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(K, I, P)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(S, N, D)), MeasureOf(angle 1))
- Equals(LengthOf(Line(N, S)), y-6)
- Equals(LengthOf(Line(E, O)), x+5)
- Equals(MeasureOf(Angle(I, J, E)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(F, L, G)), MeasureOf(angle 3))
- Eq... | 48 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(K, I, P)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(S, N, D)), MeasureOf(angle 1))",
"Equals(LengthOf(Line(N, S)), y-6)",
"Equals(LengthOf(Line(E, O)), x+5)",
"Equals(MeasureOf(Angle(I, J, E)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(F, L, G)), MeasureOf(angle 3))",
"E... | [
"BA",
"BC",
"BD",
"BH",
"BI",
"BJ",
"BP",
"BY",
"CI",
"CJ",
"CP",
"CY",
"DA",
"DF",
"DH",
"DL",
"DM",
"DN",
"EO",
"ES",
"FL",
"FM",
"FN",
"GK",
"HA",
"IG",
"IJ",
"IK",
"IL",
"IP",
"IY",
"JE",
"JN",
"JO",
"JP",
"JS",
"JY",
"LG",
"LK",
"LM"... | {"A": [384.0, 279.0], "B": [139.0, 278.0], "C": [138.0, 0.0], "D": [283.0, 279.0], "E": [1.0, 94.0], "F": [312.0, 28.0], "G": [384.0, 188.0], "H": [27.0, 278.0], "I": [138.0, 187.0], "J": [137.0, 93.0], "K": [27.0, 187.0], "L": [293.0, 188.0], "M": [275.0, 347.0], "N": [304.0, 93.0], "O": [24.0, 93.0], "P": [136.0, 25.... | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(K, L, N)), 18)
- Equals(MeasureOf(Angle(J, L, K)), 25)
- Equals(MeasureOf(Angle(N, L, M)), 20)
- Equals(LengthOf(Line(K, L)), LengthOf(Line(N, L)))
- Equals(LengthOf(Line(N, M)), LengthOf(Line(M, L)))
$\triangle K L N$ and $\triangle L M N$ are isosceles and $m \angle J K N... | 20 | [
"Isosceles(Triangle(K,L,N))",
"Isosceles(Triangle(L,M,N))",
"Equals(MeasureOf(Angle(J,K,N)),130)",
"Find(MeasureOf(Angle(L,N,M)))"
] | [
"Equals(MeasureOf(Angle(K, L, N)), 18)",
"Equals(MeasureOf(Angle(J, L, K)), 25)",
"Equals(MeasureOf(Angle(N, L, M)), 20)",
"Equals(LengthOf(Line(K, L)), LengthOf(Line(N, L)))",
"Equals(LengthOf(Line(N, M)), LengthOf(Line(M, L)))"
] | [
"KN",
"NM",
"ML",
"LJ",
"JK",
"KL",
"NL"
] | {"J": [5.0, 94.0], "K": [69.0, 3.0], "L": [55.0, 219.0], "M": [133.0, 134.0], "N": [138.0, 18.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(N, M)), 26)
- Equals(LengthOf(Line(P, Q)), 3x+5)
-
- PointLiesOnCircle(P, Circle(O, radius_0_0))
- PointLiesOnCircle(N, Circle(O, radius_0_0))
- PointLiesOnCircle(Q, Circle(O, radius_0_0))
- PointLiesOnCircle(M, Circle(O, radius_0_0))
Find $x$. | 7 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(N, M)), 26)",
"Equals(LengthOf(Line(P, Q)), 3x+5)",
"",
"PointLiesOnCircle(P, Circle(O, radius_0_0))",
"PointLiesOnCircle(N, Circle(O, radius_0_0))",
"PointLiesOnCircle(Q, Circle(O, radius_0_0))",
"PointLiesOnCircle(M, Circle(O, radius_0_0))"
] | [
"NM",
"PQ"
] | {"M": [30.0, 68.0], "N": [264.0, 77.0], "O": [143.0, 157.0], "P": [43.0, 260.0], "Q": [274.0, 221.0]} | [
"O"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), y)
- Equals(LengthOf(Line(A, C)), 14)
- Equals(MeasureOf(Angle(C, B, A)), 30)
- Equals(LengthOf(Line(A, B)), x)
- Perpendicular(Line(A, C), Line(A, B))
Find x | 14 \sqrt { 3 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(B, C)), y)",
"Equals(LengthOf(Line(A, C)), 14)",
"Equals(MeasureOf(Angle(C, B, A)), 30)",
"Equals(LengthOf(Line(A, B)), x)",
"Perpendicular(Line(A, C), Line(A, B))"
] | [
"AB",
"AC",
"BC"
] | {"A": [246.00245090713452, 137.66665670362954], "B": [1.3381596645304228, 138.9972703536672], "C": [245.33471380269293, 1.1877438329031804]} | [] |
Diagram Logic Form:
- PointLiesOnLine(C, Line(R, P))
- PointLiesOnLine(C, Line(S, Q))
- PointLiesOnCircle(R, Circle(C, radius_4_0))
- PointLiesOnCircle(S, Circle(C, radius_4_0))
- PointLiesOnCircle(Q, Circle(C, radius_4_0))
- PointLiesOnCircle(P, Circle(C, radius_4_0))
$P Q R S$ is a rhombus inscribed in a circle. Fin... | 45 | [
"InscribedIn(Rhombus(P,Q,R,S),Circle($))",
"Find(MeasureOf(Angle(Q,R,P)))"
] | [
"PointLiesOnLine(C, Line(R, P))",
"PointLiesOnLine(C, Line(S, Q))",
"PointLiesOnCircle(R, Circle(C, radius_4_0))",
"PointLiesOnCircle(S, Circle(C, radius_4_0))",
"PointLiesOnCircle(Q, Circle(C, radius_4_0))",
"PointLiesOnCircle(P, Circle(C, radius_4_0))"
] | [
"CP",
"QC",
"QP",
"RC",
"RP",
"RQ",
"RS",
"SC",
"SP",
"SQ"
] | {"C": [81.0, 82.0], "P": [69.0, 2.0], "Q": [162.0, 66.0], "R": [96.0, 161.0], "S": [2.0, 97.0]} | [
"C"
] |
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 y. | \frac { 15 } { 2 } | [
"Find(y)"
] | [
"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:
- PointLiesOnLine(E, Line(B, D))
- PointLiesOnLine(E, Line(A, C))
ABCD is a rhombus. If EB = 9, AB = 12 and $m\angle ABD = 55$ . Find $m\angle ACB$ | 35 | [
"Rhombus(A,B,C,D)",
"Equals(LengthOf(Line(E,B)),9)",
"Equals(LengthOf(Line(A,B)),12)",
"Equals(MeasureOf(Angle(A,B,D)),55)",
"Find(MeasureOf(Angle(A,C,B)))"
] | [
"PointLiesOnLine(E, Line(B, D))",
"PointLiesOnLine(E, Line(A, C))"
] | [
"BA",
"BD",
"BC",
"BE",
"AD",
"AC",
"AE",
"DC",
"DE",
"CE"
] | {"B": [243.1611090480451, 0.026497646449143986], "A": [1.099114777678551, 17.453155634667112], "D": [78.45017421921474, 225.77639322137333], "C": [320.54726647843233, 213.2402434543077], "E": [160.05631466857648, 113.92265214195517]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, B)), 39)
- Equals(LengthOf(Line(C, H)), 5x-8)
- Equals(LengthOf(Line(A, D)), y)
- Equals(LengthOf(Line(A, B)), 41)
- Equals(LengthOf(Line(D, C)), 72-3x)
- PointLiesOnLine(E, Line(A, B))
- PointLiesOnLine(D, Line(B, C))
- PointLiesOnCircle(D, Circle(A, radius_0_0))
- PointLi... | 12.6 | [
"Tangent(Line($),Circle($))",
"Find(y)"
] | [
"Equals(LengthOf(Line(D, B)), 39)",
"Equals(LengthOf(Line(C, H)), 5x-8)",
"Equals(LengthOf(Line(A, D)), y)",
"Equals(LengthOf(Line(A, B)), 41)",
"Equals(LengthOf(Line(D, C)), 72-3x)",
"PointLiesOnLine(E, Line(A, B))",
"PointLiesOnLine(D, Line(B, C))",
"PointLiesOnCircle(D, Circle(A, radius_0_0))",
"... | [
"AD",
"BC",
"CH",
"DB",
"DC"
] | {"A": [253.0, 92.0], "B": [486.0, 194.0], "C": [0.0, 197.0], "D": [249.0, 196.0], "E": [346.0, 131.0], "H": [204.0, 12.0]} | [
"A"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(J, K)), 2b+3)
- Equals(LengthOf(Line(J, M)), 3a)
- Equals(LengthOf(Line(L, K)), 21)
- Equals(MeasureOf(Angle(R, L, K)), 70)
- Equals(MeasureOf(Angle(M, L, J)), 30)
- Equals(LengthOf(Line(L, M)), 45)
- PointLiesOnLine(R, Line(L, J))
- PointLiesOnLine(R, Line(M, K))
Use paralle... | 21 | [
"Parallelogram(J,K,L,M)",
"Equals(LengthOf(Line(J,K)),2b+3)",
"Equals(LengthOf(Line(J,M)),3a)",
"Find(b)"
] | [
"Equals(LengthOf(Line(J, K)), 2b+3)",
"Equals(LengthOf(Line(J, M)), 3a)",
"Equals(LengthOf(Line(L, K)), 21)",
"Equals(MeasureOf(Angle(R, L, K)), 70)",
"Equals(MeasureOf(Angle(M, L, J)), 30)",
"Equals(LengthOf(Line(L, M)), 45)",
"PointLiesOnLine(R, Line(L, J))",
"PointLiesOnLine(R, Line(M, K))"
] | [
"JK",
"JM",
"JR",
"KR",
"LJ",
"LK",
"LM",
"LR",
"MK",
"MR"
] | {"J": [25.0, 1.0], "K": [299.0, 0.0], "L": [274.0, 144.0], "M": [1.0, 143.0], "R": [150.0, 72.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, A)), 2.5)
- PointLiesOnLine(C, Line(D, B))
- PointLiesOnLine(A, Line(C, F))
- PointLiesOnLine(C, Line(A, G))
- PointLiesOnLine(A, Line(F, G))
- PointLiesOnLine(C, Line(F, G))
- Perpendicular(Line(A, C), Line(C, B))
- Equals(LengthOf(Line(D, C)), LengthOf(Line(C, B)))
Accor... | 2.5 | [
"UseTheorem(Perpendicular_Bisector_Theorem)",
"Find(LengthOf(Line(A,B)))"
] | [
"Equals(LengthOf(Line(D, A)), 2.5)",
"PointLiesOnLine(C, Line(D, B))",
"PointLiesOnLine(A, Line(C, F))",
"PointLiesOnLine(C, Line(A, G))",
"PointLiesOnLine(A, Line(F, G))",
"PointLiesOnLine(C, Line(F, G))",
"Perpendicular(Line(A, C), Line(C, B))",
"Equals(LengthOf(Line(D, C)), LengthOf(Line(C, B)))"
] | [
"AF",
"AG",
"BA",
"BC",
"CA",
"CF",
"CG",
"DA",
"DB",
"DC",
"FG"
] | {"A": [402.0, 104.0], "B": [50.0, 208.0], "C": [50.0, 103.0], "D": [50.0, 0.0], "F": [555.0, 104.0], "G": [0.0, 103.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(X, C, D)), 18)
- Equals(LengthOf(Line(C, D)), 22)
- Equals(MeasureOf(Angle(X, D, C)), 105)
Find x. Round side measures to the nearest tenth. | 8.1 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(X, C, D)), 18)",
"Equals(LengthOf(Line(C, D)), 22)",
"Equals(MeasureOf(Angle(X, D, C)), 105)"
] | [
"CD",
"XC",
"DX"
] | {"C": [79.0, 1.0], "D": [61.0, 163.0], "X": [0.0, 174.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 13)
- Equals(LengthOf(Line(A, L)), 5)
- Equals(LengthOf(Line(B, N)), x)
- Equals(LengthOf(Line(C, N)), 7)
- Equals(LengthOf(Line(D, L)), 6)
- PointLiesOnLine(M, Line(A, B))
- PointLiesOnLine(L, Line(A, D))
- PointLiesOnLine(N, Line(B, C))
- PointLiesOnLine(P, Line(D, C... | 8 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), 13)",
"Equals(LengthOf(Line(A, L)), 5)",
"Equals(LengthOf(Line(B, N)), x)",
"Equals(LengthOf(Line(C, N)), 7)",
"Equals(LengthOf(Line(D, L)), 6)",
"PointLiesOnLine(M, Line(A, B))",
"PointLiesOnLine(L, Line(A, D))",
"PointLiesOnLine(N, Line(B, C))",
"PointLiesOnLine(P, Li... | [
"AB",
"AD",
"AL",
"AM",
"BC",
"BM",
"BN",
"CN",
"CP",
"DC",
"DL",
"DP"
] | {"A": [0.0, 54.0], "B": [260.0, 1.0], "C": [261.0, 281.0], "D": [15.0, 277.0], "L": [8.0, 165.0], "M": [106.0, 33.0], "N": [260.0, 157.0], "P": [131.0, 280.0], "Q": [132.0, 157.0]} | [
"Q"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(S, A, T)), 93)
- Equals(MeasureOf(Angle(R, A, S)), x)
- PointLiesOnCircle(S, Circle(A, radius_3_0))
- PointLiesOnCircle(T, Circle(A, radius_3_0))
- PointLiesOnCircle(R, Circle(A, radius_3_0))
- Equals(LengthOf(Line(S, R)), LengthOf(Line(T, S)))
Find $x$. | 93 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(S, A, T)), 93)",
"Equals(MeasureOf(Angle(R, A, S)), x)",
"PointLiesOnCircle(S, Circle(A, radius_3_0))",
"PointLiesOnCircle(T, Circle(A, radius_3_0))",
"PointLiesOnCircle(R, Circle(A, radius_3_0))",
"Equals(LengthOf(Line(S, R)), LengthOf(Line(T, S)))"
] | [
"SA",
"SR",
"TA",
"TS"
] | {"A": [147.0, 148.0], "R": [18.0, 77.0], "S": [86.0, 276.0], "T": [281.0, 197.0]} | [
"A"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, D, C)), x)
- Equals(MeasureOf(Angle(B, A, D)), x)
- Equals(MeasureOf(Angle(D, C, B)), 2x)
- Equals(MeasureOf(Angle(C, B, A)), 2x)
Find $m\angle C$ | 120 | [
"Find(MeasureOf(Angle(C)))"
] | [
"Equals(MeasureOf(Angle(A, D, C)), x)",
"Equals(MeasureOf(Angle(B, A, D)), x)",
"Equals(MeasureOf(Angle(D, C, B)), 2x)",
"Equals(MeasureOf(Angle(C, B, A)), 2x)"
] | [
"BA",
"CB",
"CD",
"DA"
] | {"A": [0.0, 80.0], "B": [48.0, 2.0], "C": [193.0, 3.0], "D": [236.0, 78.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, C, B)), 5x+21)
- Equals(MeasureOf(Angle(C, D, G)), 12x+6)
- PointLiesOnLine(C, Line(A, P))
- PointLiesOnLine(D, Line(C, B))
- PointLiesOnLine(C, Line(B, F))
- PointLiesOnLine(D, Line(B, F))
- PointLiesOnLine(C, Line(D, F))
- PointLiesOnLine(D, Line(E, G))
Find $x$ so tha... | 9 | [
"Parallel(Line(p),Line(q))",
"Find(x)"
] | [
"Equals(MeasureOf(Angle(A, C, B)), 5x+21)",
"Equals(MeasureOf(Angle(C, D, G)), 12x+6)",
"PointLiesOnLine(C, Line(A, P))",
"PointLiesOnLine(D, Line(C, B))",
"PointLiesOnLine(C, Line(B, F))",
"PointLiesOnLine(D, Line(B, F))",
"PointLiesOnLine(C, Line(D, F))",
"PointLiesOnLine(D, Line(E, G))"
] | [
"AC",
"AP",
"BD",
"BF",
"CB",
"CD",
"CF",
"CP",
"DE",
"DF",
"DG",
"EG"
] | {"A": [103.0, 0.0], "B": [410.0, 79.0], "C": [71.0, 79.0], "D": [339.0, 79.0], "E": [311.0, 147.0], "F": [0.0, 79.0], "G": [366.0, 15.0], "P": [48.0, 137.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, F, I)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(D, L, B)), 35)
- Equals(MeasureOf(Angle(B, A, G)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(G, A, E)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(E, J, I)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(H, B, F)), ... | 62 | [
"Find(MeasureOf(Angle(1)))"
] | [
"Equals(MeasureOf(Angle(B, F, I)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(D, L, B)), 35)",
"Equals(MeasureOf(Angle(B, A, G)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(G, A, E)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(E, J, I)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(H, B, F)), Me... | [
"AB",
"AC",
"AD",
"AE",
"AF",
"AG",
"AI",
"AJ",
"AK",
"AL",
"BC",
"BD",
"BE",
"BF",
"BG",
"BH",
"BJ",
"BL",
"CE",
"CG",
"CI",
"CJ",
"CK",
"CL",
"DF",
"DH",
"DI",
"DJ",
"DK",
"DL",
"EG",
"EJ",
"EL",
"FI",
"FJ",
"FL",
"GL",
"IJ",
"IK",
"IL"... | {"A": [413.0, 65.0], "B": [773.0, 255.0], "C": [1.0, 254.0], "D": [744.0, 22.0], "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": [399.0, 69.0], "K": [357.0, 87.0], "L": [424.0, 60.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(E, Line(A, C))
- PointLiesOnLine(E, Line(B, D))
$A B C D$ is a rectangle. If $A C=30-x$ and $B D=4 x-60$
find $x$ | 18 | [
"Rectangle(A,B,C,D)",
"Equals(LengthOf(Line(A,C)),30-x)",
"Equals(LengthOf(Line(B,D)),4x-60)",
"Find(x)"
] | [
"PointLiesOnLine(E, Line(A, C))",
"PointLiesOnLine(E, Line(B, D))"
] | [
"AB",
"AD",
"AC",
"AE",
"BD",
"BC",
"BE",
"DC",
"DE",
"CE"
] | {"A": [2.7551722341044638, 126.31887320292836], "B": [326.39530841120234, 127.56011768402897], "D": [0.0, 0.0], "C": [326.0869838556023, 1.5191631409757633], "E": [164.1376729906699, 64.44669368958819]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(K, D, J)), 4x)
- Equals(MeasureOf(Angle(A, M, D)), 56)
- Equals(MeasureOf(Angle(E, L, O)), 3y-11)
- Parallel(Line(P, J), Line(A, B))
- Parallel(Line(A, B), Line(O, G))
- Parallel(Line(P, J), Line(O, G))
- PointLiesOnLine(D, Line(J, P))
- PointLiesOnLine(M, Line(A, B))
- Poin... | 31 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(K, D, J)), 4x)",
"Equals(MeasureOf(Angle(A, M, D)), 56)",
"Equals(MeasureOf(Angle(E, L, O)), 3y-11)",
"Parallel(Line(P, J), Line(A, B))",
"Parallel(Line(A, B), Line(O, G))",
"Parallel(Line(P, J), Line(O, G))",
"PointLiesOnLine(D, Line(J, P))",
"PointLiesOnLine(M, Line(A, B))",
... | [
"PD",
"DJ",
"PJ",
"AM",
"MB",
"AB",
"OL",
"LG",
"OG",
"KD",
"DM",
"ML",
"LE",
"KM",
"DL",
"ME",
"KL",
"DE",
"KE"
] | {"A": [64.0, 143.0], "B": [221.0, 33.0], "D": [72.0, 63.0], "E": [276.0, 144.0], "G": [280.0, 65.0], "J": [161.0, 2.0], "K": [3.0, 35.0], "L": [205.0, 116.0], "M": [139.0, 89.0], "O": [127.0, 172.0], "P": [5.0, 108.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 11)
- Equals(LengthOf(Line(A, C)), x)
- Equals(LengthOf(Line(B, C)), 9)
- Perpendicular(Line(A, C), Line(B, C))
Find x. | 2 \sqrt { 10 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), 11)",
"Equals(LengthOf(Line(A, C)), x)",
"Equals(LengthOf(Line(B, C)), 9)",
"Perpendicular(Line(A, C), Line(B, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [1.3365059736820513, 0.0040719714712196264], "B": [329.513343144469, 1.332401275447637], "C": [129.15908273492826, 163.53751038682393]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 24)
- Equals(LengthOf(Line(C, B)), 10)
- Equals(LengthOf(Line(A, B)), 26)
- Perpendicular(Line(A, C), Line(C, B))
Express the ratio of $\sin A$ as a decimal to the nearest hundredth. | 0.38 | [
"Find(RatioOf(SinOf(Angle(A))))"
] | [
"Equals(LengthOf(Line(A, C)), 24)",
"Equals(LengthOf(Line(C, B)), 10)",
"Equals(LengthOf(Line(A, B)), 26)",
"Perpendicular(Line(A, C), Line(C, B))"
] | [
"AC",
"AB",
"CB"
] | {"A": [2.842170943040401e-14, 128.0], "C": [301.8951128955662, 0.8503432197901901], "B": [358.0, 129.0]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, C, P)), 57)
- Equals(MeasureOf(Angle(A, F, D)), 3x - 9)
- PointLiesOnLine(F, Line(A, B))
- PointLiesOnLine(C, Line(F, E))
- PointLiesOnLine(F, Line(C, D))
- PointLiesOnLine(C, Line(D, E))
- PointLiesOnLine(F, Line(D, E))
- PointLiesOnLine(C, Line(P, G))
Find $x$ so that ... | 44 | [
"Parallel(Line(p),Line(q))",
"Find(x)"
] | [
"Equals(MeasureOf(Angle(E, C, P)), 57)",
"Equals(MeasureOf(Angle(A, F, D)), 3x - 9)",
"PointLiesOnLine(F, Line(A, B))",
"PointLiesOnLine(C, Line(F, E))",
"PointLiesOnLine(F, Line(C, D))",
"PointLiesOnLine(C, Line(D, E))",
"PointLiesOnLine(F, Line(D, E))",
"PointLiesOnLine(C, Line(P, G))"
] | [
"AB",
"AF",
"BF",
"CD",
"CE",
"CG",
"CP",
"DE",
"FC",
"FD",
"FE",
"PG"
] | {"A": [334.0, 136.0], "B": [0.0, 136.0], "C": [153.0, 82.0], "D": [84.0, 189.0], "E": [206.0, 1.0], "F": [118.0, 136.0], "G": [0.0, 82.0], "P": [334.0, 82.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(Q, R)), 15)
- Equals(LengthOf(Line(P, Q)), 17)
- Equals(LengthOf(Line(P, R)), 8)
- Perpendicular(Line(Q, R), Line(P, R))
Express the ratio of $\tan Q$ as a decimal to the nearest hundredth. | 0.53 | [
"Find(RatioOf(TanOf(Angle(Q))))"
] | [
"Equals(LengthOf(Line(Q, R)), 15)",
"Equals(LengthOf(Line(P, Q)), 17)",
"Equals(LengthOf(Line(P, R)), 8)",
"Perpendicular(Line(Q, R), Line(P, R))"
] | [
"PQ",
"PR",
"QR"
] | {"P": [133.0, 318.0], "Q": [133.0, 0.3333333333333428], "R": [0.825264447428566, 244.09011237543288]} | [] |
Diagram Logic Form:
- PointLiesOnLine(A, Line(J, K))
- PointLiesOnLine(B, Line(J, L))
If $J L=27, B L=9,$ and $J K=18,$ find $J A$. | 12 | [
"Equals(LengthOf(Line(J,L)),27)",
"Equals(LengthOf(Line(B,L)),9)",
"Equals(LengthOf(Line(J,K)),18)",
"Find(LengthOf(Line(J,A)))"
] | [
"PointLiesOnLine(A, Line(J, K))",
"PointLiesOnLine(B, Line(J, L))"
] | [
"JB",
"JL",
"BL",
"JA",
"JK",
"AK",
"AB",
"KL"
] | {"A": [113.0, 71.0], "B": [153.0, 164.0], "J": [0.0, 164.0], "K": [196.0, 3.0], "L": [270.0, 164.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(Z, X, V)), 2x+65)
- Equals(MeasureOf(Angle(Y, X, W)), 4x+15)
- PointLiesOnLine(X, Line(W, Z))
- PointLiesOnLine(X, Line(Y, V))
- PointLiesOnCircle(W, Circle(X, radius_1_0))
- PointLiesOnCircle(Y, Circle(X, radius_1_0))
- PointLiesOnCircle(V, Circle(X, radius_1_0))
- PointLie... | 115 | [
"Find(MeasureOf(Angle(Z,X,V)))"
] | [
"Equals(MeasureOf(Angle(Z, X, V)), 2x+65)",
"Equals(MeasureOf(Angle(Y, X, W)), 4x+15)",
"PointLiesOnLine(X, Line(W, Z))",
"PointLiesOnLine(X, Line(Y, V))",
"PointLiesOnCircle(W, Circle(X, radius_1_0))",
"PointLiesOnCircle(Y, Circle(X, radius_1_0))",
"PointLiesOnCircle(V, Circle(X, radius_1_0))",
"Poin... | [
"XV",
"XW",
"XY",
"XZ",
"YV",
"ZW"
] | {"V": [177.0, 56.0], "W": [158.0, 141.0], "X": [96.0, 84.0], "Y": [20.0, 115.0], "Z": [35.0, 28.0]} | [
"X"
] |
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 $m\angle G$ | 107 | [
"Find(MeasureOf(Angle(G)))"
] | [
"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(MeasureOf(Angle(C, B, E)), 60)
- Equals(LengthOf(Line(E, A)), y)
- Equals(LengthOf(Line(C, B)), LengthOf(a))
- Equals(MeasureOf(Angle(C, A, B)), 30)
- Equals(LengthOf(Line(A, C)), LengthOf(b))
- PointLiesOnLine(E, Line(A, B))
- Perpendicular(Line(E, A), Line(E, C))
- Perpendicular(Line(E, C... | 14 \sqrt { 3 } | [
"Equals(x,7\\sqrt{3})",
"Find(a)"
] | [
"Equals(MeasureOf(Angle(C, B, E)), 60)",
"Equals(LengthOf(Line(E, A)), y)",
"Equals(LengthOf(Line(C, B)), LengthOf(a))",
"Equals(MeasureOf(Angle(C, A, B)), 30)",
"Equals(LengthOf(Line(A, C)), LengthOf(b))",
"PointLiesOnLine(E, Line(A, B))",
"Perpendicular(Line(E, A), Line(E, C))",
"Perpendicular(Line(... | [
"AB",
"AC",
"CB",
"EA",
"EB",
"EC"
] | {"A": [242.0, 139.0], "B": [2.0, 2.0], "C": [1.0, 140.0], "E": [60.0, 35.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 21)
- Equals(LengthOf(Line(S, C)), 17)
Find the area of the kite. | 178.5 | [
"Find(AreaOf(Kite($)))"
] | [
"Equals(LengthOf(Line(A, B)), 21)",
"Equals(LengthOf(Line(S, C)), 17)"
] | [
"AC",
"AS",
"CB",
"SB",
"AB",
"CS"
] | {"A": [72.0, 1.0], "B": [71.0, 184.0], "C": [2.0, 129.0], "S": [149.0, 130.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(M, L)), 17)
- Equals(LengthOf(Line(N, M)), 2x+7)
- Equals(LengthOf(Line(N, L)), 3x-4)
- Equals(LengthOf(Line(L, N)), LengthOf(Line(N, M)))
Find $MN$. | 29 | [
"Find(LengthOf(Line(L,N)))"
] | [
"Equals(LengthOf(Line(M, L)), 17)",
"Equals(LengthOf(Line(N, M)), 2x+7)",
"Equals(LengthOf(Line(N, L)), 3x-4)",
"Equals(LengthOf(Line(L, N)), LengthOf(Line(N, M)))"
] | [
"ML",
"NL",
"NM"
] | {"L": [2.0, 238.0], "M": [436.0, 1.0], "N": [267.0, 238.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(K, O, M)), MeasureOf(angle 6))
- Equals(MeasureOf(Angle(B, P, C)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(M, O, C)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(K, P, B)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(K, O, M)), MeasureOf(angle 3))
- Equals(MeasureOf(A... | 43 | [
"Equals(MeasureOf(Angle(3)),43)",
"Find(MeasureOf(Angle(7)))"
] | [
"Equals(MeasureOf(Angle(K, O, M)), MeasureOf(angle 6))",
"Equals(MeasureOf(Angle(B, P, C)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(M, O, C)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(K, P, B)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(K, O, M)), MeasureOf(angle 3))",
"Equals(MeasureOf(Ang... | [
"BF",
"BH",
"BP",
"GH",
"GJ",
"GN",
"HF",
"HJ",
"HN",
"KC",
"KO",
"KP",
"MN",
"MO",
"MQ",
"NJ",
"NQ",
"ON",
"OQ",
"PF",
"PH"
] | {"A": [412.0, 168.0], "B": [38.0, 3.0], "C": [396.0, 71.0], "F": [284.0, 225.0], "G": [93.0, 165.0], "H": [218.0, 166.0], "I": [449.0, 167.0], "J": [490.0, 165.0], "K": [0.0, 71.0], "M": [163.0, 2.0], "N": [347.0, 165.0], "O": [243.0, 73.0], "P": [113.0, 72.0], "Q": [412.0, 224.0], "R": [292.0, 166.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), x)
- Equals(MeasureOf(Angle(B, A, C)), 25)
- Equals(LengthOf(Line(B, C)), 15)
- Perpendicular(Line(A, B), Line(B, C))
Find x. | 32.2 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), x)",
"Equals(MeasureOf(Angle(B, A, C)), 25)",
"Equals(LengthOf(Line(B, C)), 15)",
"Perpendicular(Line(A, B), Line(B, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [0.0, -1.4210854715202004e-14], "B": [309.05801340867384, 61.34478581854079], "C": [278.4291596481377, 233.13498517807443]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 1.9)
- Equals(MeasureOf(Angle(C, B, A)), 25)
- Equals(LengthOf(Line(B, C)), 2.3)
- Perpendicular(Line(A,E), Line(C,B))
- PointLiesOnLine(E, Line(B,C))
Find the area of the triangle. Round to the nearest hundredth. | 0.92 | [
"Find(AreaOf(Triangle($)))"
] | [
"Equals(LengthOf(Line(A, B)), 1.9)",
"Equals(MeasureOf(Angle(C, B, A)), 25)",
"Equals(LengthOf(Line(B, C)), 2.3)",
"Perpendicular(Line(A,E), Line(C,B))",
"PointLiesOnLine(E, Line(B,C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [95.0, 0.0], "B": [321.0, 107.0], "C": [0.0, 109.0], "E": [97.0, 87.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), x)
- Equals(LengthOf(Line(F, K)), 15)
- Equals(AreaOf(Pentagon(A, D, B, O, C)), 272)
- Equals(AreaOf(Pentagon(F, G, H, J, K)), 153)
-
For the pair of similar figures, use the given areas to find $x$. | 20.0 | [
"Similar(Shape($1),Shape($2))",
"Find(x)"
] | [
"Equals(LengthOf(Line(A, C)), x)",
"Equals(LengthOf(Line(F, K)), 15)",
"Equals(AreaOf(Pentagon(A, D, B, O, C)), 272)",
"Equals(AreaOf(Pentagon(F, G, H, J, K)), 153)",
""
] | [
"AC",
"AD",
"BD",
"BO",
"OC"
] | {"A": [122.0, 66.0], "B": [1.0, 136.0], "C": [58.0, 1.0], "D": [122.0, 138.0], "O": [1.0, 65.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(L, B, D)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(D, B, F)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(B, F, M)), MeasureOf(angle 5))
- Equals(MeasureOf(Angle(G, B, L)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(M, F, T)), MeasureOf(angle 6))
- Equals(MeasureOf(A... | 75 | [
"Equals(MeasureOf(Angle(9)),75)",
"Find(MeasureOf(Angle(5)))"
] | [
"Equals(MeasureOf(Angle(L, B, D)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(D, B, F)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(B, F, M)), MeasureOf(angle 5))",
"Equals(MeasureOf(Angle(G, B, L)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(M, F, T)), MeasureOf(angle 6))",
"Equals(MeasureOf(Ang... | [
"BD",
"BG",
"BJ",
"BL",
"BT",
"CE",
"DG",
"FB",
"FI",
"FJ",
"FL",
"FM",
"FT",
"IM",
"JC",
"JE",
"JL",
"TJ",
"TL"
] | {"B": [56.0, 114.0], "C": [296.0, 243.0], "D": [57.0, 1.0], "E": [296.0, 39.0], "F": [207.0, 150.0], "G": [57.0, 208.0], "I": [208.0, 225.0], "J": [297.0, 172.0], "L": [0.0, 101.0], "M": [208.0, 19.0], "T": [366.0, 188.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(F, A, P)), 33)
- Equals(LengthOf(Line(A, B)), 10.9)
- Equals(LengthOf(Line(P, A)), 13)
- Equals(LengthOf(Line(E, P)), 14.9)
- Equals(MeasureOf(Angle(P, C, D)), 28.5)
- PointLiesOnLine(D, Line(E, C))
- PointLiesOnLine(H, Line(E, P))
- PointLiesOnLine(I, Line(E, P))
- PointLie... | 33 | [
"IsIncenterOf(Point(P),Triangle(A,E,C))",
"Find(MeasureOf(Angle(D,A,C)))"
] | [
"Equals(MeasureOf(Angle(F, A, P)), 33)",
"Equals(LengthOf(Line(A, B)), 10.9)",
"Equals(LengthOf(Line(P, A)), 13)",
"Equals(LengthOf(Line(E, P)), 14.9)",
"Equals(MeasureOf(Angle(P, C, D)), 28.5)",
"PointLiesOnLine(D, Line(E, C))",
"PointLiesOnLine(H, Line(E, P))",
"PointLiesOnLine(I, Line(E, P))",
"P... | [
"AB",
"AC",
"AD",
"AJ",
"AP",
"BC",
"BI",
"CD",
"EA",
"EB",
"EC",
"ED",
"EF",
"EH",
"EI",
"EJ",
"EP",
"FA",
"FC",
"FJ",
"FP",
"GA",
"GE",
"GF",
"GJ",
"HB",
"HI",
"HP",
"JD",
"JP",
"PB",
"PC",
"PD",
"PI"
] | {"A": [276.0, 2.0], "B": [357.0, 181.0], "C": [445.0, 380.0], "D": [219.0, 345.0], "E": [1.0, 311.0], "F": [143.0, 151.0], "G": [239.0, 54.0], "H": [80.0, 280.0], "I": [116.0, 267.0], "J": [262.0, 35.0], "P": [238.0, 223.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(L, K)), 3y)
- Equals(LengthOf(Line(L, J)), 7)
- Equals(LengthOf(Line(L, M)), 9x)
- Equals(LengthOf(Line(N, K)), 36)
- Equals(LengthOf(Line(N, J)), y+15)
- PointLiesOnLine(J, Line(N, L))
- PointLiesOnLine(J, Line(M, K))
If KLMN is a parallelogram, find the value of the indicat... | 4 | [
"Parallelogram(K,L,M,N)",
"Find(x)"
] | [
"Equals(LengthOf(Line(L, K)), 3y)",
"Equals(LengthOf(Line(L, J)), 7)",
"Equals(LengthOf(Line(L, M)), 9x)",
"Equals(LengthOf(Line(N, K)), 36)",
"Equals(LengthOf(Line(N, J)), y+15)",
"PointLiesOnLine(J, Line(N, L))",
"PointLiesOnLine(J, Line(M, K))"
] | [
"KJ",
"LJ",
"LK",
"LM",
"MJ",
"MK",
"NJ",
"NK",
"NL",
"NM"
] | {"J": [181.0, 72.0], "K": [0.0, 4.0], "L": [270.0, 1.0], "M": [359.0, 138.0], "N": [92.0, 142.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(N, A, P)), 120)
- Equals(MeasureOf(Angle(Q,A, P)), 100)
- PointLiesOnCircle(P, Circle(A, radius_0_0))
- PointLiesOnCircle(Q, Circle(A, radius_0_0))
- PointLiesOnCircle(N, Circle(A, radius_0_0))
Find $m \angle P$. | 70 | [
"Find(MeasureOf(Angle(P)))"
] | [
"Equals(MeasureOf(Angle(N, A, P)), 120)",
"Equals(MeasureOf(Angle(Q,A, P)), 100)",
"PointLiesOnCircle(P, Circle(A, radius_0_0))",
"PointLiesOnCircle(Q, Circle(A, radius_0_0))",
"PointLiesOnCircle(N, Circle(A, radius_0_0))"
] | [
"PN",
"PQ"
] | {"A": [160.0, 158.0], "N": [15.0, 95.0], "P": [286.0, 66.0], "Q": [229.0, 299.0]} | [
"A"
] |
Diagram Logic Form:
- PointLiesOnLine(Q, Line(T, U))
- PointLiesOnCircle(V, Circle(Q, radius_7_0))
- PointLiesOnCircle(T, Circle(Q, radius_7_0))
- PointLiesOnCircle(U, Circle(Q, radius_7_0))
If $QV=8$, what it the diameter of $\odot Q$. | 16 | [
"Equals(LengthOf(Line(Q,V)),8)",
"Find(DiameterOf(Circle(Q)))"
] | [
"PointLiesOnLine(Q, Line(T, U))",
"PointLiesOnCircle(V, Circle(Q, radius_7_0))",
"PointLiesOnCircle(T, Circle(Q, radius_7_0))",
"PointLiesOnCircle(U, Circle(Q, radius_7_0))"
] | [
"QV",
"TQ",
"TU",
"UQ"
] | {"Q": [194.0, 189.0], "T": [194.0, -0.0], "U": [196.0, 387.0], "V": [379.0, 139.0]} | [
"Q"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, G, H)), MeasureOf(angle 6))
- Equals(LengthOf(Line(H, G)), 1)
- Equals(LengthOf(Line(E, G)), 2)
- Equals(LengthOf(Line(B, E)), 2)
- Equals(MeasureOf(Angle(E, B, F)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(G, H, C)), MeasureOf(angle 8))
- Equals(MeasureOf(Angle(H, C,... | 77 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(MeasureOf(Angle(E, G, H)), MeasureOf(angle 6))",
"Equals(LengthOf(Line(H, G)), 1)",
"Equals(LengthOf(Line(E, G)), 2)",
"Equals(LengthOf(Line(B, E)), 2)",
"Equals(MeasureOf(Angle(E, B, F)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(G, H, C)), MeasureOf(angle 8))",
"Equals(MeasureOf(Angle(H, C... | [
"AC",
"AD",
"BE",
"BF",
"CH",
"DF",
"EG",
"HG"
] | {"A": [0.0, 264.0], "B": [266.0, 97.0], "C": [1.0, 0.0], "D": [360.0, 265.0], "E": [265.0, 32.0], "F": [362.0, 99.0], "G": [192.0, 29.0], "H": [194.0, 4.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 2x)
- Equals(LengthOf(Line(B, C)), 10)
- PointLiesOnLine(C, Line(A, X))
- Equals(LengthOf(Line(A, C)), LengthOf(Line(X, C)))
- Equals(LengthOf(Line(F, G)), x)
- Equals(LengthOf(Line(E, F)), 5)
- PointLiesOnLine(G, Line(E, H))
- Equals(LengthOf(Line(E, G)), LengthOf(Lin... | 5 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), 2x)",
"Equals(LengthOf(Line(B, C)), 10)",
"PointLiesOnLine(C, Line(A, X))",
"Equals(LengthOf(Line(A, C)), LengthOf(Line(X, C)))",
"Equals(LengthOf(Line(F, G)), x)",
"Equals(LengthOf(Line(E, F)), 5)",
"PointLiesOnLine(G, Line(E, H))",
"Equals(LengthOf(Line(E, G)), LengthOf... | [
"AB",
"AC",
"AX",
"BC",
"EG",
"EH",
"FE",
"FG",
"FH",
"GH",
"XB",
"XC"
] | {"A": [0.0, 93.0], "B": [61.0, 1.0], "C": [115.0, 93.0], "X": [228.0, 92.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(E, A)), y)
- Equals(LengthOf(Line(A, T)), 2x-5)
- Equals(LengthOf(Line(A, B)), 4z)
- Equals(LengthOf(Line(D, A)), 6)
- Equals(LengthOf(Line(F, A)), 4.6)
- Equals(LengthOf(Line(A, U)), 2.9)
- PointLiesOnLine(U, Line(F, D))
- PointLiesOnLine(T, Line(F, E))
- PointLiesOnLine(A, L... | 5.8 | [
"IsMidpointOf(Point(S),Line(D,E))",
"IsMidpointOf(Point(T),Line(E,F))",
"IsMidpointOf(Point(U),Line(D,F))",
"Find(y)"
] | [
"Equals(LengthOf(Line(E, A)), y)",
"Equals(LengthOf(Line(A, T)), 2x-5)",
"Equals(LengthOf(Line(A, B)), 4z)",
"Equals(LengthOf(Line(D, A)), 6)",
"Equals(LengthOf(Line(F, A)), 4.6)",
"Equals(LengthOf(Line(A, U)), 2.9)",
"PointLiesOnLine(U, Line(F, D))",
"PointLiesOnLine(T, Line(F, E))",
"PointLiesOnLi... | [
"AB",
"AT",
"AU",
"DA",
"DB",
"DE",
"DT",
"DU",
"EA",
"EB",
"ET",
"EU",
"FA",
"FB",
"FD",
"FE",
"FT",
"FU"
] | {"A": [193.0, 203.0], "B": [128.0, 151.0], "D": [1.0, 308.0], "E": [252.0, 1.0], "F": [327.0, 307.0], "T": [289.0, 151.0], "U": [162.0, 308.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 11)
- Equals(LengthOf(Line(B, C)), 25)
Find the area of the kite. | 137.5 | [
"Find(AreaOf(Kite($)))"
] | [
"Equals(LengthOf(Line(A, D)), 11)",
"Equals(LengthOf(Line(B, C)), 25)"
] | [
"AC",
"BA",
"BD",
"DC",
"AD"
] | {"A": [122.0, 2.0], "B": [183.0, 27.0], "C": [1.0, 80.0], "D": [146.0, 79.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 18)
- Equals(LengthOf(Line(A, C)), x)
- Equals(MeasureOf(Angle(A, B, C)), 25)
- Perpendicular(Line(A, B), Line(A, C))
Find x to the nearest hundredth. | 8.39 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), 18)",
"Equals(LengthOf(Line(A, C)), x)",
"Equals(MeasureOf(Angle(A, B, C)), 25)",
"Perpendicular(Line(A, B), Line(A, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [243.63531132924095, 1.347597441752427], "B": [0.0, 113.0], "C": [294.8504574243491, 114.3294628196106]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, D)), 27)
- Equals(LengthOf(Line(C, A)), b)
- Equals(LengthOf(Line(B, D)), 15)
- Equals(LengthOf(Line(C, B)), 28)
- PointLiesOnLine(A, Line(B, C))
- Equals(MeasureOf(Angle(B, D, A)), MeasureOf(Angle(A, D, C)))
Find $b$. | 18 | [
"Find(b)"
] | [
"Equals(LengthOf(Line(C, D)), 27)",
"Equals(LengthOf(Line(C, A)), b)",
"Equals(LengthOf(Line(B, D)), 15)",
"Equals(LengthOf(Line(C, B)), 28)",
"PointLiesOnLine(A, Line(B, C))",
"Equals(MeasureOf(Angle(B, D, A)), MeasureOf(Angle(A, D, C)))"
] | [
"BA",
"BC",
"BD",
"CA",
"CD",
"DA"
] | {"A": [221.0, 211.0], "B": [42.0, 303.0], "C": [542.0, 45.0], "D": [0.0, 0.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, H)), 11)
Find the area of the regular polygon. Round to the nearest tenth. | 584.2 | [
"Find(AreaOf(Regular(Polygon($))))"
] | [
"Equals(LengthOf(Line(B, H)), 11)"
] | [
"AD",
"AF",
"BG",
"BH",
"CE",
"DG",
"FC",
"HE"
] | {"A": [1.0, 134.0], "B": [189.0, 135.0], "C": [56.0, 1.0], "D": [57.0, 191.0], "E": [135.0, 2.0], "F": [2.0, 56.0], "G": [134.0, 191.0], "H": [191.0, 59.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 8)
- Equals(LengthOf(Line(A, B)), 25)
- Equals(LengthOf(Line(C, D)), x)
- Equals(LengthOf(Line(A, C)), z)
- Equals(LengthOf(Line(B, C)), y)
- PointLiesOnLine(A, Line(B, D))
- Perpendicular(Line(A, B), Line(A, C))
- Perpendicular(Line(C, D), Line(B, C))
Find y. | 5 \sqrt { 33 } | [
"Find(y)"
] | [
"Equals(LengthOf(Line(A, D)), 8)",
"Equals(LengthOf(Line(A, B)), 25)",
"Equals(LengthOf(Line(C, D)), x)",
"Equals(LengthOf(Line(A, C)), z)",
"Equals(LengthOf(Line(B, C)), y)",
"PointLiesOnLine(A, Line(B, D))",
"Perpendicular(Line(A, B), Line(A, C))",
"Perpendicular(Line(C, D), Line(B, C))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [71.0, 34.0], "B": [373.0, 179.0], "C": [1.0, 180.0], "D": [1.0, 1.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, A)), 8)
- Equals(LengthOf(Line(D, H)), x)
- Equals(MeasureOf(Angle(D, A, B)), 30)
- Equals(MeasureOf(Angle(A, B, C)), 45)
- Equals(LengthOf(Line(H, F)), 6)
- PointLiesOnLine(F, Line(A, B))
- PointLiesOnLine(H, Line(A, B))
- PointLiesOnLine(H, Line(A, F))
- PointLiesOnLine(F... | 4 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(D, A)), 8)",
"Equals(LengthOf(Line(D, H)), x)",
"Equals(MeasureOf(Angle(D, A, B)), 30)",
"Equals(MeasureOf(Angle(A, B, C)), 45)",
"Equals(LengthOf(Line(H, F)), 6)",
"PointLiesOnLine(F, Line(A, B))",
"PointLiesOnLine(H, Line(A, B))",
"PointLiesOnLine(H, Line(A, F))",
"PointLiesO... | [
"AB",
"AF",
"AH",
"BF",
"CB",
"CF",
"DA",
"DC",
"DH",
"HB",
"HF"
] | {"A": [0.0, 117.0], "B": [467.0, 116.0], "C": [359.0, 8.0], "D": [193.0, 7.0], "F": [357.0, 116.0], "H": [194.0, 117.0]} | [
""
] |
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... | 8.94 | [
"Circle(K)",
"Equals(LengthOf(Line(M,N)),16)",
"Equals(MeasureOf(Arc(M,N)),98)",
"Find(LengthOf(Line(L,N)))"
] | [
"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(MeasureOf(Angle(L, K, J)), 340)
- Equals(LengthOf(Major(Arc(L, J))), 56.37)
-
- PointLiesOnCircle(J, Circle(K, radius_4_0))
- PointLiesOnCircle(L, Circle(K, radius_4_0))
Find the radius of $\odot K$. Round to the nearest hundredth. | 19.00 | [
"Find(RadiusOf(Circle(K)))"
] | [
"Equals(MeasureOf(Angle(L, K, J)), 340)",
"Equals(LengthOf(Major(Arc(L, J))), 56.37)",
"",
"PointLiesOnCircle(J, Circle(K, radius_4_0))",
"PointLiesOnCircle(L, Circle(K, radius_4_0))"
] | [
"JK",
"JL",
"LK"
] | {"J": [116.0, 2.0], "K": [143.0, 142.0], "L": [163.0, 2.0]} | [
"K"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), x)
- Equals(MeasureOf(Angle(B, A, C)), 60)
- Equals(LengthOf(Line(B, C)), 15)
- Equals(LengthOf(Line(A, B)), y)
- Perpendicular(Line(A, C), Line(B, C))
Find y. | 10 \sqrt { 3 } | [
"Find(y)"
] | [
"Equals(LengthOf(Line(A, C)), x)",
"Equals(MeasureOf(Angle(B, A, C)), 60)",
"Equals(LengthOf(Line(B, C)), 15)",
"Equals(LengthOf(Line(A, B)), y)",
"Perpendicular(Line(A, C), Line(B, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [158.4745374135434, 0.6612991921679736], "B": [1.0, 268.0], "C": [0.6666666666666643, 0.0020833333333172277]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, A)), 9x-1)
- Equals(LengthOf(Line(C, A)), 4x+1)
- Equals(LengthOf(Line(C, B)), 5x-0.5)
- Equals(LengthOf(Line(C, A)), LengthOf(Line(B, C)))
Find the length of $CB$ in the isosceles triangle ABC. | 7 | [
"Isosceles(Triangle(A,B,C))",
"Find(LengthOf(Line(C,B)))"
] | [
"Equals(LengthOf(Line(B, A)), 9x-1)",
"Equals(LengthOf(Line(C, A)), 4x+1)",
"Equals(LengthOf(Line(C, B)), 5x-0.5)",
"Equals(LengthOf(Line(C, A)), LengthOf(Line(B, C)))"
] | [
"BA",
"CA",
"CB"
] | {"A": [0.0, 1.0], "B": [539.0, 1.0], "C": [273.0, 136.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 4)
- Equals(MeasureOf(Angle(C, A, B)), 37)
- Equals(LengthOf(Line(A, B)), 5)
- PointLiesOnLine(D, Line(A,B))
- Perpendicular(Line(C,D), Line(A,B))
-
Find the area of the triangle. Round to the nearest hundredth. | 6.02 | [
"Find(AreaOf(Triangle($)))"
] | [
"Equals(LengthOf(Line(A, C)), 4)",
"Equals(MeasureOf(Angle(C, A, B)), 37)",
"Equals(LengthOf(Line(A, B)), 5)",
"PointLiesOnLine(D, Line(A,B))",
"Perpendicular(Line(C,D), Line(A,B))",
""
] | [
"AB",
"AC",
"BC"
] | {"A": [2.0, 158.0], "B": [326.0, 158.0], "C": [207.0, 0.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(P, Q)), 11.1)
- Equals(MeasureOf(Angle(N, Q, P)), 83)
- Equals(LengthOf(Line(R, P)), 20)
- Equals(LengthOf(Line(M, N)), 3x-4)
- Equals(LengthOf(Line(P, N)), 2y+5)
- Equals(LengthOf(Line(N, Q)), 15.4)
- Equals(MeasureOf(Angle(Q, N, M)), 33)
- Equals(LengthOf(Line(M, N)), 3x-4)
... | 6.1 | [
"Parallelogram(M,N,P,R)",
"Find(z)"
] | [
"Equals(LengthOf(Line(P, Q)), 11.1)",
"Equals(MeasureOf(Angle(N, Q, P)), 83)",
"Equals(LengthOf(Line(R, P)), 20)",
"Equals(LengthOf(Line(M, N)), 3x-4)",
"Equals(LengthOf(Line(P, N)), 2y+5)",
"Equals(LengthOf(Line(N, Q)), 15.4)",
"Equals(MeasureOf(Angle(Q, N, M)), 33)",
"Equals(LengthOf(Line(M, N)), 3x... | [
"MN",
"MQ",
"NQ",
"PM",
"PN",
"PQ",
"RM",
"RN",
"RP",
"RQ"
] | {"M": [65.0, 0.0], "N": [260.0, 1.0], "P": [197.0, 166.0], "Q": [131.0, 83.0], "R": [0.0, 166.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(Y, X)), 4x+5)
- Equals(LengthOf(Line(W, Y)), 6x+3)
- Equals(LengthOf(Line(W, X)), 9x)
- Equals(LengthOf(Line(X, x)), LengthOf(Line(W, Y)))
- Equals(LengthOf(Line(W, Y)), LengthOf(Line(Y, X)))
Find the length of $XW$ | 9 | [
"Find(LengthOf(Line(W,Y)))"
] | [
"Equals(LengthOf(Line(Y, X)), 4x+5)",
"Equals(LengthOf(Line(W, Y)), 6x+3)",
"Equals(LengthOf(Line(W, X)), 9x)",
"Equals(LengthOf(Line(X, x)), LengthOf(Line(W, Y)))",
"Equals(LengthOf(Line(W, Y)), LengthOf(Line(Y, X)))"
] | [
"WX",
"WY",
"YX"
] | {"W": [0.0, 155.0], "X": [92.0, 1.0], "Y": [180.0, 156.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, A)), 3y-8)
- Equals(MeasureOf(Angle(F, B, A)), 20)
- Equals(LengthOf(Line(D, A)), 13)
- Equals(LengthOf(Line(B, C)), 2x+7)
- Equals(MeasureOf(Angle(B, F, C)), 49)
- Equals(MeasureOf(Angle(A, D, F)), 59)
- Equals(LengthOf(Line(D, C)), 10)
- PointLiesOnLine(F, Line(D, B))
- P... | 6 | [
"Parallelogram(A,B,C,D)",
"Find(y)"
] | [
"Equals(LengthOf(Line(B, A)), 3y-8)",
"Equals(MeasureOf(Angle(F, B, A)), 20)",
"Equals(LengthOf(Line(D, A)), 13)",
"Equals(LengthOf(Line(B, C)), 2x+7)",
"Equals(MeasureOf(Angle(B, F, C)), 49)",
"Equals(MeasureOf(Angle(A, D, F)), 59)",
"Equals(LengthOf(Line(D, C)), 10)",
"PointLiesOnLine(F, Line(D, B))... | [
"DB",
"DC",
"DA",
"DF",
"BC",
"BA",
"BF",
"CA",
"CF",
"AF"
] | {"D": [0.6777316735823149, 240.0], "B": [391.78928168839576, 0.6027205312470016], "C": [296.2613185887417, 239.18904318857386], "A": [97.31243783713673, 1.3959393100317925], "F": [196.76472404260394, 119.72046420903439]} | [] |
Diagram Logic Form:
- PointLiesOnLine(R, Line(U, S))
- PointLiesOnCircle(V, Circle(R, radius_0_0))
- PointLiesOnCircle(U, Circle(R, radius_0_0))
- PointLiesOnCircle(T, Circle(R, radius_0_0))
- PointLiesOnCircle(S, Circle(R, radius_0_0))
In $\odot R$, If $SU=16.2$, what is $RT$? | 8.1 | [
"Circle(R)",
"Equals(LengthOf(Line(S,U)),16.2)",
"Find(LengthOf(Line(R,T)))"
] | [
"PointLiesOnLine(R, Line(U, S))",
"PointLiesOnCircle(V, Circle(R, radius_0_0))",
"PointLiesOnCircle(U, Circle(R, radius_0_0))",
"PointLiesOnCircle(T, Circle(R, radius_0_0))",
"PointLiesOnCircle(S, Circle(R, radius_0_0))"
] | [
"RS",
"RT",
"RU",
"US",
"UV"
] | {"R": [166.0, 164.0], "S": [62.0, 37.0], "T": [256.0, 25.0], "U": [271.0, 296.0], "V": [3.0, 196.0]} | [
"R"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(F, G)), 24)
- Equals(LengthOf(Line(C, B)), x)
- Equals(AreaOf(Kite(A,B,C,D)), 846)
- Equals(AreaOf(Kite(E,F,G,H)), 376)
For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure. | \frac { 3 } { 2 } | [
"Similar(Shape($1),Shape($2))",
"Find(ScaleFactorOf(Blue(Shape($)),Green(Shape($))))"
] | [
"Equals(LengthOf(Line(F, G)), 24)",
"Equals(LengthOf(Line(C, B)), x)",
"Equals(AreaOf(Kite(A,B,C,D)), 846)",
"Equals(AreaOf(Kite(E,F,G,H)), 376)"
] | [
"AB",
"AD",
"BC",
"DC"
] | {"A": [2.0, 57.0], "B": [86.0, 143.0], "C": [131.0, 19.0], "D": [46.0, 1.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(O, Line(E, C))
- PointLiesOnLine(O, Line(A, B))
- PointLiesOnCircle(E, Circle(O, radius_0_0))
- PointLiesOnCircle(F, Circle(O, radius_0_0))
- PointLiesOnCircle(A, Circle(O, radius_0_0))
- PointLiesOnCircle(C, Circle(O, radius_0_0))
- PointLiesOnCircle(D, Circle(O, radius_0_0))
- Po... | 225 | [
"Circle(O)",
"IsDiameterOf(Line(E,C),Circle(O))",
"IsDiameterOf(Line(A,B),Circle(O))",
"Equals(Angle(B,O,D),Angle(D,O,E))",
"Equals(Angle(D,O,E),Angle(E,O,F))",
"Equals(Angle(E,O,F),Angle(F,O,A))",
"Find(MeasureOf(Arc(C,B,F)))"
] | [
"PointLiesOnLine(O, Line(E, C))",
"PointLiesOnLine(O, Line(A, B))",
"PointLiesOnCircle(E, Circle(O, radius_0_0))",
"PointLiesOnCircle(F, Circle(O, radius_0_0))",
"PointLiesOnCircle(A, Circle(O, radius_0_0))",
"PointLiesOnCircle(C, Circle(O, radius_0_0))",
"PointLiesOnCircle(D, Circle(O, radius_0_0))",
... | [
"AB",
"CE",
"OA",
"OB",
"OC",
"OD",
"OE",
"OF"
] | {"A": [28.0, 147.0], "B": [139.0, 29.0], "C": [146.0, 144.0], "D": [82.0, 2.0], "E": [26.0, 28.0], "F": [2.0, 89.0], "O": [85.0, 85.0]} | [
"O"
] |
Diagram Logic Form:
- PointLiesOnLine(K, Line(G, J))
In the figure, $ \overline{GK} \cong \overline{GH}$ and $ \overline{HK} \cong \overline{KJ}$. If $m \angle HGK=42$, find $m \angle HJK$. | 34.5 | [
"Equals(LengthOf(Line(G,K)),Line(G,H))",
"Equals(LengthOf(Line(H,K)),Line(K,J))",
"Equals(MeasureOf(Angle(H,G,K)),42)",
"Find(MeasureOf(Angle(H,J,K)))"
] | [
"PointLiesOnLine(K, Line(G, J))"
] | [
"GH",
"GJ",
"GK",
"HJ",
"HK",
"JK"
] | {"G": [0.0, 87.0], "H": [157.0, 3.0], "J": [217.0, 86.0], "K": [127.0, 86.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(U, Line(Z, X))
- PointLiesOnLine(U, Line(W, Y))
WXYZ is a kite. If $m\angle WXY = 13x + 24$, $m\angle WZY = 35$, and $m\angle ZWX = 13x + 14$, find $m\angle ZYX$. | 105 | [
"Kite(W,X,Y,Z)",
"Equals(MeasureOf(Angle(W,X,Y)),13x+24)",
"Equals(MeasureOf(Angle(W,Z,Y)),35)",
"Equals(MeasureOf(Angle(Z,W,X)),13x+14)",
"Find(MeasureOf(Angle(Z,Y,X)))"
] | [
"PointLiesOnLine(U, Line(Z, X))",
"PointLiesOnLine(U, Line(W, Y))"
] | [
"WU",
"WY",
"XU",
"XW",
"XY",
"YU",
"ZU",
"ZW",
"ZX",
"ZY"
] | {"U": [148.0, 91.0], "W": [146.0, 1.0], "X": [218.0, 91.0], "Y": [147.0, 180.0], "Z": [0.0, 90.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, C)), y+8)
- Equals(MeasureOf(Angle(C, D, A)), 4x)
- Equals(MeasureOf(Angle(D, A, B)), 2x-6)
- Equals(LengthOf(Line(A, B)), 5y)
Find $y$ in the given parallelogram | 2 | [
"Parallelogram($)",
"Find(y)"
] | [
"Equals(LengthOf(Line(D, C)), y+8)",
"Equals(MeasureOf(Angle(C, D, A)), 4x)",
"Equals(MeasureOf(Angle(D, A, B)), 2x-6)",
"Equals(LengthOf(Line(A, B)), 5y)"
] | [
"AB",
"AD",
"BC",
"DC"
] | {"A": [1.0, 211.0], "B": [326.0, 211.0], "C": [440.0, 1.0], "D": [114.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), 72)
- Equals(LengthOf(Line(A, C)), z)
- Equals(LengthOf(Line(B, P)), 8y)
- Equals(LengthOf(Line(A, P)), y)
- Equals(LengthOf(Line(A, B)), x)
- PointLiesOnLine(E, Line(A, C))
- PointLiesOnLine(P, Line(B, C))
- Perpendicular(Line(C, P), Line(P, D))
Find z | 4 \sqrt { 3 } | [
"Find(z)"
] | [
"Equals(LengthOf(Line(B, C)), 72)",
"Equals(LengthOf(Line(A, C)), z)",
"Equals(LengthOf(Line(B, P)), 8y)",
"Equals(LengthOf(Line(A, P)), y)",
"Equals(LengthOf(Line(A, B)), x)",
"PointLiesOnLine(E, Line(A, C))",
"PointLiesOnLine(P, Line(B, C))",
"Perpendicular(Line(C, P), Line(P, D))"
] | [
"AB",
"AC",
"AP",
"AD",
"AE",
"BC",
"BP",
"CP",
"CD",
"CE",
"PD",
"PE",
"DE"
] | {"A": [1.8378285904892877, 130.8609925956696], "B": [191.0, 134.0], "C": [0.015275722797611024, 1.3438903773609923], "P": [64.53019142902158, 45.636048526863085], "D": [16.546762589928058, 116.13669064748201], "E": [1.270321361058599, 112.31758034026464]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(F, B, D)), 120)
- Equals(MeasureOf(Angle(H, E, B)), 160)
- Equals(MeasureOf(Angle(E, A, D)), x)
- PointLiesOnLine(E, Line(A, B))
- PointLiesOnLine(G, Line(B, D))
- PointLiesOnLine(G, Line(E, C))
- PointLiesOnLine(B, Line(L, F))
- PointLiesOnLine(E, Line(G, H))
- PointLiesOnL... | 50 | [
"Parallel(Line(l),Line(m))",
"Find(x)"
] | [
"Equals(MeasureOf(Angle(F, B, D)), 120)",
"Equals(MeasureOf(Angle(H, E, B)), 160)",
"Equals(MeasureOf(Angle(E, A, D)), x)",
"PointLiesOnLine(E, Line(A, B))",
"PointLiesOnLine(G, Line(B, D))",
"PointLiesOnLine(G, Line(E, C))",
"PointLiesOnLine(B, Line(L, F))",
"PointLiesOnLine(E, Line(G, H))",
"Point... | [
"AB",
"AD",
"AE",
"BD",
"BE",
"BF",
"BG",
"BL",
"CH",
"DG",
"EC",
"EG",
"EH",
"GC",
"GH",
"LF"
] | {"A": [87.0, 83.0], "B": [301.0, 7.0], "C": [408.0, 61.0], "D": [212.0, 156.0], "E": [150.0, 61.0], "F": [407.0, 7.0], "G": [268.0, 61.0], "H": [0.0, 61.0], "L": [0.0, 7.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(E, Line(D, A))
- PointLiesOnLine(B, Line(A, C))
- Parallel(Line(E, B), Line(D, C))
If $AD=27,AB=8$, and $AE=12$, find $BC$. | 10 | [
"Equals(LengthOf(Line(A,D)),27)",
"Equals(LengthOf(Line(A,B)),8)",
"Equals(LengthOf(Line(A,E)),12)",
"Find(LengthOf(Line(B,C)))"
] | [
"PointLiesOnLine(E, Line(D, A))",
"PointLiesOnLine(B, Line(A, C))",
"Parallel(Line(E, B), Line(D, C))"
] | [
"AB",
"AC",
"AE",
"CB",
"DA",
"DC",
"DE",
"EB"
] | {"A": [1.0, 217.0], "B": [152.0, 59.0], "C": [207.0, 1.0], "D": [323.0, 218.0], "E": [238.0, 218.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), 32)
- Equals(LengthOf(Line(B, D)), y)
- Equals(MeasureOf(Angle(C, A, B)), 54)
- Equals(LengthOf(Line(C, D)), x)
- PointLiesOnLine(D, Line(A, C))
- Perpendicular(Line(B, D), Line(A, D))
- Equals(LengthOf(Line(B, C)), LengthOf(Line(A, B)))
Find y. Round to the nearest t... | 25.9 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(B, C)), 32)",
"Equals(LengthOf(Line(B, D)), y)",
"Equals(MeasureOf(Angle(C, A, B)), 54)",
"Equals(LengthOf(Line(C, D)), x)",
"PointLiesOnLine(D, Line(A, C))",
"Perpendicular(Line(B, D), Line(A, D))",
"Equals(LengthOf(Line(B, C)), LengthOf(Line(A, B)))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [201.0, 137.0], "B": [100.5696511732943, 1.0780175417517626], "C": [0.8290790972777557, 136.66747872881973], "D": [101.98916588158562, 137.25244582940792]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, D, H)), 3x)
- Equals(MeasureOf(Angle(H, D, E)), x)
- PointLiesOnLine(D, Line(A, E))
Find $x$. | 45 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(A, D, H)), 3x)",
"Equals(MeasureOf(Angle(H, D, E)), x)",
"PointLiesOnLine(D, Line(A, E))"
] | [
"AD",
"DE",
"DH"
] | {"A": [5.0, 9.0], "D": [161.0, 8.0], "E": [350.0, 10.0], "H": [260.0, 106.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, A, B)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(E, L, C)), 35)
- Equals(MeasureOf(Angle(C, H, G)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(G, H, F)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(F, J, B)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(I, C, A)), ... | 39 | [
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(C, A, B)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(E, L, C)), 35)",
"Equals(MeasureOf(Angle(C, H, G)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(G, H, F)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(F, J, B)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(I, C, A)), Me... | [
"AB",
"AC",
"AE",
"AH",
"AJ",
"AL",
"BD",
"BE",
"BH",
"BJ",
"BK",
"BL",
"CD",
"CE",
"CF",
"CG",
"CH",
"CI",
"CJ",
"CL",
"DF",
"DG",
"DK",
"EH",
"EI",
"EJ",
"EK",
"EL",
"FG",
"HD",
"HF",
"HG",
"HJ",
"HK",
"HL",
"JD",
"JF",
"JK",
"JL",
"LD"... | {"A": [906.0, 2.0], "B": [377.0, 80.0], "C": [773.0, 255.0], "D": [1.0, 254.0], "E": [744.0, 22.0], "F": [255.0, 255.0], "G": [410.0, 247.0], "H": [413.0, 65.0], "I": [761.0, 161.0], "J": [399.0, 69.0], "K": [357.0, 87.0], "L": [424.0, 60.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(L, G)), 3)
- Equals(LengthOf(Line(E, L)), 4)
- Equals(LengthOf(Line(G, O)), x)
- Equals(LengthOf(Line(E, S)), 9)
- PointLiesOnLine(G, Line(L, O))
- PointLiesOnCircle(E, Circle(B, radius_3_0))
- PointLiesOnCircle(O, Circle(B, radius_3_0))
- PointLiesOnCircle(S, Circle(B, radius... | 14.3 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(L, G)), 3)",
"Equals(LengthOf(Line(E, L)), 4)",
"Equals(LengthOf(Line(G, O)), x)",
"Equals(LengthOf(Line(E, S)), 9)",
"PointLiesOnLine(G, Line(L, O))",
"PointLiesOnCircle(E, Circle(B, radius_3_0))",
"PointLiesOnCircle(O, Circle(B, radius_3_0))",
"PointLiesOnCircle(S, Circle(B, ra... | [
"SL",
"ES",
"EG",
"EL",
"GO",
"LG",
"LO"
] | {"S": [187.0, 124.0], "B": [90.0, 102.0], "E": [160.0, 38.0], "G": [128.0, 14.0], "L": [155.0, 3.0], "O": [4.0, 67.0]} | [
"B"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), 5)
- Equals(LengthOf(Line(A, C)), 8x)
- Equals(LengthOf(Line(B, C)), 110x+53)
- Equals(LengthOf(Line(A, C)), 73)
- Equals(LengthOf(Line(A, B)), 150x+91)
A plane travels from Des Moines to Phoenix, on to Atlanta, and back to Des Moines, as shown below. Find the distanc... | 1153 | [
"Equals(PerimeterOf(Triangle(A,B,C)), 3482)",
"Find(LengthOf(C,B))"
] | [
"Equals(LengthOf(Line(B, C)), 5)",
"Equals(LengthOf(Line(A, C)), 8x)",
"Equals(LengthOf(Line(B, C)), 110x+53)",
"Equals(LengthOf(Line(A, C)), 73)",
"Equals(LengthOf(Line(A, B)), 150x+91)"
] | [
"AB",
"AC",
"BC"
] | {"A": [517.0, 161.0], "B": [1.0, 151.0], "C": [343.0, 1.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(V, W)), 3x-6)
- Equals(LengthOf(Line(Y, W)), 5)
- Equals(LengthOf(Line(Z, W)), 6)
- Equals(LengthOf(Line(W, X)), x+4)
- PointLiesOnLine(W, Line(Z, Y))
- PointLiesOnLine(W, Line(V, X))
Find VW | 12 | [
"Find(LengthOf(Line(V,W)))"
] | [
"Equals(LengthOf(Line(V, W)), 3x-6)",
"Equals(LengthOf(Line(Y, W)), 5)",
"Equals(LengthOf(Line(Z, W)), 6)",
"Equals(LengthOf(Line(W, X)), x+4)",
"PointLiesOnLine(W, Line(Z, Y))",
"PointLiesOnLine(W, Line(V, X))"
] | [
"VW",
"VX",
"WX",
"YW",
"YX",
"ZV",
"ZW",
"ZY"
] | {"V": [0.0, 0.0], "W": [149.0, 95.0], "X": [271.0, 173.0], "Y": [228.0, 28.0], "Z": [54.0, 179.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, E)), 4)
- Equals(LengthOf(Line(D, E)), 7)
- Equals(LengthOf(Line(Y, E)), 11)
- PointLiesOnLine(E, Line(A, C))
- PointLiesOnLine(E, Line(D, Y))
Find the area of the kite. | 72 | [
"Find(AreaOf(Kite($)))"
] | [
"Equals(LengthOf(Line(A, E)), 4)",
"Equals(LengthOf(Line(D, E)), 7)",
"Equals(LengthOf(Line(Y, E)), 11)",
"PointLiesOnLine(E, Line(A, C))",
"PointLiesOnLine(E, Line(D, Y))"
] | [
"AD",
"CD",
"CY",
"AY",
"AC",
"DY",
"AE",
"EC",
"DE",
"EY"
] | {"A": [118.0, 1.0], "C": [70.0, 124.0], "D": [4.0, 25.0], "Y": [244.0, 126.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, B, C)), 60)
- Equals(LengthOf(Line(B, C)), 2x+5)
- Equals(LengthOf(Line(B, A)), 3x-13)
- Equals(MeasureOf(Angle(B, C, D)), MeasureOf(Angle(B, D, C)))
- Equals(MeasureOf(Angle(B, A, D)), MeasureOf(Angle(B, D, A)))
Find $x$. | 18 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(D, B, C)), 60)",
"Equals(LengthOf(Line(B, C)), 2x+5)",
"Equals(LengthOf(Line(B, A)), 3x-13)",
"Equals(MeasureOf(Angle(B, C, D)), MeasureOf(Angle(B, D, C)))",
"Equals(MeasureOf(Angle(B, A, D)), MeasureOf(Angle(B, D, A)))"
] | [
"AB",
"AD",
"BC",
"BD",
"DC"
] | {"A": [211.0, 105.0], "B": [84.0, 2.0], "C": [1.0, 143.0], "D": [164.0, 144.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 2x+3)
- Equals(LengthOf(Line(J, D)), 4y)
- Equals(LengthOf(Line(A, C)), 8y-36)
- Equals(LengthOf(Line(B, J)), 5x)
Find $y$ so that each quadrilateral is a parallelogram. | 9 | [
"Parallelogram($)",
"Find(y)"
] | [
"Equals(LengthOf(Line(A, D)), 2x+3)",
"Equals(LengthOf(Line(J, D)), 4y)",
"Equals(LengthOf(Line(A, C)), 8y-36)",
"Equals(LengthOf(Line(B, J)), 5x)"
] | [
"AB",
"AD",
"AJ",
"BC",
"CA",
"CD",
"CJ",
"DB",
"JB",
"JD"
] | {"A": [60.0, 10.0], "B": [149.0, 96.0], "C": [1.0, 97.0], "D": [207.0, 9.0], "J": [104.0, 53.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, A, D)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(A, F, C)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(F, B, D)), 50)
- Equals(MeasureOf(Angle(G, F, D)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(E, G, F)), 120)
- Equals(MeasureOf(Angle(H, G, E)), MeasureOf(angle... | 128 | [
"Find(MeasureOf(Angle(1)))"
] | [
"Equals(MeasureOf(Angle(E, A, D)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(A, F, C)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(F, B, D)), 50)",
"Equals(MeasureOf(Angle(G, F, D)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(E, G, F)), 120)",
"Equals(MeasureOf(Angle(H, G, E)), MeasureOf(angle 4... | [
"AD",
"AE",
"AF",
"AG",
"DB",
"DF",
"EC",
"EG",
"FB",
"FC",
"FG",
"FH",
"GB",
"GC",
"GH",
"BC",
"BH",
"CH"
] | {"A": [347.0, 0.0], "B": [2.668304281417761, 152.0019777347379], "C": [603.7846342718385, 152.44708834706938], "D": [134.0, 309.0], "E": [525.0866788714857, 315.4867257182659], "F": [241.97619116041153, 152.3584832461636], "G": [433.2547647177885, 152.64185891069303], "H": [675.0, 153.0]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), x)
- Equals(MeasureOf(Angle(A, C, B)), 62)
- Equals(LengthOf(Line(A, C)), 60)
- Perpendicular(Line(A, B), Line(B, C))
Find x | 28.2 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(B, C)), x)",
"Equals(MeasureOf(Angle(A, C, B)), 62)",
"Equals(LengthOf(Line(A, C)), 60)",
"Perpendicular(Line(A, B), Line(B, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [0.0, 85.0], "B": [147.0, -7.105427357601002e-15], "C": [195.1922010718906, 83.66568102014415]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(F, C, E)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(C, F, B)), 70)
- Equals(MeasureOf(Angle(B, A, D)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(C, D, B)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(D, B, A)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(F, D, A)), ... | 55 | [
"Find(MeasureOf(Angle(1)))"
] | [
"Equals(MeasureOf(Angle(F, C, E)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(C, F, B)), 70)",
"Equals(MeasureOf(Angle(B, A, D)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(C, D, B)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(D, B, A)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(F, D, A)), 35... | [
"AB",
"AD",
"AE",
"AF",
"BD",
"BF",
"DC",
"DE",
"DF",
"EC",
"FC"
] | {"A": [39.0, 172.0], "B": [536.0, 307.0], "C": [255.0, 2.0], "D": [39.0, 307.0], "E": [40.0, 1.0], "F": [119.0, 194.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(G, A)), 12)
- Equals(LengthOf(Line(A, H)), 6)
- Equals(LengthOf(Line(A, F)), x)
- Equals(LengthOf(Line(A, E)), 5)
- PointLiesOnLine(A, Line(G, E))
- PointLiesOnLine(A, Line(F, H))
- PointLiesOnCircle(G, Circle(J, radius_5_0))
- PointLiesOnCircle(F, Circle(J, radius_5_0))
- Poi... | 10 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(G, A)), 12)",
"Equals(LengthOf(Line(A, H)), 6)",
"Equals(LengthOf(Line(A, F)), x)",
"Equals(LengthOf(Line(A, E)), 5)",
"PointLiesOnLine(A, Line(G, E))",
"PointLiesOnLine(A, Line(F, H))",
"PointLiesOnCircle(G, Circle(J, radius_5_0))",
"PointLiesOnCircle(F, Circle(J, radius_5_0))",... | [
"AE",
"AF",
"AH",
"FH",
"GA",
"GE"
] | {"A": [125.0, 129.0], "E": [138.0, 181.0], "F": [24.0, 158.0], "G": [90.0, -0.0], "H": [190.0, 110.0], "J": [96.0, 94.0]} | [
"J"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), 4x-17)
- Equals(MeasureOf(Angle(C, B, F)), 3y+5)
- Equals(MeasureOf(Angle(D, F, B)), 5y-13)
- Equals(LengthOf(Line(D, F)), 2x-1)
-
Find $y$ so that the quadrilateral is a parallelogram | 9 | [
"Parallelogram($)",
"Find(y)"
] | [
"Equals(LengthOf(Line(B, C)), 4x-17)",
"Equals(MeasureOf(Angle(C, B, F)), 3y+5)",
"Equals(MeasureOf(Angle(D, F, B)), 5y-13)",
"Equals(LengthOf(Line(D, F)), 2x-1)",
""
] | [
"BC",
"CF",
"FD",
"DB",
"BF"
] | {"B": [1.0, 0.0], "C": [334.0, 2.0], "D": [1.0, 202.0], "F": [335.0, 201.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(N, C, A)), MeasureOf(angle 8))
- Equals(MeasureOf(Angle(C, E, B)), 110)
- Equals(MeasureOf(Angle(A, E, C)), MeasureOf(angle 7))
- Equals(MeasureOf(Angle(C, A, B)), MeasureOf(angle 6))
- Equals(MeasureOf(Angle(N, E, D)), MeasureOf(angle 5))
- Equals(MeasureOf(Angle(E, A, H)),... | 20 | [
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(N, C, A)), MeasureOf(angle 8))",
"Equals(MeasureOf(Angle(C, E, B)), 110)",
"Equals(MeasureOf(Angle(A, E, C)), MeasureOf(angle 7))",
"Equals(MeasureOf(Angle(C, A, B)), MeasureOf(angle 6))",
"Equals(MeasureOf(Angle(N, E, D)), MeasureOf(angle 5))",
"Equals(MeasureOf(Angle(E, A, H)), M... | [
"AB",
"AC",
"AD",
"AE",
"AF",
"AG",
"AH",
"AI",
"AK",
"AL",
"AM",
"BD",
"BI",
"BK",
"BL",
"CE",
"CF",
"DI",
"DK",
"DL",
"EB",
"ED",
"EI",
"EK",
"EL",
"FJ",
"GD",
"GH",
"GM",
"HJ",
"HM",
"IK",
"IL",
"JM",
"KL",
"NA",
"NC",
"NE",
"NF",
"NG"... | {"A": [133.0, 186.0], "B": [476.0, 63.0], "C": [219.0, 0.0], "D": [23.0, 230.0], "E": [325.0, 120.0], "F": [73.0, 313.0], "G": [47.0, 155.0], "H": [531.0, 326.0], "I": [519.0, 49.0], "J": [556.0, 315.0], "K": [498.0, 57.0], "L": [3.0, 233.0], "M": [551.0, 339.0], "N": [484.0, 314.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), x)
- Equals(LengthOf(Line(C, D)), y)
- Equals(LengthOf(Line(A, C)), z)
- Equals(LengthOf(Line(B, D)), 12)
- Equals(LengthOf(Line(A, D)), 4)
- Perpendicular(Line(B, C), Line(A, C))
- Perpendicular(Line(C, D), Line(A, D))
Find y. | 4 \sqrt { 3 } | [
"Find(y)"
] | [
"Equals(LengthOf(Line(B, C)), x)",
"Equals(LengthOf(Line(C, D)), y)",
"Equals(LengthOf(Line(A, C)), z)",
"Equals(LengthOf(Line(B, D)), 12)",
"Equals(LengthOf(Line(A, D)), 4)",
"Perpendicular(Line(B, C), Line(A, C))",
"Perpendicular(Line(C, D), Line(A, D))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [361.1376140301252, 156.33479480470498], "B": [2.0047504670402816, 156.99722444622364], "C": [269.2113029719176, 1.1686769152841237], "D": [272.0, 151.0]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), y)
- Equals(LengthOf(Line(A, B)), 12)
- Equals(MeasureOf(Angle(A, C, B)), 60)
- PointLiesOnLine(B, Line(C, D))
- Perpendicular(Line(A, B), Line(B, D))
- Equals(LengthOf(Line(A, D)), LengthOf(Line(A, C)))
Find x | 8 \sqrt { 3 } | [
"Find(y)"
] | [
"Equals(LengthOf(Line(A, C)), y)",
"Equals(LengthOf(Line(A, B)), 12)",
"Equals(MeasureOf(Angle(A, C, B)), 60)",
"PointLiesOnLine(B, Line(C, D))",
"Perpendicular(Line(A, B), Line(B, D))",
"Equals(LengthOf(Line(A, D)), LengthOf(Line(A, C)))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [106.84239389295558, 0.5634498496363705], "B": [109.0, 185.0], "C": [1.3333333333333286, 185.0], "D": [212.66666666666666, 185.0]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(V, A, X)), p-nta5)
- Equals(LengthOf(Line(J, V)), 42)
- Equals(LengthOf(Line(Z, V)), 63)
- PointLiesOnLine(B, Line(X, A))
- PointLiesOnLine(A, Line(Z, V))
Polygons $FGHJK$ and $VWXUZ$ are similar regular pentagons. Find the scale factor. | 2:3 | [
"Similar(Pentagon(F,G,H,J,K),Pentagon(V,W,X,U,Z))",
"Find(ScaleFactorOf(Shape($1),Shape($2)))"
] | [
"Equals(MeasureOf(Angle(V, A, X)), p-nta5)",
"Equals(LengthOf(Line(J, V)), 42)",
"Equals(LengthOf(Line(Z, V)), 63)",
"PointLiesOnLine(B, Line(X, A))",
"PointLiesOnLine(A, Line(Z, V))"
] | [
"UX",
"UZ",
"XJ",
"XA",
"ZA",
"ZV",
"JV",
"VA",
"AB"
] | {"U": [235.0577695995351, 86.21638984391393], "J": [1.9489169091497018, 86.21144519883609], "A": [119.0, 223.24489795918367], "X": [118.5, 0.36974789915967676], "V": [46.328988655563606, 223.98648322471638], "Z": [191.7499393056567, 222.3316338917213], "B": [119.0, 121.0]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(L, J, E)), 84)
- Equals(MeasureOf(Angle(A, H, D)), 52)
- Equals(MeasureOf(Angle(B, J, A)), x)
- PointLiesOnLine(E, Line(A, B))
- PointLiesOnLine(L, Line(A, B))
- PointLiesOnLine(B, Line(A, C))
- PointLiesOnLine(E, Line(A, C))
- PointLiesOnLine(G, Line(A, C))
- PointLiesOnLin... | 20 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(L, J, E)), 84)",
"Equals(MeasureOf(Angle(A, H, D)), 52)",
"Equals(MeasureOf(Angle(B, J, A)), x)",
"PointLiesOnLine(E, Line(A, B))",
"PointLiesOnLine(L, Line(A, B))",
"PointLiesOnLine(B, Line(A, C))",
"PointLiesOnLine(E, Line(A, C))",
"PointLiesOnLine(G, Line(A, C))",
"PointLi... | [
"AB",
"AC",
"AD",
"AE",
"AF",
"AG",
"AH",
"AI",
"AJ",
"AK",
"AL",
"BC",
"BE",
"BF",
"BG",
"BI",
"BJ",
"BK",
"BL",
"CE",
"CF",
"CG",
"CK",
"CL",
"DF",
"DH",
"DI",
"DK",
"EF",
"EG",
"EJ",
"EK",
"EL",
"FG",
"FH",
"FI",
"FK",
"FL",
"GK",
"GL"... | {"A": [31.0, 158.0], "B": [122.0, 89.0], "C": [197.0, 34.0], "D": [129.0, 1.0], "E": [90.0, 114.0], "F": [0.0, 181.0], "G": [162.0, 60.0], "H": [97.0, 45.0], "I": [68.0, 86.0], "J": [56.0, 154.0], "K": [15.0, 160.0], "L": [78.0, 123.0]} | [
"B"
] |
Diagram Logic Form:
- PointLiesOnLine(Z, Line(Y, V))
- PointLiesOnLine(Z, Line(W, U))
- PointLiesOnCircle(V, Circle(Z, radius_1_0))
- PointLiesOnCircle(W, Circle(Z, radius_1_0))
- PointLiesOnCircle(Y, Circle(Z, radius_1_0))
- PointLiesOnCircle(U, Circle(Z, radius_1_0))
- PointLiesOnCircle(X, Circle(Z, radius_1_0))
In ... | 52 | [
"Circle(Z)",
"Equals(Angle(W,Z,X),Angle(X,Z,Y))",
"Equals(MeasureOf(Angle(V,Z,U)),4x)",
"Equals(MeasureOf(Angle(U,Z,Y)),2x+24)",
"IsDiameterOf(Line(V,Y),Circle($))",
"IsDiameterOf(Line(W,U),Circle($))",
"Find(MeasureOf(Arc(W,X)))"
] | [
"PointLiesOnLine(Z, Line(Y, V))",
"PointLiesOnLine(Z, Line(W, U))",
"PointLiesOnCircle(V, Circle(Z, radius_1_0))",
"PointLiesOnCircle(W, Circle(Z, radius_1_0))",
"PointLiesOnCircle(Y, Circle(Z, radius_1_0))",
"PointLiesOnCircle(U, Circle(Z, radius_1_0))",
"PointLiesOnCircle(X, Circle(Z, radius_1_0))"
] | [
"VY",
"VZ",
"WU",
"ZU",
"ZW",
"ZX",
"ZY"
] | {"U": [168.0, 88.0], "V": [66.0, 2.0], "W": [0.0, 83.0], "X": [33.0, 151.0], "Y": [107.0, 165.0], "Z": [84.0, 85.0]} | [
"Z"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, A)), 26)
- Equals(LengthOf(Line(E, F)), 8)
- Equals(MeasureOf(Angle(A, G, F)), 108)
- Equals(LengthOf(Line(D, A)), 12)
- Equals(LengthOf(Line(G, F)), 14)
- Equals(LengthOf(Line(D, G)), 4.5)
- PointLiesOnLine(E, Line(B, A))
- PointLiesOnLine(G, Line(D, A))
Polygon ABCD ~ po... | 7.5 | [
"Similar(Quadrilateral(A,B,C,D),Quadrilateral(A,E,F,G))",
"Equals(MeasureOf(Angle(A,G,F)),108)",
"Equals(LengthOf(Line(G,F)),14)",
"Equals(LengthOf(Line(A,D)),12)",
"Equals(LengthOf(Line(D,G)),4.5)",
"Equals(LengthOf(Line(E,F)),8)",
"Equals(LengthOf(Line(A,B)),26)",
"Find(LengthOf(Line(A,G)))"
] | [
"Equals(LengthOf(Line(B, A)), 26)",
"Equals(LengthOf(Line(E, F)), 8)",
"Equals(MeasureOf(Angle(A, G, F)), 108)",
"Equals(LengthOf(Line(D, A)), 12)",
"Equals(LengthOf(Line(G, F)), 14)",
"Equals(LengthOf(Line(D, G)), 4.5)",
"PointLiesOnLine(E, Line(B, A))",
"PointLiesOnLine(G, Line(D, A))"
] | [
"AE",
"AG",
"BA",
"BE",
"CB",
"CD",
"DA",
"DG",
"EF",
"GF"
] | {"A": [1.0, 27.0], "B": [250.0, 1.0], "C": [249.0, 133.0], "D": [37.0, 132.0], "E": [156.0, 9.0], "F": [159.0, 87.0], "G": [22.0, 89.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, E, D)), MeasureOf(angle 7))
- Equals(MeasureOf(Angle(D, F, B)), 63)
- Equals(MeasureOf(Angle(F, D, E)), 69)
- Equals(MeasureOf(Angle(F, B, D)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(B, D, F)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(E, D, G)), 47)
- Equals(Mea... | 32 | [
"Equals(MeasureOf(Angle(4)),MeasureOf(Angle(5)))",
"Find(MeasureOf(Angle(4)))"
] | [
"Equals(MeasureOf(Angle(C, E, D)), MeasureOf(angle 7))",
"Equals(MeasureOf(Angle(D, F, B)), 63)",
"Equals(MeasureOf(Angle(F, D, E)), 69)",
"Equals(MeasureOf(Angle(F, B, D)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(B, D, F)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(E, D, G)), 47)",
"Equals(Me... | [
"AB",
"AD",
"AF",
"BC",
"BD",
"BF",
"BG",
"CE",
"CG",
"DC",
"DE",
"DF",
"DG"
] | {"A": [226.0, 268.0], "B": [0.0, 139.0], "C": [438.0, 139.0], "D": [161.0, 139.0], "E": [292.0, 1.0], "F": [96.0, 8.0], "G": [570.0, 139.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(J, Line(L, G))
- PointLiesOnLine(G, Line(L, B))
- PointLiesOnLine(J, Line(L, B))
- PointLiesOnLine(K, Line(L, J))
- PointLiesOnLine(K, Line(L, G))
- PointLiesOnLine(K, Line(L, B))
- PointLiesOnLine(G, Line(J, B))
- PointLiesOnLine(I, Line(C, G))
- PointLiesOnLine(G, Line(F, H))
- P... | 2.5 | [
"IntersectAt(Circle(G),Circle(J),Circle(K),Point(L))",
"Equals(LengthOf(Line(G,H)),10)",
"Find(LengthOf(Line(J,K)))"
] | [
"PointLiesOnLine(J, Line(L, G))",
"PointLiesOnLine(G, Line(L, B))",
"PointLiesOnLine(J, Line(L, B))",
"PointLiesOnLine(K, Line(L, J))",
"PointLiesOnLine(K, Line(L, G))",
"PointLiesOnLine(K, Line(L, B))",
"PointLiesOnLine(G, Line(J, B))",
"PointLiesOnLine(I, Line(C, G))",
"PointLiesOnLine(G, Line(F, ... | [
"FH",
"GB",
"GF",
"GH",
"JB",
"JG",
"KB",
"KG",
"KJ",
"KL",
"LB",
"LG",
"LJ"
] | {"B": [9.0, 67.0], "C": [177.0, 169.0], "D": [176.0, 116.0], "F": [68.0, 213.0], "G": [110.0, 111.0], "H": [152.0, 10.0], "I": [160.0, 153.0], "J": [159.0, 134.0], "K": [185.0, 145.0], "L": [210.0, 154.0]} | [
"G",
"J",
"K"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 15)
- Equals(LengthOf(Line(B, D)), y)
- Equals(LengthOf(Line(A, C)), 19)
- Equals(LengthOf(Line(A, B)), x)
- Equals(LengthOf(Line(B, C)), z)
- PointLiesOnLine(A, Line(C, D))
- Perpendicular(Line(A, C), Line(A, B))
- Perpendicular(Line(B, D), Line(B, C))
Find x. | \sqrt { 285 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, D)), 15)",
"Equals(LengthOf(Line(B, D)), y)",
"Equals(LengthOf(Line(A, C)), 19)",
"Equals(LengthOf(Line(A, B)), x)",
"Equals(LengthOf(Line(B, C)), z)",
"PointLiesOnLine(A, Line(C, D))",
"Perpendicular(Line(A, C), Line(A, B))",
"Perpendicular(Line(B, D), Line(B, C))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [109.67633459436738, 98.35014712063892], "B": [0.4592633224537508, 215.50569334697258], "C": [242.3823064770932, 216.67140600315955], "D": [0.663770656302006, 1.9588715721017707]} | [] |
Diagram Logic Form:
- PointLiesOnLine(P, Line(M, K))
- PointLiesOnLine(Q, Line(M, N))
- PointLiesOnLine(R, Line(M, L))
- PointLiesOnLine(N, Line(K, L))
- PointLiesOnLine(Q, Line(R, P))
- Perpendicular(Line(K, N), Line(N, Q))
- Perpendicular(Line(M, R), Line(M, P))
If PR || KL, KN = 9, LN = 16, PM = 2 KP, find ML | 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)))"
] | [
"PointLiesOnLine(P, Line(M, K))",
"PointLiesOnLine(Q, Line(M, N))",
"PointLiesOnLine(R, Line(M, L))",
"PointLiesOnLine(N, Line(K, L))",
"PointLiesOnLine(Q, Line(R, P))",
"Perpendicular(Line(K, N), Line(N, Q))",
"Perpendicular(Line(M, R), Line(M, P))"
] | [
"MK",
"MR",
"MN",
"ML",
"MP",
"MQ",
"KN",
"KL",
"KP",
"RL",
"RP",
"RQ",
"NL",
"NQ",
"PQ"
] | {"M": [249.3379381877399, 251.00262860081872], "K": [499.99869834895844, 1.331994793395836], "R": [83.50150150150151, 84.00150150150151], "N": [249.99802374666012, 0.4999920949866379], "L": [0.0, 0.0], "P": [416.33335307565653, 84.99800405112472], "Q": [249.66601185756718, 84.4990000355017]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(P, N)), 8)
- Equals(LengthOf(Line(N, Q)), 12)
- Equals(LengthOf(Line(P, Q)), 20)
- Equals(LengthOf(Line(J, H)), 4x+7)
- Equals(LengthOf(Line(J, K)), 25)
- Equals(LengthOf(Line(K, H)), 6x-2)
- Equals(MeasureOf(Angle(H, J, K)), MeasureOf(Angle(P, Q, N)))
- Equals(MeasureOf(Angle... | 15 | [
"Find(LengthOf(Line(H,J)))"
] | [
"Equals(LengthOf(Line(P, N)), 8)",
"Equals(LengthOf(Line(N, Q)), 12)",
"Equals(LengthOf(Line(P, Q)), 20)",
"Equals(LengthOf(Line(J, H)), 4x+7)",
"Equals(LengthOf(Line(J, K)), 25)",
"Equals(LengthOf(Line(K, H)), 6x-2)",
"Equals(MeasureOf(Angle(H, J, K)), MeasureOf(Angle(P, Q, N)))",
"Equals(MeasureOf(A... | [
"KH",
"JH",
"JK",
"PN",
"NQ",
"PQ"
] | {"H": [2.0, 271.0], "K": [253.0, 272.0], "J": [100.0, 0.0], "P": [253.0, 80.0], "N": [400.0, 80.0], "Q": [330.0, 220.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(G, A, H)), 28)
- PointLiesOnCircle(A, Circle(B, radius_3_0))
- PointLiesOnCircle(G, Circle(B, radius_3_0))
- PointLiesOnCircle(H, Circle(B, radius_3_0))
Find the measure of $m \widehat{GH}$. | 56 | [
"Find(MeasureOf(Arc(G,H)))"
] | [
"Equals(MeasureOf(Angle(G, A, H)), 28)",
"PointLiesOnCircle(A, Circle(B, radius_3_0))",
"PointLiesOnCircle(G, Circle(B, radius_3_0))",
"PointLiesOnCircle(H, Circle(B, radius_3_0))"
] | [
"AG",
"AH"
] | {"A": [22.0, 178.0], "B": [111.0, 112.0], "G": [177.0, 22.0], "H": [222.0, 120.0]} | [
"B"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(J, K, H)), 36)
- Equals(MeasureOf(Angle(H, K, C)), 54)
- Equals(MeasureOf(Angle(A, J, K)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(K, H, A)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(F, H, K)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(F, C, G)), 120)
- PointLies... | 90 | [
"Parallel(Line(K,H),Line(J,I))",
"Find(MeasureOf(Angle(3)))"
] | [
"Equals(MeasureOf(Angle(J, K, H)), 36)",
"Equals(MeasureOf(Angle(H, K, C)), 54)",
"Equals(MeasureOf(Angle(A, J, K)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(K, H, A)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(F, H, K)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(F, C, G)), 120)",
"PointLie... | [
"AH",
"AD",
"AL",
"AJ",
"HC",
"HK",
"HD",
"HE",
"HF",
"HL",
"HJ",
"DL",
"DJ",
"LJ",
"JK",
"BC",
"BK",
"BG",
"BI",
"CK",
"CE",
"CF",
"CG",
"CI",
"KG",
"KI",
"GI",
"EF"
] | {"A": [258.8421052631579, 75.28947368421052], "B": [118.0, 48.0], "C": [60.28155339805825, 150.5], "H": [213.5701754385965, 148.33333333333331], "K": [147.19697918838656, 1.4260753910971715], "D": [237.5, 112.0], "E": [281.0, 150.0], "F": [0.0, 150.0], "G": [97.0, 83.0], "I": [110.64788732394366, 61.056338028169016], "... | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(R, C)), 26)
- Equals(LengthOf(Line(A, B)), 15)
- PointLiesOnLine(A, Line(V, R))
- PointLiesOnLine(B, Line(T, C))
For trapezoid $R S T V, A$ and $B$ are midpoints of the legs. Find $V T$. | 4 | [
"Trapezoid(R,S,T,V)",
"IsMidpointOf(Point(A),LegOf(Trapezoid(R,S,T,V)))",
"IsMidpointOf(Point(B),LegOf(Trapezoid(R,S,T,V)))",
"Find(LengthOf(Line(V,T)))"
] | [
"Equals(LengthOf(Line(R, C)), 26)",
"Equals(LengthOf(Line(A, B)), 15)",
"PointLiesOnLine(A, Line(V, R))",
"PointLiesOnLine(B, Line(T, C))"
] | [
"AB",
"CB",
"RA",
"RC",
"TB",
"TC",
"VA",
"VR",
"VT"
] | {"A": [45.0, 48.0], "B": [175.0, 52.0], "C": [222.0, 1.0], "R": [0.0, 0.0], "T": [129.0, 102.0], "V": [96.0, 103.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, B, C)), 7x-8)
- Equals(MeasureOf(Angle(B, C, A)), 5y-3)
- Equals(MeasureOf(Angle(D, A, C)), 5x)
- Equals(MeasureOf(Angle(A, D, B)), 4x+7)
- PointLiesOnLine(I, Line(D, B))
- PointLiesOnLine(I, Line(A, C))
- PointLiesOnCircle(D, Circle(J, radius_9_0))
- PointLiesOnCircle(B,... | 20 | [
"Find(MeasureOf(Angle(A)))"
] | [
"Equals(MeasureOf(Angle(D, B, C)), 7x-8)",
"Equals(MeasureOf(Angle(B, C, A)), 5y-3)",
"Equals(MeasureOf(Angle(D, A, C)), 5x)",
"Equals(MeasureOf(Angle(A, D, B)), 4x+7)",
"PointLiesOnLine(I, Line(D, B))",
"PointLiesOnLine(I, Line(A, C))",
"PointLiesOnCircle(D, Circle(J, radius_9_0))",
"PointLiesOnCircl... | [
"AC",
"AI",
"BC",
"BI",
"CJ",
"DA",
"DB",
"DI",
"IC",
"IJ"
] | {"A": [12.0, 133.0], "B": [171.0, 1.0], "C": [317.0, 208.0], "D": [242.0, 297.0], "I": [214.0, 183.0], "J": [167.0, 159.0]} | [
"J"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), 3y-4)
- Equals(MeasureOf(Angle(D, C, A)), 54)
- Equals(LengthOf(Line(B, A)), 5x)
- Equals(MeasureOf(Angle(C, A, D)), 49)
- Equals(LengthOf(Line(D, A)), 29)
- Equals(LengthOf(Line(D, C)), 25)
- Equals(MeasureOf(Angle(A, D, B)), 34)
- PointLiesOnLine(F, Line(B, D))
- Poi... | 34 | [
"Parallelogram(A,B,C,D)",
"Find(MeasureOf(Angle(F,B,C)))"
] | [
"Equals(LengthOf(Line(B, C)), 3y-4)",
"Equals(MeasureOf(Angle(D, C, A)), 54)",
"Equals(LengthOf(Line(B, A)), 5x)",
"Equals(MeasureOf(Angle(C, A, D)), 49)",
"Equals(LengthOf(Line(D, A)), 29)",
"Equals(LengthOf(Line(D, C)), 25)",
"Equals(MeasureOf(Angle(A, D, B)), 34)",
"PointLiesOnLine(F, Line(B, D))",... | [
"AC",
"AF",
"BA",
"BC",
"BD",
"BF",
"CF",
"DA",
"DC",
"DF"
] | {"A": [40.0, 146.0], "B": [0.0, 0.0], "C": [205.0, 1.0], "D": [244.0, 146.0], "F": [123.0, 73.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(Q, Line(W, A))
- PointLiesOnLine(X, Line(W, P))
- PointLiesOnLine(P, Line(H, A))
- PointLiesOnLine(X, Line(H, Q))
-
If $\overline{W P}$ is a median and an angle bisector, $A P=3 y+11$, $P H=7 y-5$, $m \angle H W P=x+12$, $m \angle P A W=3 x-2$, and $m \angle H W A=4 x-16$, find $... | 4 | [
"IsMedianOf(Line(W,P),Shape($))",
"BisectsAngle(Line(W,P),Angle($))",
"Equals(LengthOf(Line(A,P)),3y+11)",
"Equals(LengthOf(Line(P,H)),7y-5)",
"Equals(MeasureOf(Angle(H,W,P)),x+12)",
"Equals(MeasureOf(Angle(P,A,W)),3x-2)",
"Equals(MeasureOf(Angle(H,W,A)),4x-16)",
"Find(y)"
] | [
"PointLiesOnLine(Q, Line(W, A))",
"PointLiesOnLine(X, Line(W, P))",
"PointLiesOnLine(P, Line(H, A))",
"PointLiesOnLine(X, Line(H, Q))",
""
] | [
"HA",
"HP",
"HQ",
"PA",
"QA",
"WA",
"WH",
"WP",
"WQ",
"XH",
"XP",
"XQ",
"XW"
] | {"A": [210.0, 125.0], "H": [134.0, 1.0], "P": [172.0, 63.0], "Q": [161.0, 136.0], "W": [1.0, 167.0], "X": [148.0, 77.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(J, C, I)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(N, C, J)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(I, C, O)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(K, C, N)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(O, C, B)), MeasureOf(angle 6))
- Equals(MeasureOf(A... | 80 | [
"Equals(MeasureOf(Angle(11)),62)",
"Equals(MeasureOf(Angle(14)),38)",
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(J, C, I)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(N, C, J)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(I, C, O)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(K, C, N)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(O, C, B)), MeasureOf(angle 6))",
"Equals(MeasureOf(Ang... | [
"BC",
"BF",
"BH",
"BJ",
"BK",
"BM",
"CF",
"CG",
"CI",
"CJ",
"CN",
"CO",
"FJ",
"GI",
"HK",
"HM",
"KC",
"KG",
"KI",
"KM",
"NO"
] | {"B": [288.0, 254.0], "C": [204.0, 128.0], "F": [369.0, 376.0], "G": [119.0, 380.0], "H": [434.0, 253.0], "I": [244.0, 4.0], "J": [151.0, 47.0], "K": [160.0, 255.0], "M": [0.0, 253.0], "N": [5.0, 128.0], "O": [429.0, 128.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 8)
- Equals(LengthOf(Line(B, C)), 8)
- Equals(LengthOf(Line(A, C)), 14)
- Equals(LengthOf(Line(B, X)), x)
- PointLiesOnLine(X, Line(A, C))
- Perpendicular(Line(B, X), Line(C, X))
Find x | \sqrt { 15 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), 8)",
"Equals(LengthOf(Line(B, C)), 8)",
"Equals(LengthOf(Line(A, C)), 14)",
"Equals(LengthOf(Line(B, X)), x)",
"PointLiesOnLine(X, Line(A, C))",
"Perpendicular(Line(B, X), Line(C, X))"
] | [
"AB",
"AC",
"AX",
"BC",
"BX",
"CX"
] | {"A": [0.0, 111.0], "B": [112.0, 1.0], "C": [220.0, 110.0], "X": [113.0, 111.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 3.2)
- Equals(LengthOf(Line(A, C)), 1.1)
Find the perimeter or circumference of the figure. Round to the nearest tenth. | 8.6 | [
"Find(PerimeterOf(Shape($)))"
] | [
"Equals(LengthOf(Line(A, B)), 3.2)",
"Equals(LengthOf(Line(A, C)), 1.1)"
] | [
"AB",
"AC",
"BD",
"CD"
] | {"A": [0.0, 0.0], "B": [246.0, 1.0], "C": [2.0, 84.0], "D": [247.0, 85.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(J, M, E)), z)
- Equals(MeasureOf(Angle(K, I, P)), 4x+6)
- Equals(MeasureOf(Angle(I, L, R)), 2y+8)
- Equals(MeasureOf(Angle(R, L, P)), 142)
- PointLiesOnLine(M, Line(E, P))
- Parallel(Line(J,N), Line(H,K))
- Parallel(Line(B,R), Line(H,K))
Find $x$ in the figure. | 34 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(J, M, E)), z)",
"Equals(MeasureOf(Angle(K, I, P)), 4x+6)",
"Equals(MeasureOf(Angle(I, L, R)), 2y+8)",
"Equals(MeasureOf(Angle(R, L, P)), 142)",
"PointLiesOnLine(M, Line(E, P))",
"Parallel(Line(J,N), Line(H,K))",
"Parallel(Line(B,R), Line(H,K))"
] | [
"JM",
"JN",
"MN",
"HI",
"HK",
"IK",
"BL",
"BR",
"LR",
"EM",
"EI",
"EL",
"EP",
"MI",
"ML",
"MP",
"IL",
"IP",
"LP"
] | {"A": [283.0, 124.0], "B": [5.0, 223.0], "C": [133.0, 26.0], "D": [337.0, 221.0], "E": [354.0, 0.0], "F": [120.0, 125.0], "G": [244.0, 221.0], "H": [2.0, 125.0], "I": [195.0, 125.0], "J": [0.0, 28.0], "K": [361.0, 125.0], "L": [70.0, 223.0], "M": [320.0, 27.0], "N": [361.0, 27.0], "O": [267.0, 221.0], "P": [24.0, 259.0... | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, F, B)), 80)
- Equals(MeasureOf(Arc(B, C)), 110)
- Equals(MeasureOf(Arc(D, A)), x)
- PointLiesOnLine(F, Line(A, B))
- PointLiesOnLine(F, Line(C, D))
- PointLiesOnCircle(A, Circle(E, radius_4_0))
- PointLiesOnCircle(B, Circle(E, radius_4_0))
- PointLiesOnCircle(C, Circle(E,... | 50 | [
"Tangent(Line($),Circle($))",
"Find(x)"
] | [
"Equals(MeasureOf(Angle(C, F, B)), 80)",
"Equals(MeasureOf(Arc(B, C)), 110)",
"Equals(MeasureOf(Arc(D, A)), x)",
"PointLiesOnLine(F, Line(A, B))",
"PointLiesOnLine(F, Line(C, D))",
"PointLiesOnCircle(A, Circle(E, radius_4_0))",
"PointLiesOnCircle(B, Circle(E, radius_4_0))",
"PointLiesOnCircle(C, Circl... | [
"AB",
"AF",
"BF",
"CD",
"FC",
"FD"
] | {"A": [13.0, 35.0], "B": [81.0, 86.0], "C": [70.0, 6.0], "D": [9.0, 72.0], "E": [53.0, 50.0], "F": [31.0, 48.0]} | [
"E"
] |
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