 183.0], "R": [420.0, 6.0], "S": [160.0, 8.0], "Z": [421.0, 185.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, M)), 16)
- Equals(LengthOf(Line(V, G)), 12)
- Equals(LengthOf(Line(H, M)), 22)
- Equals(LengthOf(Line(G, C)), x)
- Equals(MeasureOf(Angle(V, G, C)), MeasureOf(Angle(B, M, H)))
- Equals(MeasureOf(Angle(G, V, C)), MeasureOf(Angle(M, B, H)))
-
Two triangles are similar. Find... | 16.5 | [
"Similar(Triangle($1),Triangle($2))",
"Find(x)"
] | [
"Equals(LengthOf(Line(B, M)), 16)",
"Equals(LengthOf(Line(V, G)), 12)",
"Equals(LengthOf(Line(H, M)), 22)",
"Equals(LengthOf(Line(G, C)), x)",
"Equals(MeasureOf(Angle(V, G, C)), MeasureOf(Angle(B, M, H)))",
"Equals(MeasureOf(Angle(G, V, C)), MeasureOf(Angle(M, B, H)))",
""
] | [
"VG",
"GC",
"VC",
"BM",
"MH",
"BH"
] | {"B": [73.0, 18.0], "H": [410.0, 189.0], "M": [1.0, 210.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(I, G, E)), 9x)
- Equals(MeasureOf(Angle(A, C, F)), 140)
- PointLiesOnLine(C, Line(A, B))
- PointLiesOnLine(B, Line(A, H))
- PointLiesOnLine(C, Line(A, H))
- PointLiesOnLine(G, Line(C, E))
- PointLiesOnLine(B, Line(C, H))
- PointLiesOnLine(C, Line(E, F))
- PointLiesOnLine(G, ... | 16 | [
"Parallel(Line(m),Line(n))",
"Find(x)"
] | [
"Equals(MeasureOf(Angle(I, G, E)), 9x)",
"Equals(MeasureOf(Angle(A, C, F)), 140)",
"PointLiesOnLine(C, Line(A, B))",
"PointLiesOnLine(B, Line(A, H))",
"PointLiesOnLine(C, Line(A, H))",
"PointLiesOnLine(G, Line(C, E))",
"PointLiesOnLine(B, Line(C, H))",
"PointLiesOnLine(C, Line(E, F))",
"PointLiesOnL... | [
"AB",
"AC",
"AH",
"BC",
"BH",
"CE",
"CF",
"CG",
"CH",
"DI",
"EF",
"EG",
"FG",
"GD",
"GI"
] | {"A": [155.0, 60.0], "B": [29.0, 208.0], "C": [78.0, 151.0], "D": [156.0, 1.0], "E": [79.0, 2.0], "F": [78.0, 244.0], "G": [79.0, 93.0], "H": [5.0, 240.0], "I": [0.0, 186.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(P, Line(X, Y))
Given right triangle $XYZ$ with hypotenuse $\overline{XY}$, $YP$ is equal to $YZ$. If $m ∠PYZ = 26$, find $m ∠XZP$. | 13 | [
"Right(Triangle(X,Y,Z))",
"Equals(Line(X,Y),HypotenuseOf(Right(Triangle(X,Y,Z))))",
"Equals(LengthOf(Line(Y,P)),Line(Y,Z))",
"Equals(MeasureOf(Angle(P,Y,Z)),26)",
"Find(MeasureOf(Angle(X,Z,P)))"
] | [
"PointLiesOnLine(P, Line(X, Y))"
] | [
"XP",
"XY",
"XZ",
"YP",
"YZ",
"ZP"
] | {"P": [164.0, 11.0], "X": [186.0, 2.0], "Y": [0.0, 84.0], "Z": [187.0, 84.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(F, B)), 15)
- Equals(LengthOf(Line(D, F)), 5)
- Equals(LengthOf(Line(D, B)), x)
- PointLiesOnCircle(F, Circle(D, radius_3_0))
The segment is tangent to the circle. Find $x$. | 5 \sqrt { 10 } | [
"Tangent(Line($),Circle($))",
"Circle($)",
"Find(x)"
] | [
"Equals(LengthOf(Line(F, B)), 15)",
"Equals(LengthOf(Line(D, F)), 5)",
"Equals(LengthOf(Line(D, B)), x)",
"PointLiesOnCircle(F, Circle(D, radius_3_0))"
] | [
"BF",
"DB",
"FD"
] | {"B": [488.0, 124.0], "D": [126.0, 120.0], "F": [163.0, 6.0]} | [
"D"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(P, N, O)), 56)
- Equals(MeasureOf(Angle(N, B, M)), 70)
-
- PointLiesOnCircle(O, Circle(B, radius_5_0))
- PointLiesOnCircle(N, Circle(B, radius_5_0))
- PointLiesOnCircle(P, Circle(B, radius_5_0))
- PointLiesOnCircle(M, Circle(B, radius_5_0))
Find $m \angle P$. | 35 | [
"Find(MeasureOf(Angle(P)))"
] | [
"Equals(MeasureOf(Angle(P, N, O)), 56)",
"Equals(MeasureOf(Angle(N, B, M)), 70)",
"",
"PointLiesOnCircle(O, Circle(B, radius_5_0))",
"PointLiesOnCircle(N, Circle(B, radius_5_0))",
"PointLiesOnCircle(P, Circle(B, radius_5_0))",
"PointLiesOnCircle(M, Circle(B, radius_5_0))"
] | [
"NP",
"ON",
"PM"
] | {"B": [151.0, 150.0], "M": [4.0, 118.0], "N": [88.0, 287.0], "O": [288.0, 214.0], "P": [165.0, 1.0]} | [
"B"
] |
Diagram Logic Form:
- Perpendicular(Line(B, M), Line(L, M))
- Equals(LengthOf(Line(N, F)), x)
- Perpendicular(Line(F, N), Line(G, N))
- Equals(AreaOf(Quadrilateral(E,F,G,H)), 27)
- Equals(AreaOf(Quadrilateral(A,B,L,T)), 147)
For the pair of similar figures, use the given areas to find $x$. | 6.0 | [
"Similar(Shape($1),Shape($2))",
"Find(x)"
] | [
"Perpendicular(Line(B, M), Line(L, M))",
"Equals(LengthOf(Line(N, F)), x)",
"Perpendicular(Line(F, N), Line(G, N))",
"Equals(AreaOf(Quadrilateral(E,F,G,H)), 27)",
"Equals(AreaOf(Quadrilateral(A,B,L,T)), 147)"
] | [
"BA",
"LB",
"LT",
"TA"
] | {"A": [93.0, 1.0], "B": [1.0, 31.0], "L": [57.0, 151.0], "T": [120.0, 128.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 12)
- Equals(LengthOf(Line(B, C)), y)
- Equals(LengthOf(Line(B, D)), x)
- Equals(LengthOf(Line(A, C)), 10)
- Equals(LengthOf(Line(C, D)), z)
- PointLiesOnLine(D, Line(A, C))
- Perpendicular(Line(A, B), Line(B, C))
- Perpendicular(Line(B, D), Line(A, D))
Find y. | \frac { 12 } { 5 } \sqrt { 11 } | [
"Find(y)"
] | [
"Equals(LengthOf(Line(A, B)), 12)",
"Equals(LengthOf(Line(B, C)), y)",
"Equals(LengthOf(Line(B, D)), x)",
"Equals(LengthOf(Line(A, C)), 10)",
"Equals(LengthOf(Line(C, D)), z)",
"PointLiesOnLine(D, Line(A, C))",
"Perpendicular(Line(A, B), Line(B, C))",
"Perpendicular(Line(B, D), Line(A, D))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [361.0, 167.0], "B": [113.33553257765855, 1.554793631565289], "C": [0.0, 167.0], "D": [110.0, 167.0]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 15)
- Equals(LengthOf(Line(B, C)), x)
- Equals(MeasureOf(Angle(B, A, C)), 45)
- Perpendicular(Line(B, C), Line(A, C))
Find x. | \frac { 15 \sqrt { 2 } } { 2 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), 15)",
"Equals(LengthOf(Line(B, C)), x)",
"Equals(MeasureOf(Angle(B, A, C)), 45)",
"Perpendicular(Line(B, C), Line(A, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [0.0, 187.0], "B": [183.00354589315816, 1.329748687244475], "C": [183.99465287262794, 185.00008718142453]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, B)), 4)
- PointLiesOnLine(A, Line(Y, C))
- PointLiesOnLine(C, Line(Y, F))
- PointLiesOnLine(A, Line(Y, F))
- PointLiesOnLine(C, Line(F, A))
- PointLiesOnLine(C, Line(B, D))
- Perpendicular(Line(C, D), Line(C, A))
- Equals(LengthOf(Line(A, B)), LengthOf(Line(A, D)))
Find $C... | 4 | [
"Find(LengthOf(Line(C,D)))"
] | [
"Equals(LengthOf(Line(C, B)), 4)",
"PointLiesOnLine(A, Line(Y, C))",
"PointLiesOnLine(C, Line(Y, F))",
"PointLiesOnLine(A, Line(Y, F))",
"PointLiesOnLine(C, Line(F, A))",
"PointLiesOnLine(C, Line(B, D))",
"Perpendicular(Line(C, D), Line(C, A))",
"Equals(LengthOf(Line(A, B)), LengthOf(Line(A, D)))"
] | [
"AB",
"AD",
"BD",
"CA",
"CB",
"CD",
"CF",
"FA",
"YA",
"YC",
"YF"
] | {"A": [121.0, 244.0], "B": [1.0, 62.0], "C": [123.0, 62.0], "D": [242.0, 61.0], "F": [121.0, 0.0], "Y": [121.0, 270.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(F, D)), 6)
- Equals(LengthOf(Line(A, B)), 19)
- PointLiesOnLine(B, Line(C, A))
- PointLiesOnLine(E, Line(C, D))
- PointLiesOnLine(F, Line(D, A))
- PointLiesOnCircle(B, Circle(H, radius_6_0))
- PointLiesOnCircle(F, Circle(H, radius_6_0))
- PointLiesOnCircle(E, Circle(H, radius_... | 100 | [
"CircumscribedTo(Triangle(A,D,C),Circle(O))",
"Equals(LengthOf(Line(E,C)),Add(Line(D,E),Line(A,F)))",
"Find(PerimeterOf(Triangle(A,D,C)))"
] | [
"Equals(LengthOf(Line(F, D)), 6)",
"Equals(LengthOf(Line(A, B)), 19)",
"PointLiesOnLine(B, Line(C, A))",
"PointLiesOnLine(E, Line(C, D))",
"PointLiesOnLine(F, Line(D, A))",
"PointLiesOnCircle(B, Circle(H, radius_6_0))",
"PointLiesOnCircle(F, Circle(H, radius_6_0))",
"PointLiesOnCircle(E, Circle(H, rad... | [
"AB",
"CA",
"CB",
"CD",
"CE",
"DA",
"DE",
"FA",
"FD"
] | {"A": [264.0, 139.0], "B": [170.0, 131.0], "C": [0.0, 118.0], "D": [200.0, 2.0], "E": [127.0, 45.0], "F": [223.0, 52.0], "H": [175.0, 75.0]} | [
"H"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(Z, Y, W)), 58)
- Equals(MeasureOf(Angle(Y, X, Z)), MeasureOf(angle 7))
- Equals(MeasureOf(Angle(X, Z, Y)), 65)
- Equals(MeasureOf(Angle(Z, V, W)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(W, X, V)), MeasureOf(angle 5))
- Equals(MeasureOf(Angle(Z, X, W)), MeasureOf(angle ... | 57 | [
"Find(MeasureOf(Angle(5)))"
] | [
"Equals(MeasureOf(Angle(Z, Y, W)), 58)",
"Equals(MeasureOf(Angle(Y, X, Z)), MeasureOf(angle 7))",
"Equals(MeasureOf(Angle(X, Z, Y)), 65)",
"Equals(MeasureOf(Angle(Z, V, W)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(W, X, V)), MeasureOf(angle 5))",
"Equals(MeasureOf(Angle(Z, X, W)), MeasureOf(angle 6)... | [
"VX",
"WV",
"WX",
"WY",
"WZ",
"YX",
"ZV",
"ZX",
"ZY"
] | {"V": [2.0, 206.0], "W": [87.0, 336.0], "X": [172.0, 205.0], "Y": [306.0, 0.0], "Z": [402.0, 205.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(A, Line(Z, X))
- PointLiesOnLine(A, Line(Y, W))
Rhombus $WXYZ$ has an area of 100 square meters. Find $WY$ if $XZ = 10$ meters. | 20 | [
"Equals(AreaOf(Rhombus(W,X,Y,Z)),100)",
"Equals(LengthOf(Line(X,Z)),10)",
"Find(LengthOf(Line(W,Y)))"
] | [
"PointLiesOnLine(A, Line(Z, X))",
"PointLiesOnLine(A, Line(Y, W))"
] | [
"WA",
"WX",
"XA",
"YA",
"YW",
"YX",
"ZA",
"ZW",
"ZX",
"ZY"
] | {"A": [95.0, 48.0], "W": [0.0, 95.0], "X": [72.0, 3.0], "Y": [190.0, 0.0], "Z": [118.0, 94.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(K, M)), 20)
- Equals(LengthOf(Line(L, K)), z)
- Equals(LengthOf(Line(L, M)), x)
- Equals(LengthOf(Line(J, M)), 5)
- Equals(LengthOf(Line(L, J)), y)
- PointLiesOnLine(M, Line(K, J))
- Perpendicular(Line(K, M), Line(L, M))
- Perpendicular(Line(L, K), Line(L, J))
Find $x$. | 10 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(K, M)), 20)",
"Equals(LengthOf(Line(L, K)), z)",
"Equals(LengthOf(Line(L, M)), x)",
"Equals(LengthOf(Line(J, M)), 5)",
"Equals(LengthOf(Line(L, J)), y)",
"PointLiesOnLine(M, Line(K, J))",
"Perpendicular(Line(K, M), Line(L, M))",
"Perpendicular(Line(L, K), Line(L, J))"
] | [
"JM",
"KJ",
"KM",
"LJ",
"LK",
"LM"
] | {"J": [0.0, 346.0], "K": [173.0, 0.0], "L": [173.0, 347.0], "M": [33.0, 279.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 17)
- Equals(LengthOf(Line(A, C)), 7)
- Equals(LengthOf(Line(B, C)), x)
- Perpendicular(Line(A, B), Line(A, C))
Find x. | 13 \sqrt { 2 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), 17)",
"Equals(LengthOf(Line(A, C)), 7)",
"Equals(LengthOf(Line(B, C)), x)",
"Perpendicular(Line(A, B), Line(A, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [222.39734299516908, 0.13405797101449934], "B": [0.32583627500420675, 111.00373171961675], "C": [274.52500572400487, 109.00520066725542]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(H, A, J)), 47)
- Equals(MeasureOf(Angle(K, G, L)), x)
- Equals(MeasureOf(Angle(K, A, L)), 116)
- PointLiesOnLine(G, Line(J, L))
- PointLiesOnLine(G, Line(H, K))
- PointLiesOnCircle(J, Circle(A, radius_3_0))
- PointLiesOnCircle(L, Circle(A, radius_3_0))
- PointLiesOnCircle(K,... | 81.5 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(H, A, J)), 47)",
"Equals(MeasureOf(Angle(K, G, L)), x)",
"Equals(MeasureOf(Angle(K, A, L)), 116)",
"PointLiesOnLine(G, Line(J, L))",
"PointLiesOnLine(G, Line(H, K))",
"PointLiesOnCircle(J, Circle(A, radius_3_0))",
"PointLiesOnCircle(L, Circle(A, radius_3_0))",
"PointLiesOnCircl... | [
"GK",
"HG",
"HK",
"JG",
"JH",
"JL",
"LG"
] | {"A": [136.0, 138.0], "G": [194.0, 80.0], "H": [171.0, 7.0], "J": [243.0, 56.0], "K": [238.0, 224.0], "L": [6.0, 171.0]} | [
"A"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, H, B)), \frac{1}{4}x)
- Equals(MeasureOf(Angle(H, D, B)), 4x-8)
- Equals(MeasureOf(Angle(B, C, H)), 8y-12)
- Equals(MeasureOf(Angle(C, B, H)), y-8)
Find $x$ so that the quadrilateral is a parallelogram. | 30 | [
"Parallelogram($)",
"Find(x)"
] | [
"Equals(MeasureOf(Angle(D, H, B)), \\frac{1}{4}x)",
"Equals(MeasureOf(Angle(H, D, B)), 4x-8)",
"Equals(MeasureOf(Angle(B, C, H)), 8y-12)",
"Equals(MeasureOf(Angle(C, B, H)), y-8)"
] | [
"BC",
"CH",
"HD",
"DB",
"BH"
] | {"B": [10.0, 194.0], "C": [379.0, 174.0], "D": [3.0, 20.0], "H": [371.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, D)), 10)
- Equals(LengthOf(Line(B, C)), x)
- Equals(LengthOf(Line(B, D)), 4)
- Equals(LengthOf(Line(A, B)), y)
- Equals(LengthOf(Line(A, D)), z)
- PointLiesOnLine(B, Line(A, D))
- Perpendicular(Line(A, C), Line(D, C))
- Perpendicular(Line(B, C), Line(A, B))
Find y | 21 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(C, D)), 10)",
"Equals(LengthOf(Line(B, C)), x)",
"Equals(LengthOf(Line(B, D)), 4)",
"Equals(LengthOf(Line(A, B)), y)",
"Equals(LengthOf(Line(A, D)), z)",
"PointLiesOnLine(B, Line(A, D))",
"Perpendicular(Line(A, C), Line(D, C))",
"Perpendicular(Line(B, C), Line(A, B))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [1.0, 112.0], "B": [253.0, 113.0], "C": [251.0, 2.0], "D": [301.0, 112.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, F)), 20)
- Equals(LengthOf(Line(F, B)), 7)
- Equals(LengthOf(Line(A, C)), 16)
- Equals(LengthOf(Line(C, D)), 11)
Find the area of the figure. Round to the nearest tenth if necessary. | 239 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(A, F)), 20)",
"Equals(LengthOf(Line(F, B)), 7)",
"Equals(LengthOf(Line(A, C)), 16)",
"Equals(LengthOf(Line(C, D)), 11)"
] | [
"AC",
"AF",
"CD",
"FB",
"BE",
"ED"
] | {"A": [184.33333333333331, 0.0], "B": [1.6514589515331437, 63.01149851632047], "C": [182.34035110732165, 147.3204564832426], "D": [83.98453863437298, 146.67622529418486], "E": [83.34874923156949, 64.32184234170332], "F": [0.6666666666666572, 0.0]} | [] |
Diagram Logic Form:
- Perpendicular(Line(W,H), Line(X,Z))
- Perpendicular(Line(Y,G), Line(X,Z))
- PointLiesOnLine(H, Line(Z, X))
- PointLiesOnLine(H, Line(G, X))
- PointLiesOnLine(G, Line(Z, X))
- PointLiesOnLine(G, Line(Z, H))
Find the area of quadrilateral $XYZW$ if $XZ = 39$, $HW = 20$, and $YG = 21$. | 799.5 | [
"Equals(LengthOf(Line(X,Z)),39)",
"Equals(LengthOf(Line(H,W)),20)",
"Equals(LengthOf(Line(Y,G)),21)",
"Find(AreaOf(Quadrilateral(X,Y,Z,W)))"
] | [
"Perpendicular(Line(W,H), Line(X,Z))",
"Perpendicular(Line(Y,G), Line(X,Z))",
"PointLiesOnLine(H, Line(Z, X))",
"PointLiesOnLine(H, Line(G, X))",
"PointLiesOnLine(G, Line(Z, X))",
"PointLiesOnLine(G, Line(Z, H))"
] | [
"XW",
"XY",
"WZ",
"YZ"
] | {"X": [1.0, 109.0], "W": [37.0, 205.0], "Y": [77.0, 2.0], "Z": [194.0, 108.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, X)), 12x+2)
- Equals(LengthOf(Line(X, C)), 10x)
- Equals(LengthOf(Line(E, X)), x+1)
- Equals(LengthOf(Line(B, X)), x)
- PointLiesOnLine(X, Line(B, D))
- PointLiesOnLine(X, Line(E, C))
- PointLiesOnCircle(B, Circle(A, radius_0_0))
- PointLiesOnCircle(C, Circle(A, radius_0_0)... | 4 | [
"Tangent(Line($),Circle($))",
"Find(x)"
] | [
"Equals(LengthOf(Line(D, X)), 12x+2)",
"Equals(LengthOf(Line(X, C)), 10x)",
"Equals(LengthOf(Line(E, X)), x+1)",
"Equals(LengthOf(Line(B, X)), x)",
"PointLiesOnLine(X, Line(B, D))",
"PointLiesOnLine(X, Line(E, C))",
"PointLiesOnCircle(B, Circle(A, radius_0_0))",
"PointLiesOnCircle(C, Circle(A, radius_... | [
"BD",
"BE",
"BX",
"DX",
"EC",
"EX",
"XC"
] | {"A": [133.0, 134.0], "B": [144.0, 266.0], "C": [266.0, 134.0], "D": [173.0, 6.0], "E": [108.0, 265.0], "X": [148.0, 232.0]} | [
"A"
] |
Diagram Logic Form:
- PointLiesOnLine(E, Line(D, B))
- PointLiesOnLine(E, Line(C, A))
In rhombus $A B C D, A B=2 x+3$ and $B C=5 x$. Find x. | 1 | [
"Rhombus(A,B,C,D)",
"Equals(LengthOf(Line(A,B)),2x+3)",
"Equals(LengthOf(Line(B,C)),5x)",
"Find(x)"
] | [
"PointLiesOnLine(E, Line(D, B))",
"PointLiesOnLine(E, Line(C, A))"
] | [
"AE",
"BA",
"BE",
"CA",
"CB",
"CE",
"DA",
"DB",
"DC",
"DE"
] | {"A": [53.0, 1.0], "B": [196.0, 0.0], "C": [142.0, 134.0], "D": [0.0, 134.0], "E": [98.0, 68.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), y)
- Equals(MeasureOf(Angle(A, D, B)), 60)
- Equals(LengthOf(Line(A, B)), 18)
- Equals(LengthOf(Line(B, D)), z)
- Equals(MeasureOf(Angle(A, B, C)), 45)
- Equals(LengthOf(Line(B, C)), x)
- Perpendicular(Line(A, D), Line(A, B))
- Perpendicular(Line(A, C), Line(B, C))
Fi... | 6 \sqrt { 3 } | [
"Find(y)"
] | [
"Equals(LengthOf(Line(A, D)), y)",
"Equals(MeasureOf(Angle(A, D, B)), 60)",
"Equals(LengthOf(Line(A, B)), 18)",
"Equals(LengthOf(Line(B, D)), z)",
"Equals(MeasureOf(Angle(A, B, C)), 45)",
"Equals(LengthOf(Line(B, C)), x)",
"Perpendicular(Line(A, D), Line(A, B))",
"Perpendicular(Line(A, C), Line(B, C))... | [
"AB",
"AC",
"AD",
"BC",
"BD"
] | {"A": [120.67198896116696, 1.8510998678552255], "B": [121.83051708217913, 217.487077342479], "C": [225.5160051216389, 109.50704225352113], "D": [0.1874039938556109, 1.6651305683563749]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, N)), 9)
- Equals(LengthOf(Line(M, O)), 16)
Find the area of the kite. | 72 | [
"Find(AreaOf(Kite($)))"
] | [
"Equals(LengthOf(Line(B, N)), 9)",
"Equals(LengthOf(Line(M, O)), 16)"
] | [
"MB",
"NM",
"NO",
"OB"
] | {"B": [104.0, 1.0], "M": [1.0, 28.0], "N": [48.0, 124.0], "O": [209.0, 125.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, A, F)), x-11)
- Equals(MeasureOf(Angle(A, B, E)), x+10)
- Equals(MeasureOf(Angle(B, D, G)), 31)
- Equals(MeasureOf(Angle(G, C, H)), 2x-42)
- PointLiesOnLine(C, Line(A, H))
- PointLiesOnLine(A, Line(B, F))
- PointLiesOnLine(B, Line(D, E))
- PointLiesOnLine(D, Line(C, G))
... | 93 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(C, A, F)), x-11)",
"Equals(MeasureOf(Angle(A, B, E)), x+10)",
"Equals(MeasureOf(Angle(B, D, G)), 31)",
"Equals(MeasureOf(Angle(G, C, H)), 2x-42)",
"PointLiesOnLine(C, Line(A, H))",
"PointLiesOnLine(A, Line(B, F))",
"PointLiesOnLine(B, Line(D, E))",
"PointLiesOnLine(D, Line(C, G... | [
"AB",
"AC",
"AF",
"AH",
"BD",
"BE",
"BF",
"CD",
"CG",
"CH",
"DE",
"DG"
] | {"A": [85.0, 34.0], "B": [330.0, 144.0], "C": [38.0, 221.0], "D": [215.0, 210.0], "E": [382.0, 112.0], "F": [10.0, 2.0], "G": [333.0, 223.0], "H": [21.0, 296.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(R, B, S)), 103)
- PointLiesOnLine(S, Line(T, A))
- PointLiesOnLine(R, Line(T, Q))
- PointLiesOnCircle(R, Circle(B, radius_5_0))
- PointLiesOnCircle(S, Circle(B, radius_5_0))
Find the measure of $\angle T$. | 77 | [
"Find(MeasureOf(Angle(T)))"
] | [
"Equals(MeasureOf(Angle(R, B, S)), 103)",
"PointLiesOnLine(S, Line(T, A))",
"PointLiesOnLine(R, Line(T, Q))",
"PointLiesOnCircle(R, Circle(B, radius_5_0))",
"PointLiesOnCircle(S, Circle(B, radius_5_0))"
] | [
"AS",
"RQ",
"TA",
"TQ",
"TR",
"TS"
] | {"A": [242.0, 0.0], "B": [153.0, 79.0], "Q": [0.0, 92.0], "R": [123.0, 146.0], "S": [225.0, 92.0], "T": [208.0, 183.0]} | [
"B"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(Z, X, Y)), 2 * a)
- Equals(MeasureOf(Angle(Y, Z, X)), a/2)
- Perpendicular(Line(X,Y), Line(Y,Z))
In the triangle, what is the measure of $∠Z$? | 18 | [
"Triangle($)",
"Find(MeasureOf(Angle(Z)))"
] | [
"Equals(MeasureOf(Angle(Z, X, Y)), 2 * a)",
"Equals(MeasureOf(Angle(Y, Z, X)), a/2)",
"Perpendicular(Line(X,Y), Line(Y,Z))"
] | [
"XY",
"XZ",
"ZY"
] | {"X": [0.0, 0.0], "Y": [3.0, 175.0], "Z": [162.0, 176.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(P, Line(B, D))
- PointLiesOnLine(P, Line(C, A))
- Perpendicular(Line(A, P), Line(D, P))
Quadrilateral ABCD is a rhombus. If $m\angle ABC = 2x – 7$ and $m\angle BCD = 2x + 3$, find $m\angle DAB$. | 95 | [
"Rhombus(A,B,C,D)",
"Equals(MeasureOf(Angle(A,B,C)),2x-7)",
"Equals(MeasureOf(Angle(B,C,D)),2x+3)",
"Find(MeasureOf(Angle(D,A,B)))"
] | [
"PointLiesOnLine(P, Line(B, D))",
"PointLiesOnLine(P, Line(C, A))",
"Perpendicular(Line(A, P), Line(D, P))"
] | [
"BD",
"BC",
"BA",
"BP",
"DC",
"DA",
"DP",
"CA",
"CP",
"AP"
] | {"B": [220.5954165289054, 1.662674650698591], "D": [0.0, 163.0], "C": [166.77464155029716, 161.84853144795147], "A": [54.84151329243353, 1.5], "P": [111.0, 81.5]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(T, S)), 18)
- Equals(LengthOf(Line(T, U)), y+2)
- Equals(LengthOf(Line(R, V)), x)
- Equals(LengthOf(Line(B, C)), 4)
- Equals(LengthOf(Line(C, D)), 5)
- Equals(LengthOf(Line(A, E)), 3)
- Equals(MeasureOf(Angle(B, A, E)), MeasureOf(Angle(V, R, S)))
- Equals(MeasureOf(Angle(A, B,... | 13.5 | [
"Similar(Polygon($1),Polygon($2))",
"Find(x)"
] | [
"Equals(LengthOf(Line(T, S)), 18)",
"Equals(LengthOf(Line(T, U)), y+2)",
"Equals(LengthOf(Line(R, V)), x)",
"Equals(LengthOf(Line(B, C)), 4)",
"Equals(LengthOf(Line(C, D)), 5)",
"Equals(LengthOf(Line(A, E)), 3)",
"Equals(MeasureOf(Angle(B, A, E)), MeasureOf(Angle(V, R, S)))",
"Equals(MeasureOf(Angle(A... | [
"AB",
"BC",
"CD",
"DE",
"AE",
"TU",
"UV",
"VR",
"RS",
"ST"
] | {"R": [166.0, 1.0], "S": [2.0, 94.0], "T": [0.0, 297.0], "U": [253.0, 259.0], "V": [252.0, 130.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(F, K)), 12)
- Equals(LengthOf(Line(D, G)), 9)
- PointLiesOnLine(J, Line(F, D))
- PointLiesOnLine(H, Line(F, C))
- PointLiesOnLine(K, Line(F, G))
- PointLiesOnLine(G, Line(D, C))
- PointLiesOnLine(K, Line(D, H))
- PointLiesOnLine(K, Line(C, J))
In $\triangle CDF$, $K$ is the c... | 8 | [
"Triangle(C,D,F)",
"IsCentroidOf(Point(K),Triangle(C,D,F))",
"Equals(LengthOf(Line(D,K)),16)",
"Find(LengthOf(Line(K,H)))"
] | [
"Equals(LengthOf(Line(F, K)), 12)",
"Equals(LengthOf(Line(D, G)), 9)",
"PointLiesOnLine(J, Line(F, D))",
"PointLiesOnLine(H, Line(F, C))",
"PointLiesOnLine(K, Line(F, G))",
"PointLiesOnLine(G, Line(D, C))",
"PointLiesOnLine(K, Line(D, H))",
"PointLiesOnLine(K, Line(C, J))"
] | [
"CG",
"CH",
"CJ",
"DC",
"DG",
"DH",
"DJ",
"DK",
"FC",
"FD",
"FG",
"FH",
"FJ",
"FK",
"KC",
"KG",
"KH",
"KJ"
] | {"C": [1.0, 0.0], "D": [1.0, 363.0], "F": [251.0, 136.0], "G": [0.0, 175.0], "H": [125.0, 67.0], "J": [126.0, 250.0], "K": [84.0, 163.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(F, D, A)), 7y-4)
- Equals(MeasureOf(Angle(B, D, A)), 11x-1)
- Equals(MeasureOf(Angle(H, F, D)), 7x+9)
- Equals(MeasureOf(Angle(H, F, C)), z)
- Equals(MeasureOf(Angle(G, A, D)), 2y+5)
- PointLiesOnLine(F, Line(D, C))
- PointLiesOnLine(A, Line(D, E))
- Parallel(Line(A, G), Lin... | 73 | [
"Find(z)"
] | [
"Equals(MeasureOf(Angle(F, D, A)), 7y-4)",
"Equals(MeasureOf(Angle(B, D, A)), 11x-1)",
"Equals(MeasureOf(Angle(H, F, D)), 7x+9)",
"Equals(MeasureOf(Angle(H, F, C)), z)",
"Equals(MeasureOf(Angle(G, A, D)), 2y+5)",
"PointLiesOnLine(F, Line(D, C))",
"PointLiesOnLine(A, Line(D, E))",
"Parallel(Line(A, G),... | [
"AD",
"AE",
"AG",
"CF",
"DB",
"DC",
"DE",
"DF",
"FH"
] | {"A": [167.0, 178.0], "B": [0.0, 41.0], "C": [277.0, 4.0], "D": [167.0, 136.0], "E": [166.0, 245.0], "F": [191.0, 107.0], "G": [1.0, 82.0], "H": [0.0, 0.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(Q, P)), 8)
- Equals(LengthOf(Line(S, R)), 7)
- Equals(LengthOf(Line(Q, R)), x)
- PointLiesOnLine(R, Line(Q, S))
- PointLiesOnCircle(S, Circle(B, radius_4_0))
- PointLiesOnCircle(R, Circle(B, radius_4_0))
- PointLiesOnCircle(P, Circle(B, radius_4_0))
$\overline{PQ}$ is tangent... | 5.2 | [
"Tangent(Line(P,Q),Circle($))",
"Find(x)"
] | [
"Equals(LengthOf(Line(Q, P)), 8)",
"Equals(LengthOf(Line(S, R)), 7)",
"Equals(LengthOf(Line(Q, R)), x)",
"PointLiesOnLine(R, Line(Q, S))",
"PointLiesOnCircle(S, Circle(B, radius_4_0))",
"PointLiesOnCircle(R, Circle(B, radius_4_0))",
"PointLiesOnCircle(P, Circle(B, radius_4_0))"
] | [
"QP",
"QR",
"QS",
"SR"
] | {"B": [98.0, 97.0], "P": [162.0, 25.0], "Q": [297.0, 181.0], "R": [174.0, 156.0], "S": [3.0, 121.0]} | [
"B"
] |
Diagram Logic Form:
- PointLiesOnLine(S, Line(P, M))
- PointLiesOnLine(T, Line(P, Q))
- PointLiesOnLine(R, Line(M, N))
- PointLiesOnLine(S, Line(T, R))
- Equals(LengthOf(Line(Q, T)), LengthOf(Line(P, T)))
Find the ratio of $MS$ to $SP$, given that $MNPQ$ is a parallelogram with $MR=\frac{1}{4} MN$ | 0.5 | [
"Parallelogram(M,N,P,Q)",
"Equals(LengthOf(Line(M,R)),Mul(Line(M,N),\\frac{1}{4}))",
"Find(RatioOf(Line(M,S),Line(S,P)))"
] | [
"PointLiesOnLine(S, Line(P, M))",
"PointLiesOnLine(T, Line(P, Q))",
"PointLiesOnLine(R, Line(M, N))",
"PointLiesOnLine(S, Line(T, R))",
"Equals(LengthOf(Line(Q, T)), LengthOf(Line(P, T)))"
] | [
"SR",
"MN",
"MQ",
"MR",
"MS",
"NR",
"PM",
"PN",
"PQ",
"PS",
"PT",
"QT",
"TR",
"TS"
] | {"M": [0.0, 0.0], "N": [162.0, 2.0], "P": [216.0, 69.0], "Q": [57.0, 67.0], "R": [53.0, 0.0], "S": [86.0, 27.0], "T": [137.0, 68.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(G, Line(H, F))
- PointLiesOnLine(J, Line(H, K))
Find x so that $GJ \parallel FK$. $H J=x-5, J K=15, F G=18, H G=x-4 | 10 | [
"Parallel(Line(G,J),Line(F,K))",
"Equals(LengthOf(Line(H,J)),x-5)",
"Equals(LengthOf(Line(J,K)),15)",
"Equals(LengthOf(Line(F,G)),18)",
"Equals(LengthOf(Line(H,G)),x-4)",
"Find(x)"
] | [
"PointLiesOnLine(G, Line(H, F))",
"PointLiesOnLine(J, Line(H, K))"
] | [
"HF",
"HK",
"HG",
"HJ",
"FK",
"FG",
"KJ",
"GJ"
] | {"H": [166.5842546383629, 0.744637328175628], "F": [0.0, 159.0], "K": [263.0, 159.0], "G": [65.27123187522847, 96.99488241744852], "J": [223.67667761614265, 94.00610042233693]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(S, R)), 5)
- PointLiesOnLine(S, Line(Q, R))
- Perpendicular(Line(Q, P), Line(P, R))
- Perpendicular(Line(S, S), Line(Q, S))
In $\triangle P Q R, R S=3$ and $Q S=14 .$ Find $P S$ | \sqrt { 42 } | [
"Triangle(P,Q,R)",
"Equals(LengthOf(Line(R,S)),3)",
"Equals(LengthOf(Line(Q,S)),14)",
"Find(LengthOf(Line(P,S)))"
] | [
"Equals(LengthOf(Line(S, R)), 5)",
"PointLiesOnLine(S, Line(Q, R))",
"Perpendicular(Line(Q, P), Line(P, R))",
"Perpendicular(Line(S, S), Line(Q, S))"
] | [
"QP",
"QR",
"QS",
"RP",
"SP",
"SR"
] | {"P": [2.0, 0.0], "Q": [276.0, 0.0], "R": [0.0, 114.0], "S": [40.0, 98.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(C, Line(J, L))
- PointLiesOnLine(C, Line(M, K))
JKLM is a rhombus. If $CK = 8$ and $JK = 10$, Find $JC$. | 6 | [
"Rhombus(J,K,L,M)",
"Equals(LengthOf(Line(C,K)),8)",
"Equals(LengthOf(Line(J,K)),10)",
"Find(LengthOf(Line(J,C)))"
] | [
"PointLiesOnLine(C, Line(J, L))",
"PointLiesOnLine(C, Line(M, K))"
] | [
"JL",
"JM",
"JK",
"JC",
"LM",
"LK",
"LC",
"MK",
"MC",
"KC"
] | {"J": [46.331815306767865, 0.3889271030992987], "L": [140.8466827671167, 109.39967364783348], "M": [0.3179581342119491, 111.0144093351927], "K": [186.65215057325884, 0.4975503561497092], "C": [93.1696113074205, 55.696113074204945]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, V, U)), 34)
- Equals(MeasureOf(Arc(X, C)), 128)
- Equals(MeasureOf(Arc(U, W)), x)
- PointLiesOnLine(W, Line(V, A))
- PointLiesOnLine(X, Line(V, A))
- PointLiesOnLine(U, Line(V, T))
- PointLiesOnLine(C, Line(V, T))
- PointLiesOnLine(U, Line(V, C))
- PointLiesOnLine(A, Line... | 60 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(D, V, U)), 34)",
"Equals(MeasureOf(Arc(X, C)), 128)",
"Equals(MeasureOf(Arc(U, W)), x)",
"PointLiesOnLine(W, Line(V, A))",
"PointLiesOnLine(X, Line(V, A))",
"PointLiesOnLine(U, Line(V, T))",
"PointLiesOnLine(C, Line(V, T))",
"PointLiesOnLine(U, Line(V, C))",
"PointLiesOnLine(... | [
"AD",
"AW",
"AX",
"DX",
"TC",
"TU",
"UC",
"VA",
"VC",
"VD",
"VT",
"VU",
"VW",
"VX",
"WD",
"WX"
] | {"A": [242.0, 11.0], "B": [162.0, 78.0], "C": [200.0, 144.0], "D": [276.0, 10.0], "T": [245.0, 170.0], "U": [84.0, 77.0], "V": [1.0, 30.0], "W": [108.0, 22.0], "X": [206.0, 14.0]} | [
"B"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, B)), 8)
- Equals(LengthOf(Line(A, B)), 4)
- Equals(LengthOf(Line(A, D)), 3)
- Equals(LengthOf(Line(E, D)), x)
- PointLiesOnLine(B, Line(A, C))
- PointLiesOnLine(D, Line(A, E))
- PointLiesOnCircle(C, Circle(O, radius_3_0))
- PointLiesOnCircle(E, Circle(O, radius_3_0))
- Poin... | 13 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(C, B)), 8)",
"Equals(LengthOf(Line(A, B)), 4)",
"Equals(LengthOf(Line(A, D)), 3)",
"Equals(LengthOf(Line(E, D)), x)",
"PointLiesOnLine(B, Line(A, C))",
"PointLiesOnLine(D, Line(A, E))",
"PointLiesOnCircle(C, Circle(O, radius_3_0))",
"PointLiesOnCircle(E, Circle(O, radius_3_0))",
... | [
"AB",
"AC",
"AE",
"AD",
"CB",
"ED"
] | {"A": [1.0, 94.0], "B": [67.0, 68.0], "C": [207.0, 13.0], "O": [159.0, 97.0], "E": [243.0, 144.0], "D": [64.0, 107.0]} | [
"O"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, D)), 8)
- Equals(LengthOf(Line(A, B)), x)
- Equals(LengthOf(Line(A, D)), z)
- Equals(LengthOf(Line(C, D)), 3)
- Perpendicular(Line(B, D), Line(A, D))
- Perpendicular(Line(A, B), Line(A, C))
Find y | \sqrt { 33 } | [
"Find(y)"
] | [
"Equals(LengthOf(Line(B, D)), 8)",
"Equals(LengthOf(Line(A, B)), x)",
"Equals(LengthOf(Line(A, D)), z)",
"Equals(LengthOf(Line(C, D)), 3)",
"Perpendicular(Line(B, D), Line(A, D))",
"Perpendicular(Line(A, B), Line(A, C))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [93.0, 208.0], "B": [96.0, -1.0], "C": [0.0, 209.0], "D": [23.0, 175.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(M, L)), 7)
- Equals(MeasureOf(Angle(M, L, K)), 92)
- PointLiesOnCircle(M, Circle(L, radius_1_0))
Find the area of the shaded sector. Round to the nearest tenth. | 39.3 | [
"Find(AreaOf(Shaded(Sector($))))"
] | [
"Equals(LengthOf(Line(M, L)), 7)",
"Equals(MeasureOf(Angle(M, L, K)), 92)",
"PointLiesOnCircle(M, Circle(L, radius_1_0))"
] | [
"LK",
"ML"
] | {"K": [105.0, 198.0], "L": [104.0, 103.0], "M": [210.0, 106.0]} | [
"L"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(N, B)), 6)
- Equals(LengthOf(Line(E, F)), x)
- Equals(AreaOf(Trapezoid(B, N, A, L)), 72)
- Equals(AreaOf(Trapezoid(E, F, G, H)), 50)
For the pair of similar figures, use the given areas to find $x$. | 5 | [
"Similar(Shape($1),Shape($2))",
"Find(x)"
] | [
"Equals(LengthOf(Line(N, B)), 6)",
"Equals(LengthOf(Line(E, F)), x)",
"Equals(AreaOf(Trapezoid(B, N, A, L)), 72)",
"Equals(AreaOf(Trapezoid(E, F, G, H)), 50)"
] | [
"AL",
"BL",
"EF",
"EH",
"FG",
"GH",
"NA",
"NB"
] | {"A": [183.0, 152.0], "B": [1.0, 0.0], "L": [1.0, 151.0], "N": [87.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 54)
- Equals(LengthOf(Line(B, C)), x)
- Equals(MeasureOf(Angle(B, A, C)), 64)
- Equals(LengthOf(Line(A, B)), 120)
Find x. Round the side measure to the nearest tenth. | 107.9 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, C)), 54)",
"Equals(LengthOf(Line(B, C)), x)",
"Equals(MeasureOf(Angle(B, A, C)), 64)",
"Equals(LengthOf(Line(A, B)), 120)"
] | [
"AB",
"AC",
"BC"
] | {"A": [214.26399288521674, 69.54207189373727], "B": [1.2484089101034215, 170.9014518695306], "C": [129.62456468189927, 1.493841841501748]} | [] |
Diagram Logic Form:
- PointLiesOnCircle(P, Circle(U, radius_5_0))
- PointLiesOnCircle(S, Circle(U, radius_5_0))
- PointLiesOnCircle(Q, Circle(U, radius_5_0))
- PointLiesOnCircle(T, Circle(U, radius_5_0))
- PointLiesOnCircle(R, Circle(U, radius_5_0))
Equilateral pentagon $P Q R S T$ is inscribed in $\odot U$.
Find $m ... | 108 | [
"InscribedIn(Equilateral(Pentagon(P,Q,R,S,T)),Circle(U))",
"Find(MeasureOf(Angle(P,Q,R)))"
] | [
"PointLiesOnCircle(P, Circle(U, radius_5_0))",
"PointLiesOnCircle(S, Circle(U, radius_5_0))",
"PointLiesOnCircle(Q, Circle(U, radius_5_0))",
"PointLiesOnCircle(T, Circle(U, radius_5_0))",
"PointLiesOnCircle(R, Circle(U, radius_5_0))"
] | [
"PQ",
"PS",
"PT",
"QR",
"SR",
"ST"
] | {"P": [8.0, 75.0], "Q": [112.0, 2.0], "R": [211.0, 69.0], "S": [174.0, 194.0], "T": [43.0, 190.0], "U": [112.0, 111.0]} | [
"U"
] |
Diagram Logic Form:
- PointLiesOnLine(K, Line(H, M))
- PointLiesOnLine(K, Line(M, J))
- PointLiesOnLine(K, Line(H, L))
- PointLiesOnLine(K, Line(L, J))
- PointLiesOnLine(J, Line(H, M))
- PointLiesOnLine(J, Line(H, K))
- PointLiesOnLine(J, Line(H, L))
- PointLiesOnLine(L, Line(H, M))
- PointLiesOnLine(L, Line(M, K))
- P... | 3 | [
"Equals(LengthOf(Line(L,K)),4)",
"Equals(LengthOf(Line(M,P)),3)",
"Equals(LengthOf(Line(P,Q)),6)",
"Equals(LengthOf(Line(K,J)),2)",
"Equals(LengthOf(Line(R,S)),6)",
"Equals(LengthOf(Line(L,P)),2)",
"Find(LengthOf(Line(Q,R)))"
] | [
"PointLiesOnLine(K, Line(H, M))",
"PointLiesOnLine(K, Line(M, J))",
"PointLiesOnLine(K, Line(H, L))",
"PointLiesOnLine(K, Line(L, J))",
"PointLiesOnLine(J, Line(H, M))",
"PointLiesOnLine(J, Line(H, K))",
"PointLiesOnLine(J, Line(H, L))",
"PointLiesOnLine(L, Line(H, M))",
"PointLiesOnLine(L, Line(M, ... | [
"HJ",
"HK",
"HM",
"HS",
"JR",
"KJ",
"KQ",
"LH",
"LJ",
"LK",
"LM",
"MJ",
"MK",
"MQ",
"MR",
"MS",
"PM",
"PQ",
"PR",
"PS",
"QR",
"SQ",
"SR"
] | {"H": [133.0, 0.0], "J": [255.0, 55.0], "K": [359.0, 103.0], "L": [485.0, 165.0], "M": [629.0, 227.0], "P": [463.0, 227.0], "Q": [298.0, 227.0], "R": [170.0, 227.0], "S": [1.0, 226.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(E, Line(K, J))
- PointLiesOnLine(F, Line(K, J))
- PointLiesOnLine(I, Line(K, J))
- PointLiesOnLine(L, Line(K, J))
- PointLiesOnLine(B, Line(K, J))
- PointLiesOnLine(C, Line(K, J))
- PointLiesOnLine(N, Line(K, J))
- PointLiesOnLine(J, Line(K, A))
- PointLiesOnLine(E, Line(K, A))
- P... | 14.6 | [
"Equals(RadiusOf(Circle(J)),10)",
"Equals(RadiusOf(Circle(K)),8)",
"Equals(LengthOf(Line(B,C)),5.4)",
"Find(LengthOf(Line(A,B)))"
] | [
"PointLiesOnLine(E, Line(K, J))",
"PointLiesOnLine(F, Line(K, J))",
"PointLiesOnLine(I, Line(K, J))",
"PointLiesOnLine(L, Line(K, J))",
"PointLiesOnLine(B, Line(K, J))",
"PointLiesOnLine(C, Line(K, J))",
"PointLiesOnLine(N, Line(K, J))",
"PointLiesOnLine(J, Line(K, A))",
"PointLiesOnLine(E, Line(K, ... | [
"AB",
"AC",
"AD",
"AE",
"AF",
"AG",
"AH",
"AI",
"AL",
"AM",
"AN",
"AO",
"BC",
"BN",
"BO",
"CN",
"CO",
"DB",
"DC",
"DF",
"DG",
"DH",
"DI",
"DL",
"DM",
"DN",
"DO",
"EB",
"EC",
"ED",
"EF",
"EG",
"EH",
"EI",
"EL",
"EM",
"EN",
"EO",
"FB",
"FC"... | {"A": [20.0, 118.0], "B": [276.0, 218.0], "C": [405.0, 270.0], "D": [508.0, 312.0], "E": [310.0, 234.0], "F": [361.0, 254.0], "G": [118.0, 158.0], "H": [153.0, 169.0], "I": [300.0, 228.0], "J": [181.0, 182.0], "K": [413.0, 273.0], "L": [350.0, 248.0], "M": [434.0, 283.0], "N": [191.0, 184.0], "O": [424.0, 276.0]} | [
"K",
"J",
"C"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(P, Q)), 72)
- Equals(LengthOf(Line(R, Q)), 25)
- Perpendicular(Line(P, Q), Line(R, Q))
Find the measure of $∠R$ to the nearest tenth. | 70.9 | [
"Find(MeasureOf(Angle(R)))"
] | [
"Equals(LengthOf(Line(P, Q)), 72)",
"Equals(LengthOf(Line(R, Q)), 25)",
"Perpendicular(Line(P, Q), Line(R, Q))"
] | [
"RP",
"RQ",
"PQ"
] | {"R": [69.21827411167513, 195.33983177615931], "P": [0.0, 0.0], "Q": [2.999704316972206, 195.98551153163808]} | [] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.