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(T, M)), 10-2x)
- Equals(LengthOf(Line(M, J)), 12-3x)
- Equals(LengthOf(Line(I, L)), y+4/5)
- Equals(LengthOf(Line(L, C)), 2y-11/5)
- PointLiesOnLine(L, Line(J, C))
- PointLiesOnLine(T, Line(J, A))
- PointLiesOnLine(J, Line(N, T))
- PointLiesOnLine(J, Line(N, A))
- PointLiesOnL... | 2 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(T, M)), 10-2x)",
"Equals(LengthOf(Line(M, J)), 12-3x)",
"Equals(LengthOf(Line(I, L)), y+4/5)",
"Equals(LengthOf(Line(L, C)), 2y-11/5)",
"PointLiesOnLine(L, Line(J, C))",
"PointLiesOnLine(T, Line(J, A))",
"PointLiesOnLine(J, Line(N, T))",
"PointLiesOnLine(J, Line(N, A))",
"Point... | [
"CE",
"CI",
"CL",
"CO",
"CR",
"CU",
"IM",
"IP",
"IQ",
"JA",
"JC",
"JL",
"JN",
"JR",
"JT",
"JU",
"LM",
"LR",
"LS",
"LU",
"LV",
"MP",
"MQ",
"MS",
"MV",
"NA",
"NT",
"OE",
"OI",
"PQ",
"RU",
"SV",
"TA",
"TI",
"TM",
"TP",
"TQ"
] | {"A": [435.0, 79.0], "C": [122.0, 278.0], "I": [342.0, 278.0], "J": [117.0, 81.0], "L": [121.0, 179.0], "M": [291.0, 178.0], "N": [1.0, 80.0], "O": [435.0, 277.0], "P": [386.0, 353.0], "Q": [196.0, 3.0], "R": [118.0, 25.0], "S": [435.0, 178.0], "T": [238.0, 80.0], "U": [118.0, 335.0], "V": [1.0, 179.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(Q, Line(X, D))
- PointLiesOnLine(D, Line(X, T))
- PointLiesOnLine(Q, Line(X, T))
- PointLiesOnLine(D, Line(T, Q))
- PointLiesOnCircle(A, Circle(D, radius_2_0))
- PointLiesOnCircle(E, Circle(D, radius_2_0))
- PointLiesOnCircle(T, Circle(D, radius_2_0))
- PointLiesOnCircle(Q, Circle(... | 24 | [
"Equals(LengthOf(Line(E,X)),24)",
"Equals(LengthOf(Line(D,E)),7)",
"Find(LengthOf(Line(A,X)))"
] | [
"PointLiesOnLine(Q, Line(X, D))",
"PointLiesOnLine(D, Line(X, T))",
"PointLiesOnLine(Q, Line(X, T))",
"PointLiesOnLine(D, Line(T, Q))",
"PointLiesOnCircle(A, Circle(D, radius_2_0))",
"PointLiesOnCircle(E, Circle(D, radius_2_0))",
"PointLiesOnCircle(T, Circle(D, radius_2_0))",
"PointLiesOnCircle(Q, Cir... | [
"AD",
"DE",
"DQ",
"DT",
"TQ",
"XA",
"XD",
"XE",
"XQ",
"XT"
] | {"A": [336.0, 4.0], "D": [346.0, 57.0], "E": [330.0, 114.0], "Q": [290.0, 59.0], "T": [402.0, 60.0], "X": [2.0, 57.0]} | [
"D"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), 5)
- Equals(LengthOf(Line(T, C)), 5)
- PointLiesOnLine(D, Line(A, B))
- PointLiesOnCircle(A, Circle(D, radius_4_0))
- PointLiesOnCircle(B, Circle(D, radius_4_0))
One side of a square is a diameter of a circle. The length of one side of the square is 5 feet. To the nea... | 0.44 | [
"IsDiameterOf(SideOf(Square($)),Circle($))",
"Equals(SideOf(Square($)),5)",
"Shaded(Shape($))"
] | [
"Equals(LengthOf(Line(B, C)), 5)",
"Equals(LengthOf(Line(T, C)), 5)",
"PointLiesOnLine(D, Line(A, B))",
"PointLiesOnCircle(A, Circle(D, radius_4_0))",
"PointLiesOnCircle(B, Circle(D, radius_4_0))"
] | [
"DB",
"DA",
"AB",
"AT",
"BC",
"CT"
] | {"A": [58.0, 114.0], "B": [57.0, 1.0], "C": [172.0, 2.0], "D": [58.0, 56.0], "T": [171.0, 115.0]} | [
"D"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, A, B)), 50)
- Equals(MeasureOf(Angle(D, A, C)), x)
- PointLiesOnLine(A, Line(B, D))
Find x | 130 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(C, A, B)), 50)",
"Equals(MeasureOf(Angle(D, A, C)), x)",
"PointLiesOnLine(A, Line(B, D))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD"
] | {"A": [96.2873363305221, 103.66368588586619], "B": [295.0, 104.0], "C": [182.88227019160806, 1.8612822378527056], "D": [0.0, 103.0]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, J, C)), 2x)
- Equals(MeasureOf(Angle(J, C, A)), 96)
- Equals(MeasureOf(Angle(A, E, J)), 3y+44)
- Equals(MeasureOf(Angle(C, A, E)), 94)
- Parallel(Line(C,A), Line(J,E))
-
Find the value of the variable $x$ in the figure. | 42 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(E, J, C)), 2x)",
"Equals(MeasureOf(Angle(J, C, A)), 96)",
"Equals(MeasureOf(Angle(A, E, J)), 3y+44)",
"Equals(MeasureOf(Angle(C, A, E)), 94)",
"Parallel(Line(C,A), Line(J,E))",
""
] | [
"AC",
"AE",
"EJ",
"JC"
] | {"A": [14.0, 217.0], "C": [3.0, 47.0], "E": [329.0, 219.0], "J": [286.0, 1.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(U, V, W)), 3x-11)
- Equals(MeasureOf(Angle(V, U, Z)), x-8)
- Equals(MeasureOf(Angle(Y, W, V)), x+8)
- Equals(MeasureOf(Angle(U, Z, Y)), 2x+7)
- Equals(MeasureOf(Angle(Z, Y, W)), x)
Find $m\angle U$ | 60 | [
"Find(MeasureOf(Angle(U)))"
] | [
"Equals(MeasureOf(Angle(U, V, W)), 3x-11)",
"Equals(MeasureOf(Angle(V, U, Z)), x-8)",
"Equals(MeasureOf(Angle(Y, W, V)), x+8)",
"Equals(MeasureOf(Angle(U, Z, Y)), 2x+7)",
"Equals(MeasureOf(Angle(Z, Y, W)), x)"
] | [
"UV",
"VW",
"WY",
"YZ",
"ZU"
] | {"Z": [53.0, 308.0], "U": [1.0, 56.0], "V": [164.0, 1.0], "W": [330.0, 105.0], "Y": [328.0, 410.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(K, Line(J, M))
- PointLiesOnLine(L, Line(J, M))
- PointLiesOnLine(K, Line(J, L))
- PointLiesOnLine(L, Line(M, K))
- PointLiesOnLine(A, Line(K, F))
- PointLiesOnLine(B, Line(L, D))
In the figure consisting of squares $A$, $B$, and $C$, $JK = 2KL$ and $KL = 2LM$. If the perimeter of... | 189 | [
"Square(A)",
"Square(B)",
"Square(C)",
"Equals(LengthOf(Line(J,K)),Mul(Line(K,L),2))",
"Equals(LengthOf(Line(K,L)),Mul(Line(L,M),2))",
"Equals(PerimeterOf(Shape($)),66)",
"Find(AreaOf(Polygon($)))"
] | [
"PointLiesOnLine(K, Line(J, M))",
"PointLiesOnLine(L, Line(J, M))",
"PointLiesOnLine(K, Line(J, L))",
"PointLiesOnLine(L, Line(M, K))",
"PointLiesOnLine(A, Line(K, F))",
"PointLiesOnLine(B, Line(L, D))"
] | [
"JE",
"JM",
"JK",
"JL",
"EF",
"MK",
"ML",
"MG",
"KA",
"KF",
"KL",
"LD",
"LB",
"DA",
"DB",
"AF",
"BG"
] | {"J": [1.3283023697708813, 196.00386921463803], "D": [289.9986708019495, 99.96743464776252], "E": [0.6666921762200104, 0.005050891558880721], "A": [196.759975849388, 102.9752181788243], "F": [197.3383587153389, 1.9950256371010937], "M": [342.0, 197.0], "K": [197.99534808163747, 197.0789201642201], "L": [294.97397636385... | [] |
Diagram Logic Form:
- PointLiesOnLine(P, Line(Q, T))
- PointLiesOnLine(M, Line(R, S))
For trapezoid QRST, M and P are midpoints of the legs. If QR = 16, PM = 12, and TS = 4x, find x. | 2 | [
"Trapezoid(Q,R,S,T)",
"IsMidpointOf(Point(M),LegOf(Trapezoid(Q,R,S,T)))",
"IsMidpointOf(Point(P),LegOf(Trapezoid(Q,R,S,T)))",
"Equals(LengthOf(Line(Q,R)),16)",
"Equals(LengthOf(Line(P,M)),12)",
"Equals(LengthOf(Line(T,S)),4x)",
"Find(x)"
] | [
"PointLiesOnLine(P, Line(Q, T))",
"PointLiesOnLine(M, Line(R, S))"
] | [
"MS",
"PM",
"QP",
"QR",
"QT",
"RM",
"RS",
"TP",
"TS"
] | {"M": [172.0, 68.0], "P": [25.0, 70.0], "Q": [0.0, 0.0], "R": [197.0, 1.0], "S": [145.0, 140.0], "T": [50.0, 139.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(K, O, M)), MeasureOf(angle 6))
- Equals(MeasureOf(Angle(L, P, C)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(D, O, S)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(K, P, B)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(K, O, M)), MeasureOf(angle 3))
- Equals(MeasureOf(A... | 137 | [
"Equals(MeasureOf(Angle(3)),43)",
"Find(MeasureOf(Angle(16)))"
] | [
"Equals(MeasureOf(Angle(K, O, M)), MeasureOf(angle 6))",
"Equals(MeasureOf(Angle(L, P, C)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(D, O, S)), 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(R, S)), 6x+2)
- Equals(LengthOf(Line(R, T)), 4x+3)
- Equals(LengthOf(Line(R, W)), 12)
- Equals(LengthOf(Line(S, W)), 16)
- Equals(LengthOf(Line(T, W)), 9)
- PointLiesOnLine(W, Line(T, S))
- Perpendicular(Line(R, W), Line(T, W))
Find $RS$. | 20 | [
"Find(LengthOf(Line(R,S)))"
] | [
"Equals(LengthOf(Line(R, S)), 6x+2)",
"Equals(LengthOf(Line(R, T)), 4x+3)",
"Equals(LengthOf(Line(R, W)), 12)",
"Equals(LengthOf(Line(S, W)), 16)",
"Equals(LengthOf(Line(T, W)), 9)",
"PointLiesOnLine(W, Line(T, S))",
"Perpendicular(Line(R, W), Line(T, W))"
] | [
"RT",
"RS",
"RW",
"TS",
"TW",
"SW"
] | {"R": [256.19770407104005, 1.7512475828501408], "T": [434.07909604519773, 236.33333333333331], "S": [0.3629943502824631, 236.33333333333331], "W": [255.00840336134453, 237.0]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(E, B)), 10)
- Equals(LengthOf(Line(D, B)), 5\sqrt{2})
- Equals(LengthOf(Line(E, C)), 5 )
- Perpendicular(Line(E, B), Line(A, E))
- Perpendicular(Line(E, B), Line(D, B))
- Perpendicular(Line(C, E), Line(A, C))
- Perpendicular(Line(B, F), Line(D, F))
- Perpendicular(Line(A, E), ... | 45.7 | [
"Find(AreaOf(Shaded(Shape($))))"
] | [
"Equals(LengthOf(Line(E, B)), 10)",
"Equals(LengthOf(Line(D, B)), 5\\sqrt{2})",
"Equals(LengthOf(Line(E, C)), 5 )",
"Perpendicular(Line(E, B), Line(A, E))",
"Perpendicular(Line(E, B), Line(D, B))",
"Perpendicular(Line(C, E), Line(A, C))",
"Perpendicular(Line(B, F), Line(D, F))",
"Perpendicular(Line(A,... | [
"AC",
"AD",
"AE",
"BF",
"CE",
"DB",
"DF",
"EB"
] | {"A": [1.0, 152.0], "B": [211.0, 2.0], "C": [76.0, 76.0], "D": [209.0, 150.0], "E": [1.0, 1.0], "F": [137.0, 77.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(Z, Line(Y, V))
- PointLiesOnLine(Z, Line(W, U))
- PointLiesOnCircle(V, Circle(Z, radius_1_0))
- PointLiesOnCircle(W, Circle(Z, radius_1_0))
- PointLiesOnCircle(Y, Circle(Z, radius_1_0))
- PointLiesOnCircle(U, Circle(Z, radius_1_0))
- PointLiesOnCircle(X, Circle(Z, radius_1_0))
In ... | 76 | [
"Circle(Z)",
"Equals(Angle(W,Z,X),Angle(X,Z,Y))",
"Equals(MeasureOf(Angle(V,Z,U)),4x)",
"Equals(MeasureOf(Angle(U,Z,Y)),2x+24)",
"IsDiameterOf(Line(V,Y),Circle($))",
"IsDiameterOf(Line(W,U),Circle($))",
"Find(MeasureOf(Arc(W,V)))"
] | [
"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, C)), y)
- Equals(MeasureOf(Angle(B, C, A)), 60)
- Equals(LengthOf(Line(A, C)), 8)
- Equals(LengthOf(Line(A, B)), x)
- Perpendicular(Line(A, C), Line(A, B))
Find $y$. | 16 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(B, C)), y)",
"Equals(MeasureOf(Angle(B, C, A)), 60)",
"Equals(LengthOf(Line(A, C)), 8)",
"Equals(LengthOf(Line(A, B)), x)",
"Perpendicular(Line(A, C), Line(A, B))"
] | [
"AB",
"AC",
"BC"
] | {"A": [71.0, 116.0], "B": [251.0, 9.0], "C": [1.0, 1.0]} | [
""
] |
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... | 12.8 | [
"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(B,C)))"
] | [
"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(LengthOf(Line(O, B)), 20)
- Equals(LengthOf(Line(A, C)), 25)
- Equals(LengthOf(Line(A, N)), 21)
- PointLiesOnLine(N, Line(A, O))
- Perpendicular(Line(B, O), Line(N, O))
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary. | 92 | [
"Find(PerimeterOf(Parallelogram($)))"
] | [
"Equals(LengthOf(Line(O, B)), 20)",
"Equals(LengthOf(Line(A, C)), 25)",
"Equals(LengthOf(Line(A, N)), 21)",
"PointLiesOnLine(N, Line(A, O))",
"Perpendicular(Line(B, O), Line(N, O))"
] | [
"AC",
"AN",
"AO",
"CB",
"NB",
"NO",
"BO"
] | {"A": [1.0, 137.0], "B": [229.0, 1.0], "C": [93.0, 2.0], "N": [134.0, 137.0], "O": [149.0, 137.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 21)
- Equals(LengthOf(Line(C, D)), 7)
- PointLiesOnLine(D, Line(A, C))
- Perpendicular(Line(A, B), Line(B, D))
- Perpendicular(Line(B, D), Line(C, D))
Find the measure of the altitude drawn to the hypotenuse. | 7 \sqrt { 3 } | [
"Equals(Line($1,$3),HypotenuseOf(Triangle($1,$2,$3)))",
"Find(LengthOf(AltitudeOf(Triangle($1,$2,$3))))"
] | [
"Equals(LengthOf(Line(A, D)), 21)",
"Equals(LengthOf(Line(C, D)), 7)",
"PointLiesOnLine(D, Line(A, C))",
"Perpendicular(Line(A, B), Line(B, D))",
"Perpendicular(Line(B, D), Line(C, D))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [0.0, 106.0], "B": [183.0, 2.0], "C": [240.0, 103.0], "D": [179.0, 106.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 53)
- Equals(MeasureOf(Angle(C, A, B)), x)
- Equals(LengthOf(Line(B, C)), 68)
- Equals(MeasureOf(Angle(A, B, C)), 48)
Find x. Round the angle measure to the nearest degree. | 72 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, C)), 53)",
"Equals(MeasureOf(Angle(C, A, B)), x)",
"Equals(LengthOf(Line(B, C)), 68)",
"Equals(MeasureOf(Angle(A, B, C)), 48)"
] | [
"AB",
"AC",
"BC"
] | {"A": [1.3384414008875325, 0.12067809596783263], "B": [10.0, 189.0], "C": [166.72193233640894, 29.616714391770067]} | [] |
Diagram Logic Form:
- PointLiesOnLine(B, Line(G, E))
- PointLiesOnLine(B, Line(F, D))
- Perpendicular(Line(D, G), Line(G, F))
Quadrilateral DEFG is a rectangle. If DE = 14 + 2x and GF = 4(x - 3) + 6, find GF. | 34 | [
"Rectangle(D,E,F,G)",
"Equals(LengthOf(Line(D,E)),14+2x)",
"Equals(LengthOf(Line(G,F)),4(x-3)+6)",
"Find(LengthOf(Line(G,F)))"
] | [
"PointLiesOnLine(B, Line(G, E))",
"PointLiesOnLine(B, Line(F, D))",
"Perpendicular(Line(D, G), Line(G, F))"
] | [
"BE",
"DB",
"DE",
"FB",
"FD",
"FE",
"GB",
"GD",
"GE",
"GF"
] | {"B": [211.0, 90.0], "D": [1.0, 0.0], "E": [417.0, 2.0], "F": [418.0, 179.0], "G": [1.0, 179.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 14)
- Equals(MeasureOf(Angle(C, A, B)), 45)
- Equals(LengthOf(Line(B, C)), x)
- Equals(LengthOf(Line(A, C)), x)
- Perpendicular(Line(B, C), Line(A, C))
Find x. | 7 \sqrt { 2 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), 14)",
"Equals(MeasureOf(Angle(C, A, B)), 45)",
"Equals(LengthOf(Line(B, C)), x)",
"Equals(LengthOf(Line(A, C)), x)",
"Perpendicular(Line(B, C), Line(A, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [255.21213561470216, 47.64432826362484], "B": [0.0, 1.0], "C": [105.67201131808535, 150.54020278236266]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(X, W, Z)), 105)
- Equals(LengthOf(Line(Y, X)), 24)
- Equals(LengthOf(Line(Z, Y)), 28)
Use parallelogram WXYZ to find $WZ$ | 24 | [
"Parallelogram(W,X,Y,Z)",
"Find(LengthOf(Line(W,Z)))"
] | [
"Equals(MeasureOf(Angle(X, W, Z)), 105)",
"Equals(LengthOf(Line(Y, X)), 24)",
"Equals(LengthOf(Line(Z, Y)), 28)"
] | [
"ZW",
"ZY",
"WX",
"YX"
] | {"Z": [1.0, 177.0], "W": [84.0, 3.0], "X": [334.0, 1.0], "Y": [251.0, 175.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, E)), 7)
- Equals(LengthOf(Line(E, D)), x)
- PointLiesOnCircle(B, Circle(C, radius_2_0))
- PointLiesOnCircle(E, Circle(C, radius_2_0))
- Perpendicular(Line(C, E), Line(E, D))
- Perpendicular(Line(C, B), Line(B, D))
Find x. Assume that segments that appear to be tangent are ... | 7 | [
"Tangent(Line($),Circle($))",
"Find(x)"
] | [
"Equals(LengthOf(Line(C, E)), 7)",
"Equals(LengthOf(Line(E, D)), x)",
"PointLiesOnCircle(B, Circle(C, radius_2_0))",
"PointLiesOnCircle(E, Circle(C, radius_2_0))",
"Perpendicular(Line(C, E), Line(E, D))",
"Perpendicular(Line(C, B), Line(B, D))"
] | [
"CB",
"CE",
"DB",
"DE"
] | {"B": [102.0, 201.0], "C": [101.0, 100.0], "D": [2.0, 201.0], "E": [0.0, 99.0]} | [
"C"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(G, K, F)), MeasureOf(angle 16))
- Equals(MeasureOf(Angle(F, K, A)), MeasureOf(angle 15))
- Equals(MeasureOf(Angle(G, A, J)), MeasureOf(angle 14))
- Equals(MeasureOf(Angle(H, K, G)), MeasureOf(angle 9))
- Equals(MeasureOf(Angle(J, A, M)), MeasureOf(angle 13))
- Equals(Measure... | 57 | [
"Equals(MeasureOf(Angle(1)),123)",
"Find(MeasureOf(Angle(4)))"
] | [
"Equals(MeasureOf(Angle(G, K, F)), MeasureOf(angle 16))",
"Equals(MeasureOf(Angle(F, K, A)), MeasureOf(angle 15))",
"Equals(MeasureOf(Angle(G, A, J)), MeasureOf(angle 14))",
"Equals(MeasureOf(Angle(H, K, G)), MeasureOf(angle 9))",
"Equals(MeasureOf(Angle(J, A, M)), MeasureOf(angle 13))",
"Equals(MeasureOf... | [
"AD",
"AG",
"AI",
"AJ",
"AK",
"AM",
"AO",
"AP",
"AQ",
"AS",
"AV",
"AW",
"BF",
"BH",
"BL",
"BT",
"BU",
"CE",
"CN",
"CR",
"DG",
"DK",
"DM",
"DO",
"DP",
"DV",
"DW",
"EN",
"ER",
"FH",
"FT",
"FU",
"GK",
"GM",
"GO",
"GP",
"GV",
"GW",
"HT",
"HU"... | {"A": [233.0, 125.0], "B": [87.0, 140.0], "C": [186.0, 219.0], "D": [152.0, 109.0], "E": [329.0, 259.0], "F": [86.0, 0.0], "G": [2.0, 64.0], "H": [85.0, 295.0], "I": [234.0, 307.0], "J": [233.0, 15.0], "K": [84.0, 87.0], "L": [118.0, 197.0], "M": [331.0, 158.0], "N": [0.0, 165.0], "O": [181.0, 116.0], "P": [136.0, 101.... | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, I)), 15)
- Equals(LengthOf(Line(C, A)), 10)
- Equals(MeasureOf(Angle(A, C, I)), 45)
Find the area of the parallelogram. Round to the nearest tenth if necessary. | 106.1 | [
"Find(AreaOf(Parallelogram($)))"
] | [
"Equals(LengthOf(Line(C, I)), 15)",
"Equals(LengthOf(Line(C, A)), 10)",
"Equals(MeasureOf(Angle(A, C, I)), 45)"
] | [
"AB",
"AC",
"BI",
"CI"
] | {"A": [248.0, 118.0], "B": [1.0, 117.0], "C": [367.0, 1.0], "I": [117.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(T,V,U)), 23)
- PointLiesOnCircle(V, Circle(D, radius_0_0))
- PointLiesOnCircle(T, Circle(D, radius_0_0))
- PointLiesOnCircle(U, Circle(D, radius_0_0))
Find $m \widehat{TU}$. | 46 | [
"Find(MeasureOf(Arc(T,U)))"
] | [
"Equals(MeasureOf(Angle(T,V,U)), 23)",
"PointLiesOnCircle(V, Circle(D, radius_0_0))",
"PointLiesOnCircle(T, Circle(D, radius_0_0))",
"PointLiesOnCircle(U, Circle(D, radius_0_0))"
] | [
"VT",
"VU"
] | {"D": [231.0, 226.0], "T": [59.0, 362.0], "U": [205.0, 421.0], "V": [115.0, 24.0]} | [
"D"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 27)
- Equals(LengthOf(Line(B, A)), 2x+5)
- Equals(LengthOf(Line(B, C)), 3x-4)
- Equals(LengthOf(Line(B, A)), LengthOf(Line(B, C)))
Find $BC$. | 23 | [
"Find(LengthOf(Line(B,C)))"
] | [
"Equals(LengthOf(Line(A, C)), 27)",
"Equals(LengthOf(Line(B, A)), 2x+5)",
"Equals(LengthOf(Line(B, C)), 3x-4)",
"Equals(LengthOf(Line(B, A)), LengthOf(Line(B, C)))"
] | [
"BA",
"BC",
"AC"
] | {"B": [130.9832285115304, 190.00590813798362], "A": [1.2323029956115477, 1.1560770845258475], "C": [349.0, 191.0]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(W, A, X)), MeasureOf(angle 11))
- Equals(MeasureOf(Angle(A, W, Y)), MeasureOf(angle 7))
- Equals(MeasureOf(Angle(W, Y, A)), MeasureOf(angle 6))
- Equals(MeasureOf(Angle(X, W, Z)), MeasureOf(angle 8))
- Equals(MeasureOf(Angle(X, A, Z)), MeasureOf(angle 10))
- Equals(MeasureOf... | 30 | [
"Rectangle(W,X,Z,Y)",
"Equals(MeasureOf(Angle(1)),30)",
"Find(MeasureOf(Angle(8)))"
] | [
"Equals(MeasureOf(Angle(W, A, X)), MeasureOf(angle 11))",
"Equals(MeasureOf(Angle(A, W, Y)), MeasureOf(angle 7))",
"Equals(MeasureOf(Angle(W, Y, A)), MeasureOf(angle 6))",
"Equals(MeasureOf(Angle(X, W, Z)), MeasureOf(angle 8))",
"Equals(MeasureOf(Angle(X, A, Z)), MeasureOf(angle 10))",
"Equals(MeasureOf(A... | [
"WA",
"XA",
"XW",
"YA",
"YW",
"YX",
"ZA",
"ZW",
"ZX",
"ZY"
] | {"A": [156.0, 81.0], "W": [1.0, 0.0], "X": [312.0, 1.0], "Y": [2.0, 160.0], "Z": [311.0, 161.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(W, Y)), 40)
- Equals(LengthOf(Line(W, Z)), 3x-6)
- Equals(LengthOf(Line(U, Y)), 32)
- Equals(LengthOf(Line(U, Z)), x+6)
- PointLiesOnLine(U, Line(Y, Z))
- Perpendicular(Line(U, W), Line(U, Z))
- Equals(MeasureOf(Angle(Z,W,U)), MeasureOf(Angle(W,Y,U)))
Find $UZ$. | 18 | [
"Find(LengthOf(Line(U,Z)))"
] | [
"Equals(LengthOf(Line(W, Y)), 40)",
"Equals(LengthOf(Line(W, Z)), 3x-6)",
"Equals(LengthOf(Line(U, Y)), 32)",
"Equals(LengthOf(Line(U, Z)), x+6)",
"PointLiesOnLine(U, Line(Y, Z))",
"Perpendicular(Line(U, W), Line(U, Z))",
"Equals(MeasureOf(Angle(Z,W,U)), MeasureOf(Angle(W,Y,U)))"
] | [
"UW",
"UY",
"UZ",
"WY",
"WZ",
"YZ"
] | {"U": [204.0, 276.0], "W": [203.0, 2.0], "Y": [576.0, 276.0], "Z": [0.0, 276.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), y)
- Equals(LengthOf(Line(A, B)), 3)
- Equals(MeasureOf(Angle(A, C, B)), 45)
- Equals(LengthOf(Line(A, C)), x)
- Perpendicular(Line(A, B), Line(A, C))
Find x | 3 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(B, C)), y)",
"Equals(LengthOf(Line(A, B)), 3)",
"Equals(MeasureOf(Angle(A, C, B)), 45)",
"Equals(LengthOf(Line(A, C)), x)",
"Perpendicular(Line(A, B), Line(A, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [1.98387763538652, 119.68306462725644], "B": [0.0, 0.0], "C": [118.65565201157472, 120.98870531130402]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, A)), 8z)
- Equals(MeasureOf(Angle(X, Y, A)), 70)
For isosceles trapezoid $X Y Z W$ find $m \angle Z$ | 110 | [
"Isosceles(Trapezoid(X,Y,Z,W))",
"Find(MeasureOf(Angle(Z)))"
] | [
"Equals(LengthOf(Line(B, A)), 8z)",
"Equals(MeasureOf(Angle(X, Y, A)), 70)"
] | [
"XY",
"XB",
"YA",
"BA"
] | {"X": [0.25289485873089745, 108.6709896557048], "A": [77.0, 0.0], "Y": [115.66270647699443, 109.98853629305404], "B": [41.087472821542065, 1.3105870546914176]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(F, H)), 37)
- Equals(LengthOf(Line(A, I)), 18)
- Equals(LengthOf(Line(G, B)), 9)
- PointLiesOnLine(A, Line(F, H))
- PointLiesOnLine(A, Line(F, B))
- PointLiesOnLine(B, Line(F, H))
- PointLiesOnLine(B, Line(A, H))
- Perpendicular(Line(I,A), Line(F,H))
- Perpendicular(Line(B,G),... | 499.5 | [
"Find(AreaOf(Quadrilateral($)))"
] | [
"Equals(LengthOf(Line(F, H)), 37)",
"Equals(LengthOf(Line(A, I)), 18)",
"Equals(LengthOf(Line(G, B)), 9)",
"PointLiesOnLine(A, Line(F, H))",
"PointLiesOnLine(A, Line(F, B))",
"PointLiesOnLine(B, Line(F, H))",
"PointLiesOnLine(B, Line(A, H))",
"Perpendicular(Line(I,A), Line(F,H))",
"Perpendicular(Lin... | [
"AB",
"AH",
"BH",
"FA",
"FI",
"GF",
"GH",
"HI"
] | {"F": [67.0, 1.0], "G": [220.0, 32.0], "H": [246.0, 179.0], "I": [0.0, 181.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, A)), 17)
- Equals(LengthOf(Line(B, C)), 14)
- Equals(LengthOf(Line(A, C)), x)
- PointLiesOnLine(F, Line(B, A))
- PointLiesOnCircle(C, Circle(A, radius_3_0))
- PointLiesOnCircle(F, Circle(A, radius_3_0))
Assume that the segment is tangent, find the value of $x$. | \sqrt { 93 } | [
"Tangent(Line($),Circle($))",
"Find(x)"
] | [
"Equals(LengthOf(Line(B, A)), 17)",
"Equals(LengthOf(Line(B, C)), 14)",
"Equals(LengthOf(Line(A, C)), x)",
"PointLiesOnLine(F, Line(B, A))",
"PointLiesOnCircle(C, Circle(A, radius_3_0))",
"PointLiesOnCircle(F, Circle(A, radius_3_0))"
] | [
"AF",
"BA",
"BF",
"CA",
"CB"
] | {"A": [357.0, 158.0], "B": [0.0, 122.0], "C": [282.0, 290.0], "F": [206.0, 141.0]} | [
"A"
] |
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 $m\angle E$ | 102 | [
"Find(MeasureOf(Angle(E)))"
] | [
"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(A, H, D)), 14x+9)
- Equals(MeasureOf(Angle(F, E, G)), 5x+90)
- PointLiesOnLine(H, Line(A, E))
- PointLiesOnLine(E, Line(A, F))
- PointLiesOnLine(H, Line(A, F))
- PointLiesOnLine(E, Line(F, H))
- PointLiesOnLine(E, Line(G, I))
- PointLiesOnLine(H, Line(C, D))
Find $x$ so tha... | 9 | [
"Parallel(Line(m),Line(n))",
"Find(x)"
] | [
"Equals(MeasureOf(Angle(A, H, D)), 14x+9)",
"Equals(MeasureOf(Angle(F, E, G)), 5x+90)",
"PointLiesOnLine(H, Line(A, E))",
"PointLiesOnLine(E, Line(A, F))",
"PointLiesOnLine(H, Line(A, F))",
"PointLiesOnLine(E, Line(F, H))",
"PointLiesOnLine(E, Line(G, I))",
"PointLiesOnLine(H, Line(C, D))"
] | [
"AE",
"AF",
"AH",
"BG",
"BI",
"CD",
"CJ",
"DJ",
"EB",
"EF",
"EG",
"EH",
"EI",
"FH",
"GI",
"HC",
"HD",
"HJ"
] | {"A": [119.0, 1.0], "B": [194.0, 220.0], "C": [64.0, 0.0], "D": [204.0, 140.0], "E": [119.0, 153.0], "F": [119.0, 244.0], "G": [0.0, 34.0], "H": [119.0, 55.0], "I": [204.0, 238.0], "J": [76.0, 19.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(F, A, D)), 20)
- Equals(LengthOf(Line(D, A)), 9)
- Equals(MeasureOf(Angle(F, A, B)), 32)
- Equals(LengthOf(Line(B, A)), 6)
- Equals(LengthOf(Line(D, C)), 6.86)
- Equals(MeasureOf(Angle(F, B, C)), 40.1)
- PointLiesOnLine(F, Line(D, B))
- PointLiesOnLine(F, Line(C, A))
Use pa... | 9 | [
"Parallelogram(A,B,C,D)",
"Find(LengthOf(Line(B,C)))"
] | [
"Equals(MeasureOf(Angle(F, A, D)), 20)",
"Equals(LengthOf(Line(D, A)), 9)",
"Equals(MeasureOf(Angle(F, A, B)), 32)",
"Equals(LengthOf(Line(B, A)), 6)",
"Equals(LengthOf(Line(D, C)), 6.86)",
"Equals(MeasureOf(Angle(F, B, C)), 40.1)",
"PointLiesOnLine(F, Line(D, B))",
"PointLiesOnLine(F, Line(C, A))"
] | [
"AF",
"BA",
"BC",
"BF",
"CA",
"CF",
"DA",
"DB",
"DC",
"DF"
] | {"A": [127.0, 1.0], "B": [111.0, 83.0], "C": [0.0, 147.0], "D": [16.0, 63.0], "F": [65.0, 72.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, R)), 4)
- Equals(LengthOf(Line(G, point_26)), 20-5x)
- Equals(LengthOf(Line(K, P)), 3)
- Equals(LengthOf(Line(J, point_27)), 2x+6)
- Equals(LengthOf(Line(H, M)), y+2)
- Equals(LengthOf(Line(H, M)), 5)
- PointLiesOnLine(J, Line(B, I))
- PointLiesOnLine(Q, Line(B, I))
- Point... | 5 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(B, R)), 4)",
"Equals(LengthOf(Line(G, point_26)), 20-5x)",
"Equals(LengthOf(Line(K, P)), 3)",
"Equals(LengthOf(Line(J, point_27)), 2x+6)",
"Equals(LengthOf(Line(H, M)), y+2)",
"Equals(LengthOf(Line(H, M)), 5)",
"PointLiesOnLine(J, Line(B, I))",
"PointLiesOnLine(Q, Line(B, I))",
... | [
"AY",
"BI",
"BJ",
"BQ",
"BR",
"BX",
"CF",
"CH",
"CM",
"CS",
"CV",
"DK",
"DN",
"DP",
"DU",
"Dpoint_27",
"EA",
"EG",
"EL",
"EO",
"ET",
"EW",
"EY",
"EZ",
"Epoint_26",
"FD",
"FK",
"FN",
"FP",
"FU",
"Fpoint_27",
"GL",
"GO",
"GT",
"GW",
"GZ",
"Gpoint... | {"A": [320.0, 7.0], "B": [215.0, 1.0], "C": [234.0, 207.0], "D": [28.0, 132.0], "E": [320.0, 57.0], "F": [233.0, 126.0], "G": [26.0, 56.0], "H": [396.0, 211.0], "I": [21.0, 251.0], "J": [114.0, 132.0], "K": [321.0, 134.0], "L": [234.0, 59.0], "M": [322.0, 210.0], "N": [278.0, 134.0], "O": [396.0, 57.0], "P": [396.0, 13... | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(M, G, N)), x)
- Equals(MeasureOf(Angle(N, E, Q)), 75)
- Equals(MeasureOf(Angle(M, E, P)), 55)
- PointLiesOnLine(G, Line(Q, M))
- PointLiesOnLine(G, Line(P, N))
- PointLiesOnCircle(Q, Circle(E, radius_4_0))
- PointLiesOnCircle(M, Circle(E, radius_4_0))
- PointLiesOnCircle(N, ... | 115 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(M, G, N)), x)",
"Equals(MeasureOf(Angle(N, E, Q)), 75)",
"Equals(MeasureOf(Angle(M, E, P)), 55)",
"PointLiesOnLine(G, Line(Q, M))",
"PointLiesOnLine(G, Line(P, N))",
"PointLiesOnCircle(Q, Circle(E, radius_4_0))",
"PointLiesOnCircle(M, Circle(E, radius_4_0))",
"PointLiesOnCircle... | [
"MG",
"GN",
"GP",
"PN",
"QM",
"QG"
] | {"E": [228.0, 137.0], "M": [95.0, 157.0], "G": [205.0, 207.0], "N": [358.0, 102.0], "P": [149.0, 246.0], "Q": [300.0, 250.0]} | [
"E"
] |
Diagram Logic Form:
- PointLiesOnLine(T, Line(X, Z))
- PointLiesOnLine(T, Line(Y, W))
- Equals(LengthOf(Line(X, Y)), LengthOf(Line(W, Z)))
Find $WT$, if $ZX = 20$ and $TY = 15$ | 5 | [
"Equals(LengthOf(Line(Z,X)),20)",
"Equals(LengthOf(Line(T,Y)),15)",
"Find(LengthOf(Line(W,T)))"
] | [
"PointLiesOnLine(T, Line(X, Z))",
"PointLiesOnLine(T, Line(Y, W))",
"Equals(LengthOf(Line(X, Y)), LengthOf(Line(W, Z)))"
] | [
"WT",
"XT",
"XW",
"XY",
"XZ",
"YT",
"YW",
"YZ",
"ZT",
"ZW"
] | {"T": [38.0, 33.0], "W": [6.0, 23.0], "X": [45.0, 0.0], "Y": [189.0, 75.0], "Z": [1.0, 187.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(R, S)), 8)
- Equals(LengthOf(Line(R, Q)), 4)
- Equals(LengthOf(Line(K, J)), 6)
- Equals(LengthOf(Line(L, K)), 12)
- Equals(MeasureOf(Angle(R, Q, S)), 80)
- Equals(MeasureOf(Angle(Q, S, R)), x)
- Equals(MeasureOf(Angle(K, L, J)), 30)
- Equals(MeasureOf(Angle(J, K, L)), y)
- Equ... | 30 | [
"Similar(Polygon($1),Polygon($2))",
"Find(x)"
] | [
"Equals(LengthOf(Line(R, S)), 8)",
"Equals(LengthOf(Line(R, Q)), 4)",
"Equals(LengthOf(Line(K, J)), 6)",
"Equals(LengthOf(Line(L, K)), 12)",
"Equals(MeasureOf(Angle(R, Q, S)), 80)",
"Equals(MeasureOf(Angle(Q, S, R)), x)",
"Equals(MeasureOf(Angle(K, L, J)), 30)",
"Equals(MeasureOf(Angle(J, K, L)), y)",... | [
"KJ",
"JL",
"KL",
"RS",
"QS",
"RQ"
] | {"J": [1.0, 178.0], "K": [31.0, 0.0], "L": [344.0, 180.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(S, T)), 20)
- Equals(LengthOf(Line(T, C)), 12)
- Equals(LengthOf(Line(R, C)), x)
- PointLiesOnLine(C, Line(R, T))
- PointLiesOnCircle(S, Circle(R, radius_3_0))
- PointLiesOnCircle(C, Circle(R, radius_3_0))
The segment is tangent to the circle. Find $x$. Round to the nearest t... | 10.7 | [
"Tangent(Line($),Circle($))",
"Circle($)",
"Find(x)"
] | [
"Equals(LengthOf(Line(S, T)), 20)",
"Equals(LengthOf(Line(T, C)), 12)",
"Equals(LengthOf(Line(R, C)), x)",
"PointLiesOnLine(C, Line(R, T))",
"PointLiesOnCircle(S, Circle(R, radius_3_0))",
"PointLiesOnCircle(C, Circle(R, radius_3_0))"
] | [
"RC",
"SR",
"ST",
"TC",
"TR"
] | {"C": [225.0, 188.0], "R": [122.0, 122.0], "S": [227.0, 61.0], "T": [340.0, 260.0]} | [
"R"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, E, D)), 2x+10)
- Equals(MeasureOf(Angle(C, D, E)), x)
- Equals(MeasureOf(Angle(B, C, D)), 2x-20)
- PointLiesOnLine(F, Line(A, E))
- Perpendicular(Line(F, A), Line(A, B))
- Perpendicular(Line(A, B), Line(C, B))
Find $m\angle A$ | 90 | [
"Find(MeasureOf(Angle(A)))"
] | [
"Equals(MeasureOf(Angle(A, E, D)), 2x+10)",
"Equals(MeasureOf(Angle(C, D, E)), x)",
"Equals(MeasureOf(Angle(B, C, D)), 2x-20)",
"PointLiesOnLine(F, Line(A, E))",
"Perpendicular(Line(F, A), Line(A, B))",
"Perpendicular(Line(A, B), Line(C, B))"
] | [
"AB",
"AE",
"CB",
"DC",
"ED",
"FA",
"FE"
] | {"A": [1.0, 1.0], "B": [2.0, 208.0], "C": [210.0, 206.0], "D": [334.0, 80.0], "E": [211.0, 2.0], "F": [122.0, 3.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, B, C)), MeasureOf(angle 6))
- Equals(MeasureOf(Angle(A, G, F)), 104)
- Equals(MeasureOf(Angle(E, F, C)), 40)
- Equals(MeasureOf(Angle(B, F, D)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(B, A, D)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(A, D, G)), 36)
- Equals(Me... | 26 | [
"Perpendicular(Line(A,B),Line(B,C))",
"Find(MeasureOf(Angle(6)))"
] | [
"Equals(MeasureOf(Angle(E, B, C)), MeasureOf(angle 6))",
"Equals(MeasureOf(Angle(A, G, F)), 104)",
"Equals(MeasureOf(Angle(E, F, C)), 40)",
"Equals(MeasureOf(Angle(B, F, D)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(B, A, D)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(A, D, G)), 36)",
"Equals(M... | [
"AD",
"AG",
"BA",
"BC",
"BE",
"BF",
"BG",
"CD",
"CF",
"CG",
"EF",
"FD",
"FG",
"GD"
] | {"A": [114.0, 2.0], "B": [154.0, 161.0], "C": [465.0, 86.0], "D": [1.0, 84.0], "E": [346.0, 1.0], "F": [247.0, 84.0], "G": [134.0, 83.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, F, C)), 146)
- Equals(MeasureOf(Angle(A, B, C)), MeasureOf(Angle(2)))
- PointLiesOnCircle(B, Circle(F, radius_4_0))
- PointLiesOnCircle(C, Circle(F, radius_4_0))
Find $m \angle 2$. | 73 | [
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(B, F, C)), 146)",
"Equals(MeasureOf(Angle(A, B, C)), MeasureOf(Angle(2)))",
"PointLiesOnCircle(B, Circle(F, radius_4_0))",
"PointLiesOnCircle(C, Circle(F, radius_4_0))"
] | [
"AB",
"BC"
] | {"A": [293.0, 428.0], "B": [179.0, 338.0], "C": [279.0, 92.0], "F": [269.0, 232.0]} | [
"F"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(N, L)), 8)
-
- PointLiesOnLine(E, Line(N, M))
- PointLiesOnLine(F, Line(L, N))
- PointLiesOnLine(D, Line(M, L))
- PointLiesOnCircle(D, Circle(P, radius_1_0))
- PointLiesOnCircle(E, Circle(P, radius_1_0))
- PointLiesOnCircle(F, Circle(P, radius_1_0))
$\odot P$ is inscribed in... | \frac { 8 } { \sqrt 3 } \pi | [
"InscribedIn(Circle(P),Equilateral(Triangle(L,M,N)))",
"Find(CircumferenceOf(Circle(P)))"
] | [
"Equals(LengthOf(Line(N, L)), 8)",
"",
"PointLiesOnLine(E, Line(N, M))",
"PointLiesOnLine(F, Line(L, N))",
"PointLiesOnLine(D, Line(M, L))",
"PointLiesOnCircle(D, Circle(P, radius_1_0))",
"PointLiesOnCircle(E, Circle(P, radius_1_0))",
"PointLiesOnCircle(F, Circle(P, radius_1_0))"
] | [
"LN",
"ML",
"MN",
"EM",
"EN",
"FN",
"FL",
"DL",
"DM"
] | {"D": [92.0, 155.0], "E": [184.0, 313.0], "F": [271.0, 157.0], "L": [181.0, 0.0], "M": [0.0, 313.0], "N": [361.0, 313.0], "P": [184.0, 208.0]} | [
"P"
] |
Diagram Logic Form:
- PointLiesOnLine(B, Line(A, C))
- PointLiesOnLine(E, Line(A, D))
- Parallel(Line(D, C), Line(E, B))
Find $E D$ if $A B=6, B C=4,$ and $A E=9$ | 6 | [
"Equals(LengthOf(Line(A,B)),6)",
"Equals(LengthOf(Line(B,C)),4)",
"Equals(LengthOf(Line(A,E)),9)",
"Find(LengthOf(Line(E,D)))"
] | [
"PointLiesOnLine(B, Line(A, C))",
"PointLiesOnLine(E, Line(A, D))",
"Parallel(Line(D, C), Line(E, B))"
] | [
"AB",
"AC",
"AD",
"BC",
"DC",
"EA",
"EB",
"ED"
] | {"A": [1.0, 169.0], "B": [15.0, 64.0], "C": [25.0, 1.0], "D": [151.0, 16.0], "E": [96.0, 72.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, B)), 6)
- PointLiesOnLine(E, Line(C, A))
- PointLiesOnLine(E, Line(D, B))
In rhombus $A B C D, m \angle D A B=2, m \angle A D C$ and $C B=6$. Find DA | 6 | [
"Rhombus(A,B,C,D)",
"Equals(MeasureOf(Angle(D,A,B)),Mul(MeasureOf(Angle(A,D,C)),2))",
"Equals(LengthOf(Line(C,B)),6)",
"Find(LengthOf(Line(D,A)))"
] | [
"Equals(LengthOf(Line(C, B)), 6)",
"PointLiesOnLine(E, Line(C, A))",
"PointLiesOnLine(E, Line(D, B))"
] | [
"AB",
"AE",
"BE",
"CA",
"CB",
"CD",
"CE",
"DA",
"DB",
"DE"
] | {"A": [56.0, 96.0], "B": [165.0, 96.0], "C": [109.0, 2.0], "D": [0.0, 0.0], "E": [83.0, 48.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), 4)
- Equals(LengthOf(Line(C, D)), 2)
- Equals(LengthOf(Line(B, E)), 3)
- Equals(LengthOf(Line(A, E)), x)
- PointLiesOnLine(E, Line(A, B))
- PointLiesOnLine(C, Line(B, D))
- PointLiesOnCircle(A, Circle(X, radius_4_0))
- PointLiesOnCircle(C, Circle(X, radius_4_0))
- Poin... | 5 | [
"Tangent(Line($),Circle($))",
"Find(x)"
] | [
"Equals(LengthOf(Line(B, C)), 4)",
"Equals(LengthOf(Line(C, D)), 2)",
"Equals(LengthOf(Line(B, E)), 3)",
"Equals(LengthOf(Line(A, E)), x)",
"PointLiesOnLine(E, Line(A, B))",
"PointLiesOnLine(C, Line(B, D))",
"PointLiesOnCircle(A, Circle(X, radius_4_0))",
"PointLiesOnCircle(C, Circle(X, radius_4_0))",
... | [
"AB",
"AE",
"BC",
"BD",
"BE",
"BX",
"CD",
"EX"
] | {"A": [22.0, 152.0], "B": [206.0, 1.0], "C": [90.0, 31.0], "D": [22.0, 50.0], "E": [133.0, 61.0], "X": [75.0, 102.0]} | [
"X"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), x)
- Equals(LengthOf(Line(B, C)), 48)
- Equals(LengthOf(Line(A, C)), 14)
- Perpendicular(Line(B, C), Line(A, C))
Use a Pythagorean Triple to find x. | 50 | [
"UseTheorem(Pythagorean_Triple)",
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), x)",
"Equals(LengthOf(Line(B, C)), 48)",
"Equals(LengthOf(Line(A, C)), 14)",
"Perpendicular(Line(B, C), Line(A, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [92.1792087857232, 202.32285036815176], "B": [1.663043478260871, 0.7355072463768124], "C": [0.6715569443708809, 201.0072736260438]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(K, A)), 10)
- Equals(LengthOf(Line(A, P)), 12)
- Perpendicular(Line(L, K), Line(A, K))
- Perpendicular(Line(P, L), Line(K, L))
- Perpendicular(Line(P, A), Line(K, A))
- Perpendicular(Line(A, P), Line(L, P))
Find the perimeter of the figure. | 44 | [
"Find(PerimeterOf(Shape($)))"
] | [
"Equals(LengthOf(Line(K, A)), 10)",
"Equals(LengthOf(Line(A, P)), 12)",
"Perpendicular(Line(L, K), Line(A, K))",
"Perpendicular(Line(P, L), Line(K, L))",
"Perpendicular(Line(P, A), Line(K, A))",
"Perpendicular(Line(A, P), Line(L, P))"
] | [
"LK",
"KA",
"AP",
"LP"
] | {"A": [197.0, 164.0], "K": [198.0, 2.0], "L": [0.0, 0.0], "P": [2.0, 166.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(G, E, B)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(E, B, F)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(B, C, D)), 50)
- Equals(MeasureOf(Angle(G, B, D)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(A, G, B)), 120)
- Equals(MeasureOf(Angle(H, G, A)), MeasureOf(angle... | 60 | [
"Find(MeasureOf(Angle(4)))"
] | [
"Equals(MeasureOf(Angle(G, E, B)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(E, B, F)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(B, C, D)), 50)",
"Equals(MeasureOf(Angle(G, B, D)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(A, G, B)), 120)",
"Equals(MeasureOf(Angle(H, G, A)), MeasureOf(angle 4... | [
"AE",
"AF",
"AG",
"BC",
"BD",
"BH",
"CD",
"CH",
"EB",
"ED",
"EG",
"FB",
"FC",
"FG",
"FH",
"GB",
"GC",
"GH"
] | {"A": [396.0, 216.0], "B": [189.0, 107.0], "C": [1.0, 107.0], "D": [99.0, 222.0], "E": [271.0, 2.0], "F": [446.0, 107.0], "G": [333.0, 108.0], "H": [507.0, 108.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(Q, Line(R, A))
- PointLiesOnLine(P, Line(R, A))
- PointLiesOnLine(Q, Line(R, P))
- PointLiesOnLine(R, Line(A, B))
- PointLiesOnLine(Q, Line(A, B))
- PointLiesOnLine(P, Line(A, B))
- PointLiesOnLine(P, Line(A, Q))
- PointLiesOnLine(R, Line(B, Q))
- PointLiesOnLine(R, Line(B, P))
- P... | 18 | [
"IsAltitudeOf(Line(C,P),Shape($))",
"BisectsAngle(Line(C,Q),Angle(A,C,B))",
"IsMidpointOf(Point(R),Line(A,B))",
"Equals(MeasureOf(Angle(A,P,C)),72+x)",
"Find(x)"
] | [
"PointLiesOnLine(Q, Line(R, A))",
"PointLiesOnLine(P, Line(R, A))",
"PointLiesOnLine(Q, Line(R, P))",
"PointLiesOnLine(R, Line(A, B))",
"PointLiesOnLine(Q, Line(A, B))",
"PointLiesOnLine(P, Line(A, B))",
"PointLiesOnLine(P, Line(A, Q))",
"PointLiesOnLine(R, Line(B, Q))",
"PointLiesOnLine(R, Line(B, ... | [
"AB",
"AP",
"AQ",
"BP",
"BQ",
"CA",
"CB",
"CP",
"CQ",
"CR",
"QP",
"RA",
"RB",
"RP",
"RQ"
] | {"A": [1.0, 150.0], "B": [272.0, 152.0], "C": [92.0, 3.0], "P": [94.0, 151.0], "Q": [115.0, 151.0], "R": [138.0, 151.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(P, Line(Y, X))
- PointLiesOnLine(Q, Line(T, S))
- PointLiesOnCircle(Y, Circle(Z, radius_2_0))
- PointLiesOnCircle(X, Circle(Z, radius_2_0))
- PointLiesOnCircle(T, Circle(Z, radius_2_0))
- PointLiesOnCircle(S, Circle(Z, radius_2_0))
- Perpendicular(Line(Y, P), Line(Z, P))
- Perpendi... | 1.5 | [
"Circle(Z)",
"Equals(LengthOf(Line(P,Z)),Line(Z,Q))",
"Equals(LengthOf(Line(X,Y)),4a-5)",
"Equals(LengthOf(Line(S,T)),-5a+13)",
"Find(LengthOf(Line(S,Q)))"
] | [
"PointLiesOnLine(P, Line(Y, X))",
"PointLiesOnLine(Q, Line(T, S))",
"PointLiesOnCircle(Y, Circle(Z, radius_2_0))",
"PointLiesOnCircle(X, Circle(Z, radius_2_0))",
"PointLiesOnCircle(T, Circle(Z, radius_2_0))",
"PointLiesOnCircle(S, Circle(Z, radius_2_0))",
"Perpendicular(Line(Y, P), Line(Z, P))",
"Perp... | [
"QS",
"QT",
"QZ",
"TS",
"XP",
"YP",
"YX",
"ZP"
] | {"S": [3.0, 81.0], "P": [86.0, 33.0], "Q": [49.0, 127.0], "T": [100.0, 176.0], "X": [19.0, 37.0], "Y": [157.0, 31.0], "Z": [91.0, 90.0]} | [
"Z"
] |
Diagram Logic Form:
- PointLiesOnLine(S, Line(P, Q))
- PointLiesOnLine(Y, Line(P, R))
- PointLiesOnLine(A, Line(Y, X))
- PointLiesOnLine(S, Line(Y, W))
- PointLiesOnLine(A, Line(Q, R))
- PointLiesOnLine(Q, Line(X, W))
- Perpendicular(Line(P, S), Line(Y, S))
- Perpendicular(Line(Y, S), Line(Y, A))
- Perpendicular(Line(Q... | 6 | [
"Parallel(Line(P,R),Line(W,X))",
"Equals(LengthOf(Line(W,X)),10)",
"Equals(LengthOf(Line(X,Y)),6)",
"Equals(LengthOf(Line(W,Y)),8)",
"Equals(LengthOf(Line(R,Y)),5)",
"Equals(LengthOf(Line(P,S)),3)",
"Find(LengthOf(Line(P,Q)))"
] | [
"PointLiesOnLine(S, Line(P, Q))",
"PointLiesOnLine(Y, Line(P, R))",
"PointLiesOnLine(A, Line(Y, X))",
"PointLiesOnLine(S, Line(Y, W))",
"PointLiesOnLine(A, Line(Q, R))",
"PointLiesOnLine(Q, Line(X, W))",
"Perpendicular(Line(P, S), Line(Y, S))",
"Perpendicular(Line(Y, S), Line(Y, A))",
"Perpendicular... | [
"PQ",
"PR",
"PS",
"PY",
"QA",
"QR",
"QS",
"QW",
"QX",
"RA",
"SW",
"XA",
"XW",
"YA",
"YR",
"YS",
"YW",
"YX"
] | {"A": [98.0, 113.0], "P": [245.0, 3.0], "Q": [247.0, 114.0], "R": [1.0, 113.0], "S": [245.0, 70.0], "W": [341.0, 71.0], "X": [96.0, 183.0], "Y": [99.0, 69.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(R, S)), 6x-5)
- Equals(LengthOf(Line(R, Q)), 5x)
- Equals(LengthOf(Line(S, Q)), 3x+10)
- Equals(LengthOf(Line(R, S)), LengthOf(Line(R, Q)))
- Equals(LengthOf(Line(R, Q)), LengthOf(Line(S, Q)))
Find $RS$. | 25 | [
"Find(LengthOf(Line(Q,R)))"
] | [
"Equals(LengthOf(Line(R, S)), 6x-5)",
"Equals(LengthOf(Line(R, Q)), 5x)",
"Equals(LengthOf(Line(S, Q)), 3x+10)",
"Equals(LengthOf(Line(R, S)), LengthOf(Line(R, Q)))",
"Equals(LengthOf(Line(R, Q)), LengthOf(Line(S, Q)))"
] | [
"SQ",
"RS",
"RQ"
] | {"S": [329.0, 227.0], "Q": [0.0, 227.0], "R": [149.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(F, N)), 20)
- Equals(LengthOf(Line(B, F)), 10)
- Equals(LengthOf(Line(C, E)), 2)
- Equals(LengthOf(Line(A, N)), 19)
- PointLiesOnLine(E, Line(C, B))
- Perpendicular(Line(A, E), Line(E, F))
- PointLiesOnLine(F, Line(C, B))
- Perpendicular(Line(N, F), Line(E, F))
Find the area ... | 500 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(F, N)), 20)",
"Equals(LengthOf(Line(B, F)), 10)",
"Equals(LengthOf(Line(C, E)), 2)",
"Equals(LengthOf(Line(A, N)), 19)",
"PointLiesOnLine(E, Line(C, B))",
"Perpendicular(Line(A, E), Line(E, F))",
"PointLiesOnLine(F, Line(C, B))",
"Perpendicular(Line(N, F), Line(E, F))"
] | [
"AC",
"AE",
"AN",
"BE",
"BF",
"CB",
"CE",
"CF",
"EF",
"NB",
"NF"
] | {"A": [27.0, 2.0], "B": [224.0, 114.0], "C": [0.0, 113.0], "N": [140.0, 2.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(F, Line(E, A))
- PointLiesOnLine(D, Line(E, C))
- PointLiesOnLine(P, Line(E, B))
- PointLiesOnLine(B, Line(A, C))
- PointLiesOnLine(P, Line(A, D))
- PointLiesOnLine(P, Line(C, F))
In $\triangle ACE$, P is the centroid. $PF=6$ and $AD=15$. Find $PC$. | 12 | [
"Triangle(A,C,E)",
"IsCentroidOf(Point(P),Triangle(A,C,E))",
"Equals(LengthOf(Line(P,F)),6)",
"Equals(LengthOf(Line(A,D)),15)",
"Find(LengthOf(Line(P,C)))"
] | [
"PointLiesOnLine(F, Line(E, A))",
"PointLiesOnLine(D, Line(E, C))",
"PointLiesOnLine(P, Line(E, B))",
"PointLiesOnLine(B, Line(A, C))",
"PointLiesOnLine(P, Line(A, D))",
"PointLiesOnLine(P, Line(C, F))"
] | [
"EA",
"EC",
"EP",
"EF",
"ED",
"EB",
"AC",
"AP",
"AF",
"AD",
"AB",
"CP",
"CF",
"CD",
"CB",
"PF",
"PD",
"PB"
] | {"E": [285.9146937649133, 299.67691602412805], "A": [127.0160438450724, 1.8339606691751271], "C": [1.1567348902809442, 343.1437005221105], "P": [138.46792077675303, 219.05647933844355], "F": [208.78035470668488, 154.20054570259208], "D": [144.9765123133563, 321.6031817151247], "B": [61.53010279796787, 178.2850775046849... | [] |
Diagram Logic Form:
- PointLiesOnLine(M, Line(R, H))
- PointLiesOnCircle(U, Circle(M, radius_0_0))
- PointLiesOnCircle(A, Circle(M, radius_0_0))
- PointLiesOnCircle(S, Circle(M, radius_0_0))
- PointLiesOnCircle(R, Circle(M, radius_0_0))
- PointLiesOnCircle(D, Circle(M, radius_0_0))
- PointLiesOnCircle(H, Circle(M, radi... | 14 | [
"Equals(LengthOf(Line(M,D)),7)",
"Find(LengthOf(Line(R,I)))"
] | [
"PointLiesOnLine(M, Line(R, H))",
"PointLiesOnCircle(U, Circle(M, radius_0_0))",
"PointLiesOnCircle(A, Circle(M, radius_0_0))",
"PointLiesOnCircle(S, Circle(M, radius_0_0))",
"PointLiesOnCircle(R, Circle(M, radius_0_0))",
"PointLiesOnCircle(D, Circle(M, radius_0_0))",
"PointLiesOnCircle(H, Circle(M, rad... | [
"MA",
"MD",
"MH",
"MR",
"RH",
"US"
] | {"A": [18.0, 43.0], "S": [109.0, 181.0], "D": [88.0, 3.0], "H": [174.0, 61.0], "M": [88.0, 92.0], "R": [8.0, 124.0], "U": [174.0, 82.0]} | [
"M"
] |
Diagram Logic Form:
- Equals(MeasureOf(Arc(E, D)), 3a)
- Equals(MeasureOf(Arc(E, C)), 5a)
- Equals(MeasureOf(Arc(D, B)), 6a)
- Equals(MeasureOf(Arc(C, B)), 4a)
- Equals(MeasureOf(Angle(B, A, D)), MeasureOf(Angle(6)))
- PointLiesOnLine(A, Line(B, E))
- PointLiesOnCircle(B, Circle(A, radius_0_0))
- PointLiesOnCircle(C, C... | 110 | [
"Find(MeasureOf(Angle(6)))"
] | [
"Equals(MeasureOf(Arc(E, D)), 3a)",
"Equals(MeasureOf(Arc(E, C)), 5a)",
"Equals(MeasureOf(Arc(D, B)), 6a)",
"Equals(MeasureOf(Arc(C, B)), 4a)",
"Equals(MeasureOf(Angle(B, A, D)), MeasureOf(Angle(6)))",
"PointLiesOnLine(A, Line(B, E))",
"PointLiesOnCircle(B, Circle(A, radius_0_0))",
"PointLiesOnCircle(... | [
"AB",
"AC",
"AD",
"AE",
"BE",
"CD"
] | {"A": [55.0, 56.0], "B": [76.0, 114.0], "C": [8.0, 88.0], "D": [95.0, 15.0], "E": [38.0, 15.0]} | [
"A"
] |
Diagram Logic Form:
- PointLiesOnLine(B, Line(G, E))
- PointLiesOnLine(B, Line(F, D))
- Perpendicular(Line(D, G), Line(G, F))
Quadrilateral DEFG is a rectangle. If $DF = 2(x + 5) - 7$ and $EG = 3(x - 2)$, find EG. | 21 | [
"Rectangle(D,E,F,G)",
"Equals(LengthOf(Line(D,F)),2(x+5)-7)",
"Equals(LengthOf(Line(E,G)),3(x-2))",
"Find(LengthOf(Line(E,G)))"
] | [
"PointLiesOnLine(B, Line(G, E))",
"PointLiesOnLine(B, Line(F, D))",
"Perpendicular(Line(D, G), Line(G, F))"
] | [
"BE",
"DB",
"DE",
"FB",
"FD",
"FE",
"GB",
"GD",
"GE",
"GF"
] | {"B": [211.0, 90.0], "D": [1.0, 0.0], "E": [417.0, 2.0], "F": [418.0, 179.0], "G": [1.0, 179.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(N, M)), 11)
- Equals(MeasureOf(Angle(P, N, M)), 120)
- Equals(MeasureOf(Angle(N, P, M)), MeasureOf(Angle(N, M, P)))
Find $m \angle M$. | 30 | [
"Find(MeasureOf(Angle(M)))"
] | [
"Equals(LengthOf(Line(N, M)), 11)",
"Equals(MeasureOf(Angle(P, N, M)), 120)",
"Equals(MeasureOf(Angle(N, P, M)), MeasureOf(Angle(N, M, P)))"
] | [
"MP",
"NM",
"NP"
] | {"M": [510.0, 4.0], "N": [289.0, 206.0], "P": [5.0, 115.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, D)), 46)
- Equals(LengthOf(Line(H, E)), 38)
- PointLiesOnLine(H, Line(C, G))
- PointLiesOnLine(E, Line(D, F))
Refer to trapezoid $CDFG$ with median $\overline{HE}$. Find $GF$. | 30 | [
"Trapezoid(C,D,F,G)",
"IsMedianOf(Line(H,E),Trapezoid(C,D,F,G))",
"Find(LengthOf(Line(G,F)))"
] | [
"Equals(LengthOf(Line(C, D)), 46)",
"Equals(LengthOf(Line(H, E)), 38)",
"PointLiesOnLine(H, Line(C, G))",
"PointLiesOnLine(E, Line(D, F))"
] | [
"CG",
"CD",
"CH",
"GF",
"GH",
"DF",
"DE",
"HE",
"FE"
] | {"C": [0.2904965594197506, 1.3312875829148823], "F": [249.49376114081997, 149.66042780748663], "G": [64.89678224230869, 149.0012240190194], "D": [284.0, 0.0], "H": [32.39218116268589, 75.00332356917531], "E": [266.82356894813483, 76.99003024532317]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(H, J, K)), 3y+9)
- Equals(MeasureOf(Angle(G, K, J)), x+21)
- Equals(MeasureOf(Angle(J, H, G)), 2x)
- Equals(MeasureOf(Angle(H, G, K)), 4y-11)
- PointLiesOnCircle(G, Circle(O, radius_3_0))
- PointLiesOnCircle(K, Circle(O, radius_3_0))
- PointLiesOnCircle(J, Circle(O, radius_3... | 106 | [
"Find(MeasureOf(Angle(H)))"
] | [
"Equals(MeasureOf(Angle(H, J, K)), 3y+9)",
"Equals(MeasureOf(Angle(G, K, J)), x+21)",
"Equals(MeasureOf(Angle(J, H, G)), 2x)",
"Equals(MeasureOf(Angle(H, G, K)), 4y-11)",
"PointLiesOnCircle(G, Circle(O, radius_3_0))",
"PointLiesOnCircle(K, Circle(O, radius_3_0))",
"PointLiesOnCircle(J, Circle(O, radius_... | [
"GH",
"HJ",
"JK",
"KG"
] | {"G": [142.0, 312.0], "H": [12.0, 217.0], "J": [32.0, 64.0], "K": [296.0, 79.0], "O": [160.0, 157.0]} | [
"O"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, D)), 7)
- Equals(LengthOf(Line(B, C)), x)
- Equals(LengthOf(Line(D, E)), 13)
- PointLiesOnLine(B, Line(C, D))
- PointLiesOnCircle(B, Circle(A, radius_0_0))
- PointLiesOnCircle(C, Circle(A, radius_0_0))
- PointLiesOnCircle(E, Circle(A, radius_0_0))
Find x to the nearest ten... | 17.1 | [
"Tangent(Line($),Circle($))",
"Find(x)"
] | [
"Equals(LengthOf(Line(B, D)), 7)",
"Equals(LengthOf(Line(B, C)), x)",
"Equals(LengthOf(Line(D, E)), 13)",
"PointLiesOnLine(B, Line(C, D))",
"PointLiesOnCircle(B, Circle(A, radius_0_0))",
"PointLiesOnCircle(C, Circle(A, radius_0_0))",
"PointLiesOnCircle(E, Circle(A, radius_0_0))"
] | [
"BC",
"BD",
"BE",
"CD",
"DE"
] | {"A": [121.0, 68.0], "B": [62.0, 39.0], "C": [188.0, 65.0], "D": [5.0, 31.0], "E": [51.0, 83.0]} | [
"A"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(P, Q, R)), 2x-16)
- Equals(MeasureOf(Angle(S, R, Q)), 2x)
- Equals(MeasureOf(Angle(P, S, R)), x+10)
- Equals(MeasureOf(Angle(Q, P, S)), x)
Find the measure of $\angle S$ | 71 | [
"Find(MeasureOf(Angle(S)))"
] | [
"Equals(MeasureOf(Angle(P, Q, R)), 2x-16)",
"Equals(MeasureOf(Angle(S, R, Q)), 2x)",
"Equals(MeasureOf(Angle(P, S, R)), x+10)",
"Equals(MeasureOf(Angle(Q, P, S)), x)"
] | [
"PS",
"QP",
"QR",
"RS"
] | {"P": [6.0, 184.0], "Q": [111.0, 0.0], "R": [314.0, 24.0], "S": [370.0, 191.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, C)), 3y)
- Equals(LengthOf(Line(B, C)), 2x)
- Equals(LengthOf(Line(A, D)), 5x-18)
- Equals(LengthOf(Line(A, B)), 96-y)
Find $y$ so that each quadrilateral is a parallelogram. | 24 | [
"Parallelogram($)",
"Find(y)"
] | [
"Equals(LengthOf(Line(D, C)), 3y)",
"Equals(LengthOf(Line(B, C)), 2x)",
"Equals(LengthOf(Line(A, D)), 5x-18)",
"Equals(LengthOf(Line(A, B)), 96-y)"
] | [
"AB",
"AD",
"BC",
"DC"
] | {"A": [202.0, 125.0], "B": [1.0, 124.0], "C": [65.0, 3.0], "D": [269.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 9)
- Equals(LengthOf(Line(R, O)), 14)
- Equals(LengthOf(Line(P, O)), x)
- Equals(LengthOf(Line(P, Q)), y)
- Equals(LengthOf(Line(A, Y)), 18)
- Equals(LengthOf(Line(Y, B)), 21)
Find x. | 12 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, C)), 9)",
"Equals(LengthOf(Line(R, O)), 14)",
"Equals(LengthOf(Line(P, O)), x)",
"Equals(LengthOf(Line(P, Q)), y)",
"Equals(LengthOf(Line(A, Y)), 18)",
"Equals(LengthOf(Line(Y, B)), 21)"
] | [
"AC",
"AY",
"CB",
"YB",
"OP",
"PQ",
"QR",
"RO"
] | {"A": [74.0, 2.0], "B": [252.0, 218.0], "C": [183.0, 3.0], "Y": [1.0, 218.0], "O": [-100.0, 70.0], "P": [-150.0, 180.0], "Q": [-250.0, 180.0], "R": [-300.0, 70.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(G, Line(D, A))
- PointLiesOnLine(G, Line(B, F))
- PointLiesOnCircle(D, Circle(G, radius_0_0))
- PointLiesOnCircle(A, Circle(G, radius_0_0))
- PointLiesOnCircle(C, Circle(G, radius_0_0))
- PointLiesOnCircle(B, Circle(G, radius_0_0))
- PointLiesOnCircle(F, Circle(G, radius_0_0))
- Pe... | 60 | [
"Circle(G)",
"Equals(MeasureOf(Angle(A,G,B)),30)",
"Perpendicular(Line(C,G),Line(G,D))",
"Find(MeasureOf(Arc(B,C)))"
] | [
"PointLiesOnLine(G, Line(D, A))",
"PointLiesOnLine(G, Line(B, F))",
"PointLiesOnCircle(D, Circle(G, radius_0_0))",
"PointLiesOnCircle(A, Circle(G, radius_0_0))",
"PointLiesOnCircle(C, Circle(G, radius_0_0))",
"PointLiesOnCircle(B, Circle(G, radius_0_0))",
"PointLiesOnCircle(F, Circle(G, radius_0_0))",
... | [
"BF",
"DA",
"GA",
"GB",
"GC",
"GD",
"GF"
] | {"A": [4.0, 62.0], "B": [34.0, 21.0], "C": [121.0, 7.0], "D": [176.0, 123.0], "F": [149.0, 161.0], "G": [90.0, 91.0]} | [
"G"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(I, D, W)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(W, D, L)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(D, U, A)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(A, U, L)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(H, D, I)), MeasureOf(angle 5))
- Equals(MeasureOf(A... | 116 | [
"Equals(MeasureOf(Angle(12)),64)",
"Find(MeasureOf(Angle(3)))"
] | [
"Equals(MeasureOf(Angle(I, D, W)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(W, D, L)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(D, U, A)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(A, U, L)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(H, D, I)), MeasureOf(angle 5))",
"Equals(MeasureOf(Ang... | [
"AE",
"AG",
"AK",
"AQ",
"AU",
"BH",
"BN",
"DI",
"DJ",
"DL",
"DW",
"EB",
"EG",
"EH",
"EK",
"EN",
"EU",
"GK",
"GQ",
"GU",
"HD",
"HJ",
"HN",
"HW",
"IL",
"KU",
"QD",
"QI",
"QL",
"QU",
"UD",
"UI",
"UL",
"WJ"
] | {"A": [378.0, 3.0], "B": [7.0, 171.0], "D": [176.0, 72.0], "E": [277.0, 171.0], "G": [353.0, 43.0], "H": [118.0, 170.0], "I": [27.0, 71.0], "J": [72.0, 249.0], "K": [231.0, 249.0], "L": [518.0, 73.0], "N": [492.0, 172.0], "Q": [353.0, 73.0], "S": [503.0, 72.0], "T": [460.0, 73.0], "U": [334.0, 73.0], "W": [218.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, A, E)), 37)
- Equals(LengthOf(Line(E, C)), 24)
- Equals(LengthOf(Line(C, B)), 20)
- PointLiesOnLine(A, Line(D, E))
- Perpendicular(Line(C, E), Line(E, A))
Find the area of the parallelogram. Round to the nearest tenth if necessary. | 480 | [
"Find(AreaOf(Parallelogram($)))"
] | [
"Equals(MeasureOf(Angle(C, A, E)), 37)",
"Equals(LengthOf(Line(E, C)), 24)",
"Equals(LengthOf(Line(C, B)), 20)",
"PointLiesOnLine(A, Line(D, E))",
"Perpendicular(Line(C, E), Line(E, A))"
] | [
"AC",
"AD",
"AE",
"CB",
"DB",
"DE",
"CE"
] | {"A": [134.0, 0.0], "B": [142.0, 169.0], "C": [0.0, 170.0], "D": [271.0, 1.0], "E": [0.0, 0.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(T, V)), 3b+5)
- Equals(LengthOf(Line(S, T)), 15)
- Equals(LengthOf(Line(S, W)), x+11)
Use parallelogram to find $b$ | 3 | [
"Parallelogram($)",
"Find(b)"
] | [
"Equals(LengthOf(Line(T, V)), 3b+5)",
"Equals(LengthOf(Line(S, T)), 15)",
"Equals(LengthOf(Line(S, W)), x+11)"
] | [
"ST",
"SW",
"TV",
"WV"
] | {"S": [22.0, 213.0], "T": [1.0, 0.0], "V": [255.0, 45.0], "W": [277.0, 256.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, A)), 5)
- Equals(MeasureOf(Angle(A, B, C)), 46)
- PointLiesOnCircle(C, Circle(B, radius_0_0))
- PointLiesOnCircle(A, Circle(B, radius_0_0))
Find the area of the shaded sector. Round to the nearest tenth, if necessary. | 10.0 | [
"Find(AreaOf(Shaded(Sector($))))"
] | [
"Equals(LengthOf(Line(B, A)), 5)",
"Equals(MeasureOf(Angle(A, B, C)), 46)",
"PointLiesOnCircle(C, Circle(B, radius_0_0))",
"PointLiesOnCircle(A, Circle(B, radius_0_0))"
] | [
"BA",
"BC"
] | {"A": [164.0, 18.0], "B": [102.0, 106.0], "C": [207.0, 85.0]} | [
"B"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, D)), 10)
- Equals(LengthOf(Line(C, B)), 2x+4)
- Equals(LengthOf(Line(D, B)), x+2)
- Equals(LengthOf(Line(B, C)), LengthOf(Line(C, D)))
Find $BD$. | 5 | [
"Find(LengthOf(Line(B,D)))"
] | [
"Equals(LengthOf(Line(C, D)), 10)",
"Equals(LengthOf(Line(C, B)), 2x+4)",
"Equals(LengthOf(Line(D, B)), x+2)",
"Equals(LengthOf(Line(B, C)), LengthOf(Line(C, D)))"
] | [
"CB",
"CD",
"DB"
] | {"B": [2.0, 135.0], "C": [269.0, 0.0], "D": [536.0, 136.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(R, Line(Q, S))
- PointLiesOnLine(R, Line(T, Q))
- PointLiesOnLine(S, Line(R, T))
- PointLiesOnLine(S, Line(Q, T))
- PointLiesOnLine(X, Line(Q, W))
- PointLiesOnLine(X, Line(Q, V))
- PointLiesOnLine(W, Line(X, V))
- PointLiesOnLine(W, Line(Q, V))
- Parallel(Line(R, X), Line(S, W))
-... | 7.5 | [
"Equals(LengthOf(Line(Q,R)),2)",
"Equals(LengthOf(Line(X,W)),12)",
"Equals(LengthOf(Line(Q,W)),15)",
"Equals(LengthOf(Line(S,T)),5)",
"Find(LengthOf(Line(W,V)))"
] | [
"PointLiesOnLine(R, Line(Q, S))",
"PointLiesOnLine(R, Line(T, Q))",
"PointLiesOnLine(S, Line(R, T))",
"PointLiesOnLine(S, Line(Q, T))",
"PointLiesOnLine(X, Line(Q, W))",
"PointLiesOnLine(X, Line(Q, V))",
"PointLiesOnLine(W, Line(X, V))",
"PointLiesOnLine(W, Line(Q, V))",
"Parallel(Line(R, X), Line(S... | [
"QR",
"QS",
"QT",
"QV",
"QW",
"QX",
"RS",
"RT",
"RX",
"ST",
"SW",
"WV",
"XV",
"XW"
] | {"Q": [1.0, 222.0], "R": [96.0, 163.0], "S": [284.0, 61.0], "T": [392.0, 0.0], "V": [495.0, 222.0], "W": [342.0, 223.0], "X": [114.0, 222.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, A)), 0n8)
- Equals(LengthOf(Line(C, A)), 25)
- Equals(LengthOf(Line(A, B)), 15)
- Equals(LengthOf(Line(C, B)), 20)
- Perpendicular(Line(A, B), Line(C, B))
Express the ratio of $\tan C$ as a decimal to the nearest hundredth. | 0.75 | [
"Find(RatioOf(TanOf(Angle(C))))"
] | [
"Equals(LengthOf(Line(C, A)), 0n8)",
"Equals(LengthOf(Line(C, A)), 25)",
"Equals(LengthOf(Line(A, B)), 15)",
"Equals(LengthOf(Line(C, B)), 20)",
"Perpendicular(Line(A, B), Line(C, B))"
] | [
"CA",
"CB",
"AB"
] | {"C": [2.676749396759732, 131.9943553946915], "A": [237.9923266109198, 0.6709624528611187], "B": [236.00748097921243, 131.33750358131982]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 12)
- Equals(LengthOf(Line(B, D)), 6)
- Equals(LengthOf(Line(B, E)), 3)
- Equals(LengthOf(Line(B, X)), x)
- PointLiesOnLine(F, Line(A, B))
- PointLiesOnLine(B, Line(A, E))
- PointLiesOnLine(B, Line(E, F))
- PointLiesOnLine(B, Line(X, D))
- PointLiesOnCircle(A, Circle(C... | 6 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), 12)",
"Equals(LengthOf(Line(B, D)), 6)",
"Equals(LengthOf(Line(B, E)), 3)",
"Equals(LengthOf(Line(B, X)), x)",
"PointLiesOnLine(F, Line(A, B))",
"PointLiesOnLine(B, Line(A, E))",
"PointLiesOnLine(B, Line(E, F))",
"PointLiesOnLine(B, Line(X, D))",
"PointLiesOnCircle(A, C... | [
"AB",
"AE",
"BD",
"BE",
"BX",
"XD"
] | {"A": [226.0, 91.0], "B": [88.0, 187.0], "C": [116.0, 113.0], "D": [23.0, 164.0], "E": [56.0, 210.0], "X": [165.0, 215.0]} | [
"C"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(M, P)), 10)
- PointLiesOnLine(R, Line(M, Q))
- PointLiesOnLine(R, Line(L, P))
In rhombus LMPQ, $m \angle Q L M=2 x^{2}-10$, $m \angle Q P M=8 x$, and $M P=10$ .
Find $m\angle LQM$ | 70 | [
"Rhombus(L,M,P,Q)",
"Equals(MeasureOf(Angle(Q,L,M)),2x^{2}-10)",
"Equals(MeasureOf(Angle(Q,P,M)),8x)",
"Equals(LengthOf(Line(M,P)),10)",
"Find(MeasureOf(Angle(L,Q,M)))"
] | [
"Equals(LengthOf(Line(M, P)), 10)",
"PointLiesOnLine(R, Line(M, Q))",
"PointLiesOnLine(R, Line(L, P))"
] | [
"ML",
"MP",
"MQ",
"MR",
"LP",
"LQ",
"LR",
"PQ",
"PR",
"QR"
] | {"M": [155.53907318896594, 99.57644249438391], "L": [1.01404959352206, 98.5001812850777], "P": [279.2193778786047, 0.4704888096677564], "Q": [124.00406237714586, 2.4967894116105356], "R": [140.1931330472103, 49.5793991416309]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(L, K)), 4x+3)
- Equals(LengthOf(Line(J, K)), 6x-5)
- Equals(LengthOf(Line(M, P)), 3y+8)
- Equals(LengthOf(Line(Q, P)), 5y-7)
- Equals(LengthOf(Line(Q, P)), LengthOf(Line(M, P)))
- PointLiesOnLine(P, Line(M, Q))
- PointLiesOnLine(K, Line(J, L))
- Parallel(Line(J, M), Line(K, P)... | 7.5 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(L, K)), 4x+3)",
"Equals(LengthOf(Line(J, K)), 6x-5)",
"Equals(LengthOf(Line(M, P)), 3y+8)",
"Equals(LengthOf(Line(Q, P)), 5y-7)",
"Equals(LengthOf(Line(Q, P)), LengthOf(Line(M, P)))",
"PointLiesOnLine(P, Line(M, Q))",
"PointLiesOnLine(K, Line(J, L))",
"Parallel(Line(J, M), Line(K... | [
"JK",
"JL",
"JM",
"KL",
"KP",
"LQ",
"MP",
"MQ",
"PQ"
] | {"J": [100.0, 152.0], "K": [321.0, 114.0], "L": [538.0, 78.0], "M": [129.0, 254.0], "P": [364.0, 262.0], "Q": [589.0, 262.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(S, Line(R, T))
- PointLiesOnLine(V, Line(Q, U))
For trapezoid QRTU, V and S are midpoints of the legs. If QR = 12 and UT = 22, find VS. | 17 | [
"Trapezoid(Q,R,T,U)",
"IsMidpointOf(Point(V),LegOf(Trapezoid(Q,R,T,U)))",
"IsMidpointOf(Point(S),LegOf(Trapezoid(Q,R,T,U)))",
"Equals(LengthOf(Line(Q,R)),12)",
"Equals(LengthOf(Line(U,T)),22)",
"Find(LengthOf(Line(V,S)))"
] | [
"PointLiesOnLine(S, Line(R, T))",
"PointLiesOnLine(V, Line(Q, U))"
] | [
"QU",
"QV",
"RQ",
"RS",
"RT",
"SV",
"TS",
"TU",
"VU"
] | {"Q": [62.0, 2.0], "R": [185.0, 2.0], "S": [217.0, 69.0], "T": [251.0, 139.0], "U": [1.0, 140.0], "V": [32.0, 68.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(L, K)), 2)
- Equals(LengthOf(Line(J, K)), 12)
- Equals(LengthOf(Line(M, N)), 6)
- Equals(LengthOf(Line(M, L)), x)
- PointLiesOnLine(K, Line(J, L))
- PointLiesOnLine(M, Line(L, N))
- PointLiesOnCircle(J, Circle(A, radius_4_0))
- PointLiesOnCircle(M, Circle(A, radius_4_0))
- Poi... | 3.1 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(L, K)), 2)",
"Equals(LengthOf(Line(J, K)), 12)",
"Equals(LengthOf(Line(M, N)), 6)",
"Equals(LengthOf(Line(M, L)), x)",
"PointLiesOnLine(K, Line(J, L))",
"PointLiesOnLine(M, Line(L, N))",
"PointLiesOnCircle(J, Circle(A, radius_4_0))",
"PointLiesOnCircle(M, Circle(A, radius_4_0))",... | [
"JK",
"JL",
"KM",
"MN",
"LK",
"LM",
"LN"
] | {"A": [98.0, 121.0], "J": [9.0, 157.0], "K": [141.0, 37.0], "M": [174.0, 65.0], "N": [162.0, 190.0], "L": [180.0, 1.0]} | [
"A"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(G, C, B)), 32)
- Equals(MeasureOf(Angle(G, B, A)), 34)
- Equals(LengthOf(Line(A, G)), 15)
- Equals(LengthOf(Line(A, E)), 12)
- PointLiesOnLine(E, Line(B, A))
- PointLiesOnLine(D, Line(B, C))
- PointLiesOnLine(F, Line(A, C))
- PointLiesOnLine(G, Line(A, D))
- Perpendicular(Li... | 9 | [
"IsIncenterOf(Point(J),Angle(A,B,C))",
"Find(LengthOf(Line(J,F)))"
] | [
"Equals(MeasureOf(Angle(G, C, B)), 32)",
"Equals(MeasureOf(Angle(G, B, A)), 34)",
"Equals(LengthOf(Line(A, G)), 15)",
"Equals(LengthOf(Line(A, E)), 12)",
"PointLiesOnLine(E, Line(B, A))",
"PointLiesOnLine(D, Line(B, C))",
"PointLiesOnLine(F, Line(A, C))",
"PointLiesOnLine(G, Line(A, D))",
"Perpendic... | [
"AC",
"AD",
"AE",
"AG",
"BA",
"BC",
"BD",
"BE",
"BG",
"CD",
"FA",
"FB",
"FC",
"FG",
"GC",
"GD",
"GE"
] | {"A": [352.0, 448.0], "B": [2.0, 188.0], "C": [309.0, 1.0], "D": [151.0, 97.0], "E": [140.0, 291.0], "F": [327.0, 186.0], "G": [209.0, 196.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, B)), 4)
- Equals(LengthOf(Line(E, F)), 14)
- Equals(LengthOf(Line(A, C)), 8)
- PointLiesOnLine(E, Line(B, D))
- PointLiesOnLine(F, Line(C, A))
- Perpendicular(Line(E, F), Line(F, A))
Find the area of the trapezoid. | 84 | [
"Find(AreaOf(Trapezoid($)))"
] | [
"Equals(LengthOf(Line(D, B)), 4)",
"Equals(LengthOf(Line(E, F)), 14)",
"Equals(LengthOf(Line(A, C)), 8)",
"PointLiesOnLine(E, Line(B, D))",
"PointLiesOnLine(F, Line(C, A))",
"Perpendicular(Line(E, F), Line(F, A))"
] | [
"AC",
"AD",
"CB",
"DB"
] | {"A": [110.0, 182.0], "B": [42.0, 0.0], "C": [0.0, 182.0], "D": [97.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 15)
- Equals(LengthOf(Line(A, B)), y)
- Equals(LengthOf(Line(C, D)), 19)
- Equals(LengthOf(Line(B, C)), x)
- Equals(LengthOf(Line(B, D)), z)
- PointLiesOnLine(C, Line(A, D))
- Perpendicular(Line(C, D), Line(B, C))
- Perpendicular(Line(A, B), Line(B, D))
Find z. | \sqrt { 646 } | [
"Find(z)"
] | [
"Equals(LengthOf(Line(A, C)), 15)",
"Equals(LengthOf(Line(A, B)), y)",
"Equals(LengthOf(Line(C, D)), 19)",
"Equals(LengthOf(Line(B, C)), x)",
"Equals(LengthOf(Line(B, D)), z)",
"PointLiesOnLine(C, Line(A, D))",
"Perpendicular(Line(C, D), Line(B, C))",
"Perpendicular(Line(A, B), Line(B, D))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [0.663770656302006, 1.9588715721017707], "B": [0.4592633224537508, 215.50569334697258], "C": [109.67633459436738, 98.35014712063892], "D": [242.3823064770932, 216.67140600315955]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(P, Q)), 25)
- Equals(LengthOf(Line(R, T)), x)
- Equals(LengthOf(Line(R, S)), 10)
- Equals(LengthOf(Line(S, Q)), 5)
- PointLiesOnLine(T, Line(P, R))
- PointLiesOnLine(S, Line(Q, R))
- Perpendicular(Line(R, T), Line(R, S))
- Parallel(Line(P, Q), Line(T, S))
Find x | \frac { 40 } { 3 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(P, Q)), 25)",
"Equals(LengthOf(Line(R, T)), x)",
"Equals(LengthOf(Line(R, S)), 10)",
"Equals(LengthOf(Line(S, Q)), 5)",
"PointLiesOnLine(T, Line(P, R))",
"PointLiesOnLine(S, Line(Q, R))",
"Perpendicular(Line(R, T), Line(R, S))",
"Parallel(Line(P, Q), Line(T, S))"
] | [
"PT",
"PR",
"TR",
"RS",
"SQ",
"RQ",
"TS",
"PQ"
] | {"S": [86.0, 167.0], "Q": [123.0, 167.0], "P": [-0.0, 0.0], "R": [2.0, 165.0], "T": [1.0, 57.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, E)), 11)
- Equals(LengthOf(Line(E, E)), 13)
- PointLiesOnLine(E, Line(B, D))
- PointLiesOnLine(E, Line(C, O))
Find the area of the figure. Round to the nearest tenth if necessary. | 286 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(C, E)), 11)",
"Equals(LengthOf(Line(E, E)), 13)",
"PointLiesOnLine(E, Line(B, D))",
"PointLiesOnLine(E, Line(C, O))"
] | [
"BC",
"BO",
"DO",
"CD",
"DE",
"BE",
"CE",
"OE",
"CO",
"BD"
] | {"B": [129.0, 62.0], "C": [67.0, 2.0], "D": [7.0, 61.0], "O": [68.0, 121.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), 103)
- Equals(MeasureOf(Angle(A, B, C)), 43)
- Equals(MeasureOf(Angle(C, A, B)), 51)
What is the perimeter of the triangle shown below? Round to the nearest tenth. | 325.6 | [
"Find(PerimeterOf(Triangle($)))"
] | [
"Equals(LengthOf(Line(B, C)), 103)",
"Equals(MeasureOf(Angle(A, B, C)), 43)",
"Equals(MeasureOf(Angle(C, A, B)), 51)"
] | [
"AB",
"AC",
"BC"
] | {"A": [0.0, 103.0], "B": [193.0, 103.0], "C": [86.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(Y, V, W)), 25)
- Equals(MeasureOf(Angle(Z, A, X)), 110)
- Equals(MeasureOf(Angle(Y, A, W)), x)
- PointLiesOnLine(Y, Line(V, B))
- PointLiesOnLine(Z, Line(V, B))
- PointLiesOnLine(X, Line(V, C))
- PointLiesOnLine(W, Line(V, C))
- PointLiesOnLine(Y, Line(V, Z))
- PointLiesOnLi... | 60 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(Y, V, W)), 25)",
"Equals(MeasureOf(Angle(Z, A, X)), 110)",
"Equals(MeasureOf(Angle(Y, A, W)), x)",
"PointLiesOnLine(Y, Line(V, B))",
"PointLiesOnLine(Z, Line(V, B))",
"PointLiesOnLine(X, Line(V, C))",
"PointLiesOnLine(W, Line(V, C))",
"PointLiesOnLine(Y, Line(V, Z))",
"PointL... | [
"BY",
"BZ",
"CW",
"CX",
"VB",
"VC",
"VW",
"VX",
"VY",
"VZ",
"XW",
"YZ"
] | {"A": [294.0, 115.0], "B": [506.0, 0.0], "C": [507.0, 227.0], "V": [2.0, 115.0], "W": [195.0, 157.0], "X": [364.0, 195.0], "Y": [196.0, 71.0], "Z": [363.0, 33.0]} | [
"A"
] |
Diagram Logic Form:
- PointLiesOnLine(B, Line(D, E))
- PointLiesOnLine(X, Line(D, E))
- PointLiesOnLine(Y, Line(D, E))
- PointLiesOnLine(B, Line(D, G))
- PointLiesOnLine(X, Line(D, G))
- PointLiesOnLine(Y, Line(D, G))
- PointLiesOnLine(Z, Line(D, G))
- PointLiesOnLine(Y, Line(D, B))
- PointLiesOnLine(B, Line(D, X))
- P... | 2 | [
"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(A,Z)))"
] | [
"PointLiesOnLine(B, Line(D, E))",
"PointLiesOnLine(X, Line(D, E))",
"PointLiesOnLine(Y, Line(D, E))",
"PointLiesOnLine(B, Line(D, G))",
"PointLiesOnLine(X, Line(D, G))",
"PointLiesOnLine(Y, Line(D, G))",
"PointLiesOnLine(Z, Line(D, G))",
"PointLiesOnLine(Y, Line(D, B))",
"PointLiesOnLine(B, Line(D, ... | [
"BA",
"BC",
"BX",
"BY",
"BZ",
"CA",
"CW",
"DA",
"DB",
"DC",
"DE",
"DF",
"DG",
"DH",
"DX",
"DY",
"DZ",
"EA",
"EB",
"EC",
"EF",
"EG",
"EX",
"EY",
"EZ",
"FA",
"FB",
"FC",
"FG",
"FX",
"FY",
"FZ",
"GA",
"GB",
"GC",
"GX",
"GY",
"GZ",
"HC",
"HW"... | {"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": [366.0, 112.0], "G": [1.0, 108.0], "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(D, C, B)), 101)
- Parallel(Line(A, B), Line(D, C))
- Equals(LengthOf(Line(A, D)), LengthOf(Line(B, C)))
Find $m\angle D$ | 101 | [
"Find(MeasureOf(Angle(D)))"
] | [
"Equals(MeasureOf(Angle(D, C, B)), 101)",
"Parallel(Line(A, B), Line(D, C))",
"Equals(LengthOf(Line(A, D)), LengthOf(Line(B, C)))"
] | [
"AB",
"BC",
"CD",
"DA"
] | {"A": [8.0, 7.0], "B": [165.0, 8.0], "C": [138.0, 144.0], "D": [28.0, 146.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(F, K)), 16)
- Equals(LengthOf(Line(A, K)), 9)
- Perpendicular(Line(D, F), Line(F, K))
- Perpendicular(Line(F, K), Line(K, A))
- Perpendicular(Line(A, D), Line(D, F))
- Perpendicular(Line(A, D), Line(A, K))
Find the perimeter of the figure. | 50 | [
"Find(PerimeterOf(Shape($)))"
] | [
"Equals(LengthOf(Line(F, K)), 16)",
"Equals(LengthOf(Line(A, K)), 9)",
"Perpendicular(Line(D, F), Line(F, K))",
"Perpendicular(Line(F, K), Line(K, A))",
"Perpendicular(Line(A, D), Line(D, F))",
"Perpendicular(Line(A, D), Line(A, K))"
] | [
"AD",
"AK",
"DF",
"KF"
] | {"A": [277.0, 2.0], "D": [0.0, 0.0], "F": [2.0, 156.0], "K": [279.0, 157.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, B)), 40)
- Equals(LengthOf(Line(S, D)), 28)
- Equals(LengthOf(Line(D, B)), 38)
- PointLiesOnLine(S, Line(A, D))
- Perpendicular(Line(B, D), Line(D, S))
Find the area of the parallelogram. Round to the nearest tenth if necessary. | 1520 | [
"Find(AreaOf(Parallelogram($)))"
] | [
"Equals(LengthOf(Line(C, B)), 40)",
"Equals(LengthOf(Line(S, D)), 28)",
"Equals(LengthOf(Line(D, B)), 38)",
"PointLiesOnLine(S, Line(A, D))",
"Perpendicular(Line(B, D), Line(D, S))"
] | [
"AC",
"AD",
"AS",
"BD",
"CB",
"SB",
"SD"
] | {"A": [99.0, 1.0], "B": [2.0, 177.0], "C": [1.0, 73.0], "D": [99.0, 177.0], "S": [99.0, 103.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(R, P)), 3)
- PointLiesOnLine(R, Line(Q, S))
- PointLiesOnCircle(Q, Circle(P, radius_2_0))
- PointLiesOnCircle(S, Circle(P, radius_2_0))
- Perpendicular(Line(Q, R), Line(P, R))
The radius of $\odot P$ is 5 and $P R=3$. Find QS | 8 | [
"Equals(RadiusOf(Circle(P)),5)",
"Equals(LengthOf(Line(P,R)),3)",
"Find(LengthOf(Line(Q,S)))"
] | [
"Equals(LengthOf(Line(R, P)), 3)",
"PointLiesOnLine(R, Line(Q, S))",
"PointLiesOnCircle(Q, Circle(P, radius_2_0))",
"PointLiesOnCircle(S, Circle(P, radius_2_0))",
"Perpendicular(Line(Q, R), Line(P, R))"
] | [
"PR",
"QP",
"QR",
"QS",
"SP",
"SR"
] | {"P": [86.0, 89.0], "Q": [142.0, 21.0], "R": [143.0, 87.0], "S": [144.0, 156.0]} | [
"P"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, I)), 7)
- Equals(LengthOf(Line(B, H)), 3)
Find the area of the kite. | 10.5 | [
"Find(AreaOf(Kite($)))"
] | [
"Equals(LengthOf(Line(A, I)), 7)",
"Equals(LengthOf(Line(B, H)), 3)"
] | [
"AB",
"AH",
"BI",
"HI",
"BH",
"AI"
] | {"A": [45.0, 4.0], "B": [2.0, 53.0], "H": [96.0, 50.0], "I": [49.0, 207.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(P, Line(X, Z))
- PointLiesOnLine(P, Line(W, Y))
- Perpendicular(Line(W, Z), Line(X, W))
Quadrilateral WXYZ is a rectangle. If $ZY = 2x + 3$ and $WX = x + 4$, find $WX$. | 5 | [
"Rectangle(W,X,Y,Z)",
"Equals(LengthOf(Line(Z,Y)),2x+3)",
"Equals(LengthOf(Line(W,X)),x+4)",
"Find(LengthOf(Line(W,X)))"
] | [
"PointLiesOnLine(P, Line(X, Z))",
"PointLiesOnLine(P, Line(W, Y))",
"Perpendicular(Line(W, Z), Line(X, W))"
] | [
"WP",
"WY",
"WZ",
"XP",
"XW",
"XY",
"XZ",
"YP",
"YZ",
"ZP"
] | {"P": [137.0, 69.0], "W": [1.0, 137.0], "X": [275.0, 136.0], "Y": [273.0, 2.0], "Z": [0.0, 0.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), x)
- Equals(MeasureOf(Angle(C, A, B)), 20)
- Equals(MeasureOf(Angle(A, C, B)), 135)
- Equals(LengthOf(Line(B, C)), 18)
Find x. Round the side measure to the nearest tenth. | 37.2 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), x)",
"Equals(MeasureOf(Angle(C, A, B)), 20)",
"Equals(MeasureOf(Angle(A, C, B)), 135)",
"Equals(LengthOf(Line(B, C)), 18)"
] | [
"AB",
"AC",
"BC"
] | {"A": [0.0, 0.0], "B": [276.0, 104.0], "C": [135.0, 115.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(Y, X)), 8)
- Equals(MeasureOf(Angle(Y, X, Z)), 60)
- Equals(LengthOf(Line(X, Z)), 8)
Find $YZ$. | 8 | [
"Find(LengthOf(Line(Y,Z)))"
] | [
"Equals(LengthOf(Line(Y, X)), 8)",
"Equals(MeasureOf(Angle(Y, X, Z)), 60)",
"Equals(LengthOf(Line(X, Z)), 8)"
] | [
"XZ",
"YX",
"YZ"
] | {"X": [1.0, 2.0], "Y": [345.0, 92.0], "Z": [94.0, 345.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, A, E)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(E, B, A)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(D, B, E)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(A, E, B)), MeasureOf(angle 6))
- Equals(MeasureOf(Angle(B, E, C)), MeasureOf(angle 5))
- Equals(MeasureOf(A... | 73 | [
"Equals(MeasureOf(Angle(1)),58)",
"Equals(MeasureOf(Angle(2)),47)",
"Equals(MeasureOf(Angle(3)),26)",
"Find(MeasureOf(Angle(8)))"
] | [
"Equals(MeasureOf(Angle(B, A, E)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(E, B, A)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(D, B, E)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(A, E, B)), MeasureOf(angle 6))",
"Equals(MeasureOf(Angle(B, E, C)), MeasureOf(angle 5))",
"Equals(MeasureOf(Ang... | [
"BA",
"BC",
"BE",
"DA",
"DB",
"DC",
"DE",
"EA",
"EC"
] | {"A": [1.0, 8.0], "B": [198.0, 8.0], "C": [160.0, 132.0], "D": [133.0, 216.0], "E": [81.0, 131.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, M)), 7)
- Equals(LengthOf(Line(E, F)), 5)
- Equals(AreaOf(Triangle(D, E, F)), 13.5)
For the pair of similar figures, find the area of the green figure. | 78.4 | [
"Similar(Shape($1),Shape($2))",
"Find(AreaOf(Green(Shape($))))"
] | [
"Equals(LengthOf(Line(B, M)), 7)",
"Equals(LengthOf(Line(E, F)), 5)",
"Equals(AreaOf(Triangle(D, E, F)), 13.5)"
] | [
"AB",
"AM",
"BM",
"DE",
"EF",
"DF"
] | {"A": [166.0, 1.0], "B": [61.0, 89.0], "M": [1.0, 18.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(R, F)), 2)
- Equals(LengthOf(Line(R, E)), r)
- Equals(LengthOf(Line(D, F)), 16)
- Equals(LengthOf(Line(A, E)), 18.5)
- Equals(LengthOf(Line(B, D)), 9)
- Equals(LengthOf(Line(A, B)), 15)
- PointLiesOnLine(E, Line(R, A))
- PointLiesOnLine(D, Line(R, B))
- PointLiesOnLine(F, Line... | 9.0 | [
"Tangent(Line($),Circle($))",
"Find(q)"
] | [
"Equals(LengthOf(Line(R, F)), 2)",
"Equals(LengthOf(Line(R, E)), r)",
"Equals(LengthOf(Line(D, F)), 16)",
"Equals(LengthOf(Line(A, E)), 18.5)",
"Equals(LengthOf(Line(B, D)), 9)",
"Equals(LengthOf(Line(A, B)), 15)",
"PointLiesOnLine(E, Line(R, A))",
"PointLiesOnLine(D, Line(R, B))",
"PointLiesOnLine(... | [
"AB",
"AE",
"BD",
"BF",
"DF",
"RA",
"RB",
"RD",
"RE",
"RF"
] | {"A": [144.0, 233.0], "B": [1.0, 232.0], "C": [146.0, 139.0], "D": [54.0, 165.0], "E": [172.0, 47.0], "F": [148.0, 43.0], "R": [179.0, 2.0]} | [
"C"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, A)), 10)
- Equals(LengthOf(Line(C, M)), 6)
- PointLiesOnLine(M, Line(A, B))
- Perpendicular(Line(C, M), Line(M, B))
- Perpendicular(Line(C, A), Line(C, B))
Find the perimeter of $\triangle A B C$ | 30 | [
"Find(PerimeterOf(Triangle(A,B,C)))"
] | [
"Equals(LengthOf(Line(C, A)), 10)",
"Equals(LengthOf(Line(C, M)), 6)",
"PointLiesOnLine(M, Line(A, B))",
"Perpendicular(Line(C, M), Line(M, B))",
"Perpendicular(Line(C, A), Line(C, B))"
] | [
"CA",
"CM",
"CB",
"AM",
"AB",
"MB"
] | {"C": [2.2244514854558517, 162.1975404218664], "A": [0.0, 0.0], "M": [75.4325811159762, 114.37330189738408], "B": [107.43847431396972, 163.31691390178537]} | [] |
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... | 21 | [
"Equals(x,7\\sqrt{3})",
"Find(LengthOf(Line(C,E)))"
] | [
"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(MeasureOf(Arc(B, D)), 10x)
- Equals(MeasureOf(Arc(F, D)), 40)
- Equals(MeasureOf(Angle(F, C, D)), x)
- PointLiesOnLine(F, Line(B, C))
- PointLiesOnCircle(B, Circle(E, radius_4_0))
- PointLiesOnCircle(D, Circle(E, radius_4_0))
- PointLiesOnCircle(F, Circle(E, radius_4_0))
Find x. Assume tha... | 5 | [
"Tangent(Line($),Circle($))",
"Find(x)"
] | [
"Equals(MeasureOf(Arc(B, D)), 10x)",
"Equals(MeasureOf(Arc(F, D)), 40)",
"Equals(MeasureOf(Angle(F, C, D)), x)",
"PointLiesOnLine(F, Line(B, C))",
"PointLiesOnCircle(B, Circle(E, radius_4_0))",
"PointLiesOnCircle(D, Circle(E, radius_4_0))",
"PointLiesOnCircle(F, Circle(E, radius_4_0))"
] | [
"BC",
"BF",
"CD",
"CF"
] | {"B": [4.0, 34.0], "C": [169.0, 6.0], "D": [72.0, 3.0], "E": [56.0, 54.0], "F": [96.0, 14.0]} | [
"E"
] |
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