images
images listlengths 1
1
| problem
stringlengths 13
234
| answer
stringlengths 1
34
| id
int64 0
2.1k
| choices
sequencelengths 4
4
| ground_truth
stringclasses 4
values | diagram_logic_form
sequencelengths 0
456
|
|---|---|---|---|---|---|---|
<image>Find $m \angle P$. | 35 | 645 | [
"28",
"35",
"56",
"70"
] | B | [
"Equals(MeasureOf(Angle(P, N, O)), 56)",
"Equals(MeasureOf(Angle(N, B, M)), 70)",
"",
"PointLiesOnCircle(O, Circle(B, radius_5_0))",
"PointLiesOnCircle(N, Circle(B, radius_5_0))",
"PointLiesOnCircle(P, Circle(B, radius_5_0))",
"PointLiesOnCircle(M, Circle(B, radius_5_0))"
] |
|
<image>Find $x$. | 8 | 1,210 | [
"7",
"8",
"11",
"13"
] | B | [
"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))",
"PointLiesOnCircle(P, Circle(Q, radius_4_0))",
"PointLiesOnCircle(N, Circle(Q, radius_4_0))",
"PointLiesOnCircle(L, Circle(Q, radius_4_0))",
"PointLiesOnCircle(M, Circle(Q, radius_4_0))"
] |
|
<image>Find $y$ in the given parallelogram | 2 | 483 | [
"2",
"10",
"31",
"149"
] | A | [
"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)"
] |
|
<image>Find $XZ$ of isosceles $\triangle XYZ$ | 12 | 1,619 | [
"7",
"8",
"12",
"16"
] | C | [
"Equals(LengthOf(Line(X, Y)), 2x+3)",
"Equals(LengthOf(Line(A, Y)), 4x-1)",
"Equals(LengthOf(Line(X, Y)), LengthOf(Line(A, Y)))"
] |
|
<image>Find $y$. | 15.6 | 26 | [
"9",
"10.4",
"12.7",
"15.6"
] | D | [
"Equals(LengthOf(Line(A, B)), y)",
"Equals(LengthOf(Line(A, C)), x)",
"Equals(MeasureOf(Angle(A, B, C)), 30)",
"Equals(LengthOf(Line(B, C)), 18)",
"Perpendicular(Line(A, B), Line(A, C))"
] |
|
<image>In the figure, $\overline{CP}$ is an altitude, $\overline{CQ}$ is the angle bisector of $∠ACB$, and $R$ is the midpoint of $\overline{AB}$. Find $AB$ if $AR=3x+6$ and $RB = 5x - 14 $. | 72 | 746 | [
"66",
"68",
"70",
"72"
] | D | [
"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))",
"PointLiesOnLine(Q, Line(B, P))"
] |
|
<image>Find the value of x. | 130 | 1,768 | [
"30",
"90",
"110",
"130"
] | D | [
"Equals(MeasureOf(Angle(E, B, A)), 30)",
"Equals(MeasureOf(Angle(D, B, E)), x)",
"Equals(MeasureOf(Angle(C, B, D)), 110)",
"PointLiesOnCircle(A, Circle(B, radius_1_0))",
"PointLiesOnCircle(C, Circle(B, radius_1_0))",
"PointLiesOnCircle(D, Circle(B, radius_1_0))",
"PointLiesOnCircle(E, Circle(B, radius_1_0))",
"Perpendicular(Line(A, B), Line(B, C))"
] |
|
<image>Find x. Round the side measure to the nearest tenth. | 22.8 | 1,056 | [
"6.4",
"7.4",
"22.8",
"26.5"
] | C | [
"Equals(LengthOf(Line(A, E)), 13)",
"Equals(MeasureOf(Angle(C, E, A)), 18)",
"Equals(MeasureOf(Angle(E, A, C)), 141)",
"Equals(LengthOf(Line(C, E)), x)"
] |
|
<image>Find x. | 6 | 1,289 | [
"1.5",
"4",
"6",
"9"
] | C | [
"Equals(LengthOf(Line(A, B)), y)",
"Equals(LengthOf(Line(B, C)), z)",
"Equals(LengthOf(Line(B, D)), x)",
"Equals(LengthOf(Line(A, D)), 9)",
"Equals(LengthOf(Line(C, D)), 4)",
"PointLiesOnLine(D, Line(A, C))",
"Perpendicular(Line(A, B), Line(B, C))",
"Perpendicular(Line(B, D), Line(C, D))"
] |
|
<image>Find $x$. | 18 | 2,007 | [
"12",
"15",
"18",
"21"
] | C | [
"Equals(LengthOf(Line(E, B)), 5y)",
"Equals(LengthOf(Line(D, B)), \\frac{7}{3}y+8)",
"Equals(LengthOf(Line(C, E)), \\frac{1}{3}x+2)",
"Equals(LengthOf(Line(A, C)), \\frac{2}{3}x-4)",
"PointLiesOnLine(C, Line(A, E))",
"PointLiesOnLine(B, Line(D, E))",
"Equals(LengthOf(Line(A, C)), LengthOf(Line(C, E)))",
"Equals(MeasureOf(Angle(E, B, C)), MeasureOf(Angle(B, D, A)))"
] |
|
<image>Find the area of the shaded region. Round to the nearest tenth. | 7.9 | 187 | [
"3.9",
"5.2",
"7.9",
"20.4"
] | C | [
"Equals(LengthOf(Line(C, F)), 3)",
"Equals(MeasureOf(Angle(E, A, D)), 130)",
"PointLiesOnLine(A, Line(B, D))",
"PointLiesOnLine(A, Line(C, E))",
"PointLiesOnCircle(B, Circle(A, radius_0_0))",
"Equals(MeasureOf(Angle(C, A, D)), MeasureOf(Angle(B, A, E)))",
"PointLiesOnCircle(C, Circle(A, radius_0_0))",
"PointLiesOnCircle(D, Circle(A, radius_0_0))",
"PointLiesOnCircle(E, Circle(A, radius_0_0))"
] |
|
<image>Find x. | 3 \sqrt { 29 } | 250 | [
"3 \\sqrt { 21 }",
"3 \\sqrt { 29 }",
"17",
"21"
] | B | [
"Equals(LengthOf(Line(B, C)), 15)",
"Equals(LengthOf(Line(A, C)), 6)",
"Equals(LengthOf(Line(A, B)), x)",
"Perpendicular(Line(B, C), Line(A, C))"
] |
|
<image>In rhombus LMPQ, $m \angle Q L M=2 x^{2}-10$, $m \angle Q P M=8 x$, and $M P=10$ .
Find $m \angle L P Q$ | 20 | 1,130 | [
"20",
"30",
"45",
"60"
] | A | [
"Equals(LengthOf(Line(P, M)), 10)",
"PointLiesOnLine(R, Line(P, L))",
"PointLiesOnLine(R, Line(M, Q))"
] |
|
<image>Find the variable of $d$ to the nearest tenth. Assume that segments that appear to be tangent are tangent. | 16.9 | 1,058 | [
"12.8",
"14.7",
"16.9",
"18.2"
] | C | [
"Equals(LengthOf(Line(D, G)), d)",
"Equals(LengthOf(Line(D, F)), 9)",
"Equals(LengthOf(Line(H, E)), 15)",
"Equals(LengthOf(Line(D, H)), 11)",
"PointLiesOnLine(F, Line(A, D))",
"PointLiesOnLine(H, Line(D, E))",
"PointLiesOnCircle(A, Circle(C, radius_5_0))",
"PointLiesOnCircle(E, Circle(C, radius_5_0))",
"PointLiesOnCircle(F, Circle(C, radius_5_0))",
"PointLiesOnCircle(H, Circle(C, radius_5_0))",
"PointLiesOnCircle(G, Circle(C, radius_5_0))"
] |
|
<image>$m∠19 = 100 + 20x$, $m∠20 = 20x $. Find the measure of $\angle 20$. | 40 | 1,150 | [
"20",
"40",
"60",
"80"
] | B | [
"Equals(MeasureOf(Angle(C, G, B)), MeasureOf(Angle(19)))",
"Equals(MeasureOf(Angle(B, G, D)), MeasureOf(Angle(20)))",
"PointLiesOnLine(G, Line(B, E))",
"PointLiesOnLine(G, Line(C, D))"
] |
|
<image>If $CN=8$. Find $DN$. | 8 | 227 | [
"4",
"8",
"12",
"16"
] | B | [
"PointLiesOnLine(N, Line(F, D))",
"PointLiesOnCircle(E, Circle(N, radius_6_0))",
"PointLiesOnCircle(F, Circle(N, radius_6_0))",
"PointLiesOnCircle(C, Circle(N, radius_6_0))",
"PointLiesOnCircle(D, Circle(N, radius_6_0))"
] |
|
<image>The segment is tangent to the circle. Find $x$. | 9 | 1,304 | [
"6",
"8",
"9",
"12"
] | C | [
"Equals(LengthOf(Line(B, C)), 12)",
"Equals(LengthOf(Line(E, C)), 6)",
"Equals(LengthOf(Line(A, B)), x)",
"Equals(LengthOf(Line(A, E)), x)",
"",
"PointLiesOnCircle(E, Circle(A, radius_7_0))",
"PointLiesOnCircle(B, Circle(A, radius_7_0))"
] |
|
<image>Find $m\angle K$ | 62 | 1,041 | [
"62",
"72",
"116",
"160"
] | A | [
"Equals(MeasureOf(Angle(J, M, L)), 2x-8)",
"Equals(MeasureOf(Angle(M, J, K)), 3x-6)",
"Equals(MeasureOf(Angle(J, K, L)), x+10)",
"Equals(MeasureOf(Angle(K, L, M)), x)"
] |
|
<image>$\overline{AD}$ and $\overline{CG}$ are diameters of $\odot B$. Find $m \widehat {GCF}$. | 325 | 162 | [
"35",
"295",
"305",
"325"
] | D | [
"Equals(MeasureOf(Angle(C, B, D)), 55)",
"Equals(MeasureOf(Angle(G, B, F)), 35)",
"PointLiesOnLine(B, Line(A, D))",
"PointLiesOnLine(B, Line(C, G))",
"PointLiesOnCircle(F, Circle(B, radius_6_0))",
"PointLiesOnCircle(D, Circle(B, radius_6_0))",
"PointLiesOnCircle(A, Circle(B, radius_6_0))",
"PointLiesOnCircle(C, Circle(B, radius_6_0))",
"PointLiesOnCircle(G, Circle(B, radius_6_0))"
] |
|
<image>What is the length of $\overline{EF}$? | 26 | 1,537 | [
"13",
"14.5",
"26",
"29"
] | C | [
"Equals(MeasureOf(Angle(F, D, E)), 42)",
"Equals(MeasureOf(Angle(D, F, E)), 4x+11)",
"Equals(LengthOf(Line(F, E)), 2x-3)",
"Equals(LengthOf(Line(D, E)), LengthOf(Line(D, F)))"
] |
|
<image>Express the ratio of $\sin L$ as a decimal to the nearest hundredth. | 0.38 | 1,692 | [
"0.38",
"0.42",
"0.92",
"2.40"
] | A | [
"Equals(LengthOf(Line(L, J)), 13)",
"Equals(LengthOf(Line(K, J)), 5)",
"Equals(LengthOf(Line(K, L)), 12)",
"Perpendicular(Line(K, J), Line(K, L))"
] |
|
<image>Find the area of the shaded region. | 50.3 | 2,087 | [
"12.6",
"50.3",
"100.5",
"402.1"
] | B | [
"Equals(LengthOf(Line(A, C)), 0)",
"Equals(LengthOf(Line(O, E)), 12)",
"PointLiesOnLine(F, Line(C, G))",
"PointLiesOnLine(A, Line(D, E))",
"PointLiesOnLine(O, Line(D, E))",
"PointLiesOnCircle(C, Circle(B, radius_1_1))",
"PointLiesOnCircle(F, Circle(B, radius_1_1))"
] |
|
<image>The diameters of $\odot A, \odot B,$ and $\odot C$ are 10, 30 and 10 units, respectively. Find BY if $\overline{A Z} \cong \overline{C W}$ and $C W=2$. | 12 | 1,865 | [
"6",
"12",
"48",
"60"
] | B | [
"PointLiesOnLine(B, Line(D, E))",
"PointLiesOnLine(X, Line(D, E))",
"PointLiesOnLine(Y, Line(D, E))",
"PointLiesOnLine(Y, Line(D, B))",
"PointLiesOnLine(B, Line(D, F))",
"PointLiesOnLine(X, Line(D, F))",
"PointLiesOnLine(Y, Line(D, F))",
"PointLiesOnLine(Z, Line(D, F))",
"PointLiesOnLine(B, Line(D, X))",
"PointLiesOnLine(Y, Line(D, X))",
"PointLiesOnLine(B, Line(D, Z))",
"PointLiesOnLine(X, Line(D, Z))",
"PointLiesOnLine(Y, Line(D, Z))",
"PointLiesOnLine(E, Line(D, A))",
"PointLiesOnLine(B, Line(D, A))",
"PointLiesOnLine(X, Line(D, A))",
"PointLiesOnLine(Y, Line(D, A))",
"PointLiesOnLine(X, Line(E, B))",
"PointLiesOnLine(Z, Line(E, F))",
"PointLiesOnLine(A, Line(E, F))",
"PointLiesOnLine(D, Line(E, G))",
"PointLiesOnLine(B, Line(E, G))",
"PointLiesOnLine(Y, Line(E, G))",
"PointLiesOnLine(B, Line(E, Y))",
"PointLiesOnLine(X, Line(E, Y))",
"PointLiesOnLine(D, Line(E, C))",
"PointLiesOnLine(B, Line(E, C))",
"PointLiesOnLine(X, Line(E, C))",
"PointLiesOnLine(Y, Line(E, C))",
"PointLiesOnLine(A, Line(E, Z))",
"PointLiesOnLine(X, Line(B, F))",
"PointLiesOnLine(Z, Line(B, F))",
"PointLiesOnLine(D, Line(B, G))",
"PointLiesOnLine(Y, Line(B, G))",
"PointLiesOnLine(D, Line(B, C))",
"PointLiesOnLine(Y, Line(B, C))",
"PointLiesOnLine(X, Line(B, Z))",
"PointLiesOnLine(A, Line(B, Z))",
"PointLiesOnLine(E, Line(B, A))",
"PointLiesOnLine(X, Line(B, A))",
"PointLiesOnLine(D, Line(F, G))",
"PointLiesOnLine(B, Line(F, G))",
"PointLiesOnLine(X, Line(F, G))",
"PointLiesOnLine(Y, Line(F, G))",
"PointLiesOnLine(C, Line(F, G))",
"PointLiesOnLine(Z, Line(F, G))",
"PointLiesOnLine(Z, Line(F, X))",
"PointLiesOnLine(B, Line(F, Y))",
"PointLiesOnLine(X, Line(F, Y))",
"PointLiesOnLine(Z, Line(F, Y))",
"PointLiesOnLine(D, Line(F, C))",
"PointLiesOnLine(X, Line(F, C))",
"PointLiesOnLine(Y, Line(F, C))",
"PointLiesOnLine(Z, Line(F, C))",
"PointLiesOnLine(Z, Line(F, A))",
"PointLiesOnLine(D, Line(G, X))",
"PointLiesOnLine(B, Line(G, X))",
"PointLiesOnLine(Y, Line(G, X))",
"PointLiesOnLine(D, Line(G, Y))",
"PointLiesOnLine(D, Line(G, Z))",
"PointLiesOnLine(B, Line(G, Z))",
"PointLiesOnLine(X, Line(G, Z))",
"PointLiesOnLine(Y, Line(G, Z))",
"PointLiesOnLine(D, Line(G, A))",
"PointLiesOnLine(E, Line(G, A))",
"PointLiesOnLine(B, Line(G, A))",
"PointLiesOnLine(X, Line(G, A))",
"PointLiesOnLine(Y, Line(G, A))",
"PointLiesOnLine(B, Line(X, Y))",
"PointLiesOnLine(D, Line(X, C))",
"PointLiesOnLine(B, Line(X, C))",
"PointLiesOnLine(Y, Line(X, C))",
"PointLiesOnLine(E, Line(X, A))",
"PointLiesOnLine(D, Line(Y, C))",
"PointLiesOnLine(B, Line(Y, Z))",
"PointLiesOnLine(X, Line(Y, Z))",
"PointLiesOnLine(E, Line(Y, A))",
"PointLiesOnLine(B, Line(Y, A))",
"PointLiesOnLine(X, Line(Y, A))",
"PointLiesOnLine(D, Line(C, Z))",
"PointLiesOnLine(B, Line(C, Z))",
"PointLiesOnLine(X, Line(C, Z))",
"PointLiesOnLine(Y, Line(C, Z))",
"PointLiesOnLine(D, Line(C, A))",
"PointLiesOnLine(E, Line(C, A))",
"PointLiesOnLine(B, Line(C, A))",
"PointLiesOnLine(X, Line(C, A))",
"PointLiesOnLine(Y, Line(C, A))",
"PointLiesOnCircle(D, Circle(B, radius_2_0))",
"PointLiesOnCircle(E, Circle(B, radius_2_0))",
"PointLiesOnCircle(G, Circle(C, radius_9_0))",
"PointLiesOnCircle(Y, Circle(C, radius_9_0))",
"PointLiesOnCircle(F, Circle(A, radius_11_0))",
"PointLiesOnCircle(X, Circle(A, radius_11_0))"
] |
|
<image>Find y | 9.6 \sqrt { 2 } | 1,786 | [
"4.8",
"4.8 \\sqrt { 2 }",
"9.6",
"9.6 \\sqrt { 2 }"
] | D | [
"Equals(LengthOf(Line(A, C)), y)",
"Equals(MeasureOf(Angle(A, C, B)), x)",
"Equals(LengthOf(Line(A, D)), 9.6)",
"Perpendicular(Line(B, C), Line(A, B))",
"Equals(LengthOf(Line(C, D)), LengthOf(Line(B, C)))",
"Equals(LengthOf(Line(B, C)), LengthOf(Line(A, B)))",
"Equals(LengthOf(Line(C, D)), LengthOf(Line(A, D)))"
] |
|
<image>$\overline{HK}$ and $\overline{IG}$ are diameters of $\odot L$. Find $m \widehat {HGK}$. | 180 | 2,090 | [
"121",
"160",
"180",
"200"
] | C | [
"Equals(MeasureOf(Angle(H, L, I)), 59)",
"PointLiesOnLine(L, Line(G, I))",
"PointLiesOnLine(L, Line(H, K))",
"Perpendicular(Line(L, J), Line(L, I))",
"PointLiesOnCircle(H, Circle(L, radius_1_0))",
"PointLiesOnCircle(I, Circle(L, radius_1_0))",
"PointLiesOnCircle(J, Circle(L, radius_1_0))",
"PointLiesOnCircle(K, Circle(L, radius_1_0))",
"PointLiesOnCircle(G, Circle(L, radius_1_0))"
] |
|
<image>Use rhombus $A B C D$ with $m \angle 1=2 x+20, m \angle 2=5 x-4$, $A C=15,$ and $m \angle 3=y^{2}+26 .$
Find AF | 7.5 | 832 | [
"2.5",
"5",
"7.5",
"10"
] | C | [
"Equals(MeasureOf(Angle(B, A, F)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(A, F, B)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(C, A, D)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(D, F, A)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(C, F, D)), MeasureOf(angle 6))",
"Equals(MeasureOf(Angle(A, D, F)), MeasureOf(angle 5))",
"PointLiesOnLine(F, Line(B, D))",
"PointLiesOnLine(F, Line(A, C))"
] |
|
<image>If $\overline{PR} \| \overline{WX}, WX=10, XY=6, WY=8, RY=5,$ and $PS=3,$ find $SY$. | 4 | 926 | [
"3",
"4",
"5",
"6"
] | B | [
"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, S), Line(Q, A))"
] |
|
<image>$m∠9 = 2x - 4$, $m∠10 = 2x + 4$. Find the measure of $∠9$. | 86 | 486 | [
"45",
"82",
"86",
"94"
] | C | [
"Equals(MeasureOf(Angle(B,C, D)), MeasureOf(angle 10))",
"Equals(MeasureOf(Angle(B,C, E)), MeasureOf(angle 9))",
"PointLiesOnLine(C, Line(A, B))",
"PointLiesOnLine(C, Line(D, E))"
] |
|
<image>Find $x$. | 45 | 31 | [
"30",
"45",
"60",
"75"
] | B | [
"Equals(MeasureOf(Angle(G, C, E)), x)",
"Equals(MeasureOf(Angle(E, C, A)), 2x)",
"Equals(MeasureOf(Angle(D, C, A)), x)",
"PointLiesOnLine(C, Line(D, G))"
] |
|
<image>Find $h$ in each triangle. | \frac { 15 \sqrt 2 } { 2 } | 169 | [
"\\frac { 15 \\sqrt 2 } { 3 }",
"\\frac { 15 } { 2 }",
"\\frac { 15 \\sqrt 2 } { 2 }",
"15"
] | C | [
"Equals(LengthOf(Line(B, C)), LengthOf(h))",
"Equals(MeasureOf(Angle(C, A, B)), 45)",
"Equals(LengthOf(Line(A, B)), 15)",
"Perpendicular(Line(A, C), Line(B, C))"
] |
|
<image>In the figure, $ m ∠1 = 3a + 40 $, $ m ∠2 = 2a + 25 $, and $ m ∠3 = 5b - 26 $. Find $a$. | 23 | 51 | [
"23",
"25",
"27",
"29"
] | A | [
"Equals(MeasureOf(Angle(L, W, N)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(G, X, E)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(I, Y, L)), MeasureOf(angle 7))",
"Equals(MeasureOf(Angle(L, Y, Z)), MeasureOf(angle 6))",
"Equals(MeasureOf(Angle(K, Y, M)), MeasureOf(angle 5))",
"Equals(MeasureOf(Angle(E, Z, K)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(K, Z, H)), MeasureOf(angle 4))",
"PointLiesOnLine(X, Line(Z, E))",
"PointLiesOnLine(Y, Line(Z, I)) K))",
"PointLiesOnLine(Z, Line(I, K))",
"PointLiesOnLine(Y, Line(I, K))",
"PointLiesOnLine(Z, Line(K, Y))",
"PointLiesOnLine(W, Line(L, M))",
"PointLiesOnLine(Y, Line(L, M))",
"PointLiesOnLine(W, Line(L, Y))",
"PointLiesOnLine(Y, Line(M, W))",
"PointLiesOnLine(X, Line(G, N))",
"PointLiesOnLine(W, Line(G, N))",
"PointLiesOnLine(W, Line(G, X))",
"PointLiesOnLine(X, Line(N, W))",
"PointLiesOnLine(Z, Line(X, H))",
"PointLiesOnLine(Z, Line(E, H))",
"PointLiesOnLine(X, Line(E, H))",
"Parallel(Line(G,N), Line(I,K))",
"Parallel(Line(L,M), Line(E,H))"
] |
|
<image>Find $XA$. | 4 | 943 | [
"2",
"4",
"8",
"16"
] | B | [
"Equals(LengthOf(Line(A, Z)), 4)",
"PointLiesOnLine(X, Line(Y, B))",
"PointLiesOnLine(Z, Line(Y, C))",
"PointLiesOnLine(B, Line(Y, D))",
"PointLiesOnLine(X, Line(Y, D))",
"PointLiesOnLine(E, Line(Y, D))",
"PointLiesOnLine(B, Line(Y, E))",
"PointLiesOnLine(X, Line(Y, E))",
"PointLiesOnLine(A, Line(Y, F))",
"PointLiesOnLine(B, Line(X, D))",
"PointLiesOnLine(E, Line(X, D))",
"PointLiesOnLine(B, Line(X, E))",
"PointLiesOnLine(E, Line(B, D))",
"Perpendicular(Line(Y, X), Line(A, X))",
"Perpendicular(Line(A, Z), Line(Y, Z))",
"Equals(MeasureOf(Angle(X, Y, A)), MeasureOf(Angle(A, Y, Z)))"
] |
|
<image>Find the area of the figure to the nearest tenth. | 87.5 | 1,860 | [
"80.6",
"87.5",
"94.4",
"112.6"
] | B | [
"Equals(LengthOf(Line(A, D)), 8)",
"Equals(LengthOf(Line(A, E)), 4)",
"Equals(MeasureOf(Angle(C, F, E)), 60)",
"Equals(LengthOf(Line(F, C)), 10)",
"PointLiesOnLine(E, Line(A, F))",
"PointLiesOnCircle(A, Circle(E, radius_4_0))",
"PointLiesOnCircle(F, Circle(E, radius_4_0))",
"PointLiesOnCircle(G, Circle(E, radius_4_0))"
] |
|
<image>Find the measure of $∠R$ to the nearest tenth. | 39.6 | 1,147 | [
"32.5",
"39.6",
"50.4",
"57.5"
] | B | [
"Equals(LengthOf(Line(P, Q)), 37)",
"Equals(LengthOf(Line(R, Q)), 58)",
"Perpendicular(Line(P, Q), Line(R, P))"
] |
|
<image>The radius of $\odot P$ is 5 and $P R=3$. Find QS | 8 | 488 | [
"3",
"5",
"6",
"8"
] | D | [
"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))"
] |
|
<image>Find the perimeter of the $\triangle DEF$, if $\triangle ABC \sim \triangle DEF$, $AB=5, BC=6, AC=7$, and $DE=3$. | 10.8 | 1,774 | [
"6",
"10.2",
"10.8",
"13"
] | C | [
"Equals(LengthOf(Line(A, C)), 7)",
"Equals(LengthOf(Line(A, B)), 5)",
"Equals(LengthOf(Line(B, C)), 6)",
"Equals(LengthOf(Line(D, E)), 3)"
] |
|
<image>Find the measure of $AC$. | 38 | 230 | [
"19",
"30",
"38",
"76"
] | C | [
"Equals(LengthOf(Line(D, A)), 5x-6)",
"Equals(LengthOf(Line(D, C)), 3x+4)",
"PointLiesOnLine(D, Line(C, A))",
"Perpendicular(Line(D, A), Line(D, B))",
"Equals(LengthOf(Line(A, B)), LengthOf(Line(C, B)))"
] |
|
<image>Given right triangle $XYZ$ with hypotenuse $\overline{XY}$, $YP$ is equal to $YZ$. If $m ∠PYZ = 26$, find $m ∠XZP$. | 13 | 1,451 | [
"13",
"26",
"32",
"64"
] | A | [
"PointLiesOnLine(P, Line(X, Y))"
] |
|
<image>Find $AC$ if $AC=x-3$, $BE=20, AB=16,$ and $CD=x+5$ | 32 | 743 | [
"32",
"35",
"36",
"40"
] | A | [
"PointLiesOnLine(B, Line(E, A))",
"PointLiesOnLine(C, Line(A, D))",
"Parallel(Line(C, B), Line(E, D))"
] |
|
<image>Refer to trapezoid $CDFG$ with median $\overline{HE}$. Find $GF$. | 30 | 1,393 | [
"30",
"32",
"38",
"46"
] | A | [
"Equals(LengthOf(Line(C, D)), 46)",
"Equals(LengthOf(Line(H, E)), 38)",
"PointLiesOnLine(H, Line(C, G))",
"PointLiesOnLine(E, Line(D, F))"
] |
|
<image>Find $x$. | 35 | 358 | [
"30",
"35",
"40",
"45"
] | B | [
"Equals(MeasureOf(Angle(D, F, E)), 2x)",
"Equals(MeasureOf(Angle(C, E, B)), 40)",
"Equals(MeasureOf(Angle(D, E, F)), y)",
"Equals(MeasureOf(Angle(D, E, F)), Angle(E, D, F))",
"PointLiesOnLine(E, Line(F, B))",
"PointLiesOnLine(E, Line(C, D))"
] |
|
<image>find tan A | \frac { 15 } { 16 } | 255 | [
"\\frac { 15 } { 21 }",
"\\frac { 16 } { 21 }",
"\\frac { 15 } { 16 }",
"\\frac { 16 } { 15 }"
] | C | [
"Equals(LengthOf(Line(A, B)), 21)",
"Equals(LengthOf(Line(B, C)), 15)",
"Equals(LengthOf(Line(A, C)), 16)",
"Perpendicular(Line(B, C), Line(A, C))"
] |
|
<image>Parallelogram MNPQ is shown. What is the value of $x$? | 13 | 1,665 | [
"13",
"39",
"141",
"169"
] | A | [
"Equals(MeasureOf(Angle(M, Q, P)), 6x)",
"Equals(MeasureOf(Angle(Q, P, N)), 7x+11)",
"Equals(LengthOf(Line(Q, P)), x)"
] |
|
<image>In $\odot G, m \angle A G B=30$ and $\overline{C G} \perp \overline{G D}$.
Find $m \widehat{C D F}$ | 120 | 748 | [
"30",
"90",
"120",
"150"
] | 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))",
"Perpendicular(Line(G, C), Line(G, D))"
] |
|
<image>A square with side length of $9$ inches is inscribed in $\odot J$. Find the exact circumference of $\odot J$. | 9 \sqrt 2 \pi | 579 | [
"8 \\sqrt 2 \\pi",
"9 \\sqrt 2 \\pi",
"12 \\sqrt 2 \\pi",
"15 \\sqrt 2 \\pi"
] | B | [
"Equals(LengthOf(Line(N, S)), 9)",
"",
"PointLiesOnCircle(P, Circle(J, radius_5_0))",
"PointLiesOnCircle(S, Circle(J, radius_5_0))",
"PointLiesOnCircle(B, Circle(J, radius_5_0))",
"PointLiesOnCircle(N, Circle(J, radius_5_0))",
""
] |
|
<image>Find the measure of the altitude drawn to the hypotenuse. | 8 \sqrt { 2 } | 1,122 | [
"8",
"8 \\sqrt { 2 }",
"16",
"16 \\sqrt { 2 }"
] | B | [
"Equals(LengthOf(Line(J, M)), 8)",
"Equals(LengthOf(Line(K, M)), 16)",
"PointLiesOnLine(M, Line(J, K))",
"Perpendicular(Line(K, M), Line(L, M))",
"Perpendicular(Line(L, M), Line(L, K))"
] |
|
<image>If $FK = 3x - 1$, $KG = 4y + 3$, $JK = 6y - 2$, and $KH = 2x + 3$, find $x$ so that the quadrilateral is a parallelogram. | 4 | 115 | [
"4",
"5",
"10",
"12"
] | A | [
"PointLiesOnLine(K, Line(G, J))",
"PointLiesOnLine(K, Line(F, H))"
] |
|
<image>Find x | 8 | 1,038 | [
"6",
"8",
"10",
"12"
] | B | [
"Equals(LengthOf(Line(A, D)), 21)",
"Equals(LengthOf(Line(A, C)), 3x-6)",
"PointLiesOnLine(B, Line(C, D))",
"Equals(LengthOf(Line(B, D)), LengthOf(Line(B, C)))",
"Equals(LengthOf(Line(E, H)), 14)",
"Equals(LengthOf(Line(E, G)), x+4)",
"PointLiesOnLine(F, Line(G, H))",
"Equals(LengthOf(Line(H, F)), LengthOf(Line(G, F)))",
"Equals(MeasureOf(Angle(A, D, B)), MeasureOf(Angle(E, H, F)))",
"Equals(MeasureOf(Angle(A, C, B)), MeasureOf(Angle(E, G, F)))",
""
] |
|
<image>For the pair of similar figures, use the given areas to find $x$. | 10.4 | 1,906 | [
"6.0",
"10.4",
"31.2",
"54.0"
] | B | [
"Equals(LengthOf(Line(A, B)), 18)",
"Equals(LengthOf(Line(E, F)), x)",
"Equals(AreaOf(Kite(E,F,G,H)), 525)",
"Equals(AreaOf(Kite(A,B,X,C)), 1575)"
] |
|
<image>Find $m \angle H$. | 54 | 1,202 | [
"40",
"44",
"48",
"54"
] | D | [
"Equals(MeasureOf(Angle(J, H, C)), x)",
"Equals(MeasureOf(Angle(C, G, K)), 2x-54)",
"PointLiesOnLine(C, Line(J, G))",
"PointLiesOnLine(C, Line(H, K))",
"",
"PointLiesOnCircle(J, Circle(A, radius_4_0))",
"PointLiesOnCircle(G, Circle(A, radius_4_0))",
"PointLiesOnCircle(K, Circle(A, radius_4_0))",
"PointLiesOnCircle(H, Circle(A, radius_4_0))"
] |
|
<image>In $\odot O, \overline{E C}$ and $\overline{A B}$ are diameters, and $\angle B O D \cong \angle D O E \cong \angle E O F \cong \angle F O A$
Find $m\widehat{A C B}$ | 180 | 1,520 | [
"45",
"90",
"180",
"360"
] | C | [
"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))",
"PointLiesOnCircle(B, Circle(O, radius_0_0))",
"Perpendicular(Line(O, A), Line(O, C))"
] |
|
<image>Find $\angle D$ of quadrilateral ABCD | 45 | 500 | [
"45",
"90",
"135",
"180"
] | A | [
"Equals(MeasureOf(Angle(B, A, D)), 3x)",
"Equals(MeasureOf(Angle(A, D, C)), x)",
"Perpendicular(Line(B, A), Line(C, B))",
"Perpendicular(Line(C, B), Line(C, D))"
] |
|
<image>In $\odot P, m \widehat{E N}=66$ and $m \angle G P M=89$ .
Find $m \angle G M E$ | 57 | 1,053 | [
"57",
"66",
"89",
"155"
] | A | [
"PointLiesOnLine(B, Line(M, E))",
"PointLiesOnLine(B, Line(N, P))",
"PointLiesOnLine(P, Line(N, G))",
"PointLiesOnLine(B, Line(N, G))",
"PointLiesOnLine(P, Line(G, B))",
"PointLiesOnCircle(M, Circle(P, radius_4_0))",
"PointLiesOnCircle(E, Circle(P, radius_4_0))",
"PointLiesOnCircle(N, Circle(P, radius_4_0))",
"PointLiesOnCircle(G, Circle(P, radius_4_0))"
] |
|
<image>In the triangle, what is the measure of $∠Z$? | 18 | 1,381 | [
"18",
"24",
"72",
"90"
] | A | [
"Equals(MeasureOf(Angle(Z, X, Y)), 2 * a)",
"Equals(MeasureOf(Angle(Y, Z, X)), a/2)",
"Perpendicular(Line(X,Y), Line(Y,Z))"
] |
|
<image>Find x | 6.75 | 170 | [
"6",
"6.25",
"6.5",
"6.75"
] | D | [
"Equals(LengthOf(Line(B, C)), x)",
"Equals(LengthOf(Line(B, D)), 9)",
"Equals(LengthOf(Line(A, C)), 18)",
"Equals(LengthOf(Line(A, D)), 24)",
"PointLiesOnLine(B, Line(C, D))",
"Equals(MeasureOf(Angle(C, A, B)), MeasureOf(Angle(B, A, D)))"
] |
|
<image>Find y | \frac { 19 \sqrt { 2 } } { 2 } | 1,788 | [
"\\frac { 17 \\sqrt { 2 } } { 2 }",
"\\frac { 19 \\sqrt { 2 } } { 2 }",
"\\frac { 21 \\sqrt { 2 } } { 2 }",
"\\frac { 23 \\sqrt { 2 } } { 2 }"
] | B | [
"Equals(LengthOf(Line(A, B)), 19)",
"Equals(LengthOf(Line(A, C)), x)",
"Equals(MeasureOf(Angle(C, B, A)), 45)",
"Equals(LengthOf(Line(B, C)), y)",
"Perpendicular(Line(A, C), Line(B, C))"
] |
|
<image>Find $m \angle 1$. | 26 | 1,703 | [
"26",
"32",
"58",
"64"
] | A | [
"Equals(MeasureOf(Angle(B, A, D)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(F, B, A)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(F, A, C)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(D, B, F)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(A, D, B)), 64)",
"PointLiesOnLine(G, Line(E, C))",
"PointLiesOnLine(E, Line(C, D))",
"PointLiesOnLine(G, Line(C, D))",
"PointLiesOnLine(F, Line(D, A))",
"PointLiesOnLine(E, Line(D, G))",
"Perpendicular(Line(A, B), Line(C, A))",
"Perpendicular(Line(B, F), Line(D, F))",
"Perpendicular(Line(C, A), Line(C, G))",
"Perpendicular(Line(D, B), Line(E, D))"
] |
|
<image>In $\triangle PQR$, $ZQ=3a-11$, $ZP=a+5$, $PY=2 c-1$, $YR=4 c-11$, $m \angle PRZ=4 b-17$, $m \angle ZRQ=3 b-4$, $m \angle QYR=7 b+6$, and $m \angle PXR=2 a+10$. $\overline{PX}$ is an altitude of $ \triangle PQR$. Find $a$. | 40 | 1,267 | [
"10",
"20",
"30",
"40"
] | D | [
"PointLiesOnLine(A, Line(Q, Y))",
"PointLiesOnLine(X, Line(Q, R))",
"PointLiesOnLine(Z, Line(Q, P))",
"PointLiesOnLine(A, Line(Y, X))",
"PointLiesOnLine(Y, Line(R, P))",
"PointLiesOnLine(A, Line(R, Z))"
] |
|
<image>Find $AB$. | 10 | 1,269 | [
"5",
"10",
"20",
"30"
] | B | [
"Equals(MeasureOf(Angle(B, A, C)), 30)",
"Equals(MeasureOf(Angle(B, C, A)), 30)",
"Equals(LengthOf(Line(B, C)), 10)"
] |
|
<image>In $\odot B$, the diameter is 20 units long, and $m \angle A C E=45$ Find $x$ | \sqrt { 2 } | 1,376 | [
"\\sqrt { 2 }",
"2",
"4",
"5 \\sqrt { 2 }"
] | A | [
"Equals(LengthOf(Line(B, D)), 5x)",
"PointLiesOnLine(D, Line(E, C))",
"PointLiesOnCircle(C, Circle(B, radius_1_0))",
"PointLiesOnCircle(A, Circle(B, radius_1_0))",
"PointLiesOnCircle(E, Circle(B, radius_1_0))",
"Perpendicular(Line(D, E), Line(B, D))"
] |
|
<image>If $AC = 12$ and $AB = 25$, what is the measure of $∠B$ to the nearest tenth? | 28.7 | 1,044 | [
"25.6",
"28.7",
"61.3",
"64.4"
] | B | [
"Equals(LengthOf(Line(A, B)), 25)",
"Equals(LengthOf(Line(A, C)), 12)"
] |
|
<image>If $\overline{GH} \cong \overline{HK}$, $\overline{HJ} \cong \overline{YK}$, and $m \angle GJK=100$, what is the measure of $\angle HGK$ ? | 20 | 751 | [
"10",
"15",
"20",
"25"
] | C | [
"PointLiesOnLine(H, Line(J, G))"
] |
|
<image>$\overline{PM}$ is a diameter of $\odot R$. Find $m \widehat {MQ}$. | 65 | 110 | [
"45",
"55",
"65",
"75"
] | C | [
"Equals(MeasureOf(Angle(P, R, Q)), 115)",
"PointLiesOnLine(R, Line(M, P))",
"PointLiesOnCircle(Q, Circle(R, radius_1_0))",
"PointLiesOnCircle(M, Circle(R, radius_1_0))",
"PointLiesOnCircle(P, Circle(R, radius_1_0))",
"PointLiesOnCircle(N, Circle(R, radius_1_0))",
"Perpendicular(Line(R, P), Line(R, N))"
] |
|
<image>Find x. | \frac { 15 } { 14 } \sqrt { 19 } | 1,771 | [
"\\frac { 5 } { 14 } \\sqrt { 19 }",
"\\frac { 15 } { 14 } \\sqrt { 19 }",
"5",
"14"
] | B | [
"Equals(LengthOf(Line(A, Y)), 5)",
"Equals(LengthOf(Line(A, N)), x)",
"Equals(LengthOf(Line(A, B)), z)",
"Equals(LengthOf(Line(Y, N)), y)",
"Equals(LengthOf(Line(Y, B)), 14)",
"PointLiesOnLine(N, Line(Y, B))",
"Perpendicular(Line(A, Y), Line(A, B))",
"Perpendicular(Line(A, N), Line(B, N))"
] |
|
<image>In $\odot T, Z V=1,$ and $T W=13$. Find XV | 5 | 640 | [
"5",
"11",
"12",
"13"
] | A | [
"PointLiesOnLine(V, Line(T, Z))",
"PointLiesOnLine(V, Line(X, Y))",
"PointLiesOnLine(T, Line(V, W))",
"PointLiesOnLine(V, Line(Z, W))",
"PointLiesOnLine(T, Line(W, Z))",
"PointLiesOnCircle(X, Circle(T, radius_0_0))",
"PointLiesOnCircle(V, Circle(T, radius_0_0))",
"PointLiesOnCircle(W, Circle(T, radius_0_0))",
"PointLiesOnCircle(Y, Circle(T, radius_0_0))",
"Perpendicular(Line(X, V), Line(T, V))"
] |
|
<image>Use parallelogram NQRM to find w | 12 | 43 | [
"4",
"12",
"14",
"29"
] | B | [
"Equals(LengthOf(Line(Q, N)), 3x+2)",
"Equals(LengthOf(Line(Q, L)), 12)",
"Equals(LengthOf(Line(M, N)), 2y+5)",
"Equals(LengthOf(Line(Q, R)), 3y)",
"Equals(LengthOf(Line(M, L)), LengthOf(w))",
"Equals(LengthOf(Line(M, R)), 4x-2)",
"PointLiesOnLine(L, Line(Q, M))",
"PointLiesOnLine(L, Line(R, N))"
] |
|
<image>Find x | 8.5 | 657 | [
"1.5",
"2.0",
"8.0",
"8.5"
] | D | [
"Equals(LengthOf(Line(A, C)), x)",
"Equals(MeasureOf(Angle(A, B, C)), 24)",
"Equals(LengthOf(Line(A, B)), 19)",
"Perpendicular(Line(A, C), Line(A, B))"
] |
|
<image>If $ABCDE \sim PQRST,$ find the perimeter of $ABCDE$. | 30 | 403 | [
"22.5",
"27.5",
"30",
"35"
] | C | [
"Equals(LengthOf(Line(B, A)), 8)",
"Equals(LengthOf(Line(D, C)), 4)",
"Equals(LengthOf(Line(E, D)), 6)",
"Equals(LengthOf(Line(R, S)), 3)",
"Equals(LengthOf(Line(B, A)), LengthOf(Line(B, C)))",
"Equals(LengthOf(Line(E, A)), LengthOf(Line(D, C)))",
"Equals(LengthOf(Line(P, Q)), LengthOf(Line(Q, R)))",
"Equals(LengthOf(Line(R, S)), LengthOf(Line(P, T)))"
] |
|
<image>Find $m\angle Y$ | 68 | 726 | [
"34",
"68",
"70",
"136"
] | B | [
"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)"
] |
|
<image>In the figure, $m∠1 = 94$. Find the measure of $\angle 3$. | 94 | 182 | [
"76",
"86",
"94",
"96"
] | C | [
"Equals(MeasureOf(Angle(A, C, I)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(A, C, H)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(M, H, C)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(I, C, E)), MeasureOf(angle 5))",
"Equals(MeasureOf(Angle(F, H, G)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(F, C, E)), MeasureOf(angle 6))",
"Equals(MeasureOf(Angle(I, H, D)), MeasureOf(angle 7))",
"Equals(MeasureOf(Angle(D, H, F)), MeasureOf(angle 8))",
"PointLiesOnLine(H, Line(M, D))",
"PointLiesOnLine(H, Line(F, C))",
"PointLiesOnLine(H, Line(F, I))",
"PointLiesOnLine(C, Line(A, E))",
"PointLiesOnLine(C, Line(H, I))",
"PointLiesOnLine(C, Line(F, I))",
"Parallel(Line(D, M), Line(A, E))"
] |
|
<image>Find the perimeter of the figure. Round to the nearest tenth if necessary. | 54.8 | 934 | [
"54.8",
"60",
"80",
"109.6"
] | A | [
"Equals(LengthOf(Line(A, B)), 26)",
"Equals(LengthOf(Line(A, D)), 10)",
"Equals(LengthOf(Line(D, C)), 8)",
"Equals(LengthOf(Line(B, C)), 16)",
"PointLiesOnLine(C, Line(B, D))",
"Perpendicular(Line(A, D), Line(D, C))"
] |
|
<image>Refer to the figure at the right. Find z. | 11.09 | 1,275 | [
"8.80",
"9.58",
"11.09",
"13.11"
] | C | [
"Equals(LengthOf(Line(A, C)), 8.8)",
"Equals(LengthOf(Line(A, D)), x)",
"Equals(LengthOf(Line(A, B)), y)",
"Equals(LengthOf(Line(B, C)), z)",
"Equals(LengthOf(Line(B, D)), 8.5)",
"PointLiesOnLine(A, Line(C, D))",
"Perpendicular(Line(B, D), Line(B, C))"
] |
|
<image>Find $BC$. | 23 | 189 | [
"23",
"24",
"25",
"27"
] | A | [
"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)))"
] |
|
<image>Find $x$ to the nearest tenth. Assume that segments that appear to be tangent are tangent. | 4 | 565 | [
"2",
"3",
"4",
"5"
] | C | [
"Equals(LengthOf(Line(B, F)), x)",
"Equals(LengthOf(Line(B, D)), 3)",
"Equals(LengthOf(Line(C, F)), 5)",
"Equals(LengthOf(Line(A, D)), 9)",
"PointLiesOnLine(D, Line(A, B))",
"PointLiesOnLine(E, Line(A, B))",
"PointLiesOnLine(E, Line(A, D))",
"PointLiesOnLine(F, Line(B, C))",
"PointLiesOnLine(D, Line(B, E))",
"PointLiesOnCircle(A, Circle(E, radius_4_0))",
"PointLiesOnCircle(C, Circle(E, radius_4_0))",
"PointLiesOnCircle(D, Circle(E, radius_4_0))",
"PointLiesOnCircle(F, Circle(E, radius_4_0))"
] |
|
<image>In $\odot G, m \angle A G B=30$ and $\overline{C G} \perp \overline{G D}$.
Find $m \widehat{B C}$ | 60 | 1,434 | [
"30",
"45",
"60",
"90"
] | 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))",
"Perpendicular(Line(G, C), Line(G, D))"
] |
|
<image>Find x. | 17 | 1,908 | [
"8",
"12.7",
"15",
"17"
] | D | [
"Equals(LengthOf(Line(A, B)), x)",
"Equals(LengthOf(Line(A, C)), 8)",
"Equals(LengthOf(Line(B, C)), 15)",
"Perpendicular(Line(A, C), Line(B, C))"
] |
|
<image>A plane travels from Des Moines to Phoenix, on to Atlanta, and back to Des Moines, as shown below. Find the distance in miles from Des Moines to Phoenix if the total trip was 3482 miles. | 1153 | 109 | [
"73.8",
"91",
"110",
"1153"
] | D | [
"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)"
] |
|
<image>Find $x$. | 3 | 585 | [
"2",
"3",
"4",
"5"
] | B | [
"Equals(LengthOf(Line(S, X)), x+2)",
"Equals(LengthOf(Line(S, Z)), x+6)",
"Equals(LengthOf(Line(Y, S)), x+12)",
"Equals(LengthOf(Line(W, S)), x)",
"PointLiesOnLine(S, Line(W, Y))",
"PointLiesOnLine(S, Line(X, Z))",
"PointLiesOnCircle(W, Circle(B, radius_5_0))",
"PointLiesOnCircle(Y, Circle(B, radius_5_0))",
"PointLiesOnCircle(X, Circle(B, radius_5_0))",
"PointLiesOnCircle(Z, Circle(B, radius_5_0))"
] |
|
<image>JKLM is a rhombus. If $CK = 8$ and $JK = 10$, Find $JC$. | 6 | 1,270 | [
"4",
"6",
"8",
"10"
] | B | [
"PointLiesOnLine(C, Line(J, L))",
"PointLiesOnLine(C, Line(M, K))"
] |
|
<image>For the pair of similar figures, find the area of the green figure. | 12.5 | 599 | [
"12.5",
"20.0",
"51.2",
"81.9"
] | A | [
"Equals(LengthOf(Line(D, C)), 8)",
"Equals(LengthOf(Line(G, H)), 5)",
"Equals(AreaOf(Rectangle(A,B,C,D)), 32)"
] |
|
<image>In $\triangle RST$, $Z$ is the centroid and $RZ=18$. Find $ZV$. | 9 | 1,539 | [
"5",
"9",
"10",
"18"
] | B | [
"Equals(LengthOf(Line(R, W)), 14)",
"Equals(LengthOf(Line(R, Z)), 18)",
"Equals(LengthOf(Line(U, Z)), 5)",
"PointLiesOnLine(Z, Line(U, S))",
"PointLiesOnLine(W, Line(S, R))",
"PointLiesOnLine(V, Line(S, T))",
"PointLiesOnLine(U, Line(R, T))",
"PointLiesOnLine(Z, Line(R, V))",
"PointLiesOnLine(Z, Line(T, W))"
] |
|
<image>Find $m \angle A G D$ | 90 | 2,089 | [
"45",
"90",
"180",
"360"
] | B | [
"Equals(MeasureOf(Angle(A, G, C)), 60)",
"PointLiesOnLine(G, Line(E, C))",
"PointLiesOnLine(G, Line(A, B))",
"PointLiesOnCircle(E, Circle(G, radius_0_0))",
"PointLiesOnCircle(C, Circle(G, radius_0_0))",
"PointLiesOnCircle(A, Circle(G, radius_0_0))",
"PointLiesOnCircle(D, Circle(G, radius_0_0))",
"PointLiesOnCircle(B, Circle(G, radius_0_0))",
"Perpendicular(Line(G, A), Line(G, D))"
] |
|
<image>Find $x$ so that $ m \parallel n $. | 15 | 28 | [
"7",
"9",
"11",
"15"
] | D | [
"Equals(MeasureOf(Angle(G, D, F)), 8x+4)",
"Equals(MeasureOf(Angle(I, H, E)), 9x-11)",
"PointLiesOnLine(H, Line(A, E))",
"PointLiesOnLine(D, Line(H, G))",
"PointLiesOnLine(D, Line(B, F))",
"PointLiesOnLine(H, Line(D, I))",
"PointLiesOnLine(D, Line(F, J))",
"PointLiesOnLine(D, Line(C, G))",
"PointLiesOnLine(D, Line(G, I))",
"PointLiesOnLine(H, Line(G, I))"
] |
|
<image>Assume that the segment is tangent, find the value of $x$. | \sqrt { 93 } | 1,443 | [
"\\sqrt { 14 }",
"\\sqrt { 17 }",
"\\sqrt { 93 }",
"\\sqrt { 485 }"
] | C | [
"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))"
] |
|
<image>If $QV=8$, what it the diameter of $\odot Q$. | 16 | 954 | [
"7",
"8",
"11",
"16"
] | D | [
"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))"
] |
|
<image>In $\odot F, m \angle D F A=50$ and $\overline{C F} \perp \overline{F B}$. Find $m \widehat{C B E}$ | 140 | 2,095 | [
"40",
"45",
"90",
"140"
] | D | [
"Equals(MeasureOf(Angle(A, F, D)), 50)",
"PointLiesOnLine(F, Line(B, A))",
"PointLiesOnLine(F, Line(E, D))",
"PointLiesOnCircle(C, Circle(F, radius_0_0))",
"PointLiesOnCircle(B, Circle(F, radius_0_0))",
"PointLiesOnCircle(A, Circle(F, radius_0_0))",
"PointLiesOnCircle(E, Circle(F, radius_0_0))",
"PointLiesOnCircle(D, Circle(F, radius_0_0))",
"Perpendicular(Line(F, C), Line(F, B))"
] |
|
<image>For trapezoid QRTU, V and S are midpoints of the legs. If QR = 12 and UT = 22, find VS. | 17 | 1,677 | [
"5",
"12",
"17",
"22"
] | C | [
"PointLiesOnLine(S, Line(R, T))",
"PointLiesOnLine(V, Line(Q, U))"
] |
|
<image>Use a calculator to find the measure of $∠J$ to the nearest degree. | 45 | 1,679 | [
"35",
"45",
"55",
"65"
] | B | [
"Equals(LengthOf(Line(K, J)), 24)",
"Equals(LengthOf(Line(L, J)), 17)",
"Perpendicular(Line(L, J), Line(L, K))"
] |
|
<image>Find $y$. | 17 | 928 | [
"7",
"8",
"12",
"17"
] | D | [
"Equals(LengthOf(Line(H, J)), 2y-5)",
"Equals(LengthOf(Line(F, J)), y+12)",
"Equals(LengthOf(Line(F, K)), 3x+7)",
"Equals(LengthOf(Line(G, K)), 4x-1)",
"PointLiesOnLine(J, Line(H, F))",
"PointLiesOnLine(K, Line(F, G))",
"Perpendicular(Line(J, K), Line(F, K))",
"Perpendicular(Line(H, G), Line(G, K))",
"Equals(LengthOf(Line(H, J)), LengthOf(Line(F, J)))"
] |
|
<image>Use rhombus $A B C D$ with $m \angle 1=2 x+20, m \angle 2=5 x-4$, $A C=15,$ and $m \angle 3=y^{2}+26 .$
Find x | 8 | 2,067 | [
"2",
"4",
"6",
"8"
] | D | [
"Equals(MeasureOf(Angle(B, A, F)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(A, F, B)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(C, A, D)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(D, F, A)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(C, F, D)), MeasureOf(angle 6))",
"Equals(MeasureOf(Angle(A, D, F)), MeasureOf(angle 5))",
"PointLiesOnLine(F, Line(A, C))",
"PointLiesOnLine(F, Line(D, B))"
] |
|
<image>Find y in the figure. | 40 | 48 | [
"20",
"30",
"40",
"50"
] | C | [
"Equals(MeasureOf(Angle(Y, Q, F)), 4x-5)",
"Equals(MeasureOf(Angle(E, Y, Q)), 3y+1)",
"Equals(MeasureOf(Angle(M, A, Q)), 3x+11)",
"PointLiesOnLine(Y, Line(E, M))",
"PointLiesOnLine(Q, Line(F, A))",
"Parallel(Line(E, F), Line(Y, Q))",
"Parallel(Line(Y, Q), Line(M, A))",
"Parallel(Line(M, A), Line(E, F))",
"Parallel(Line(E, M), Line(F, A))"
] |
|
<image>Find the area of the trapezoid. | 84 | 471 | [
"28",
"42",
"84",
"168"
] | C | [
"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))"
] |
|
<image>Find x | 117 | 1,819 | [
"33",
"51",
"84",
"117"
] | D | [
"Equals(MeasureOf(Angle(C, A, E)), 33)",
"Equals(MeasureOf(Arc(C, B)), x)",
"Equals(MeasureOf(Arc(D, E)), 51)",
"PointLiesOnLine(E, Line(A, B))",
"PointLiesOnLine(D, Line(A, C))",
"PointLiesOnCircle(B, Circle(F, radius_5_0))",
"PointLiesOnCircle(C, Circle(F, radius_5_0))",
"PointLiesOnCircle(D, Circle(F, radius_5_0))",
"PointLiesOnCircle(E, Circle(F, radius_5_0))"
] |
|
<image>Find the area of the kite. | 60 | 1,711 | [
"40",
"60",
"80",
"120"
] | B | [
"Equals(LengthOf(Line(B, M)), 8)",
"Equals(LengthOf(Line(A, C)), 15)"
] |
|
<image>Find x. Round to the nearest tenth, if necessary. | 14.3 | 572 | [
"3",
"4",
"9",
"14.3"
] | D | [
"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_3_0))",
"PointLiesOnCircle(G, Circle(B, radius_3_0))"
] |
|
<image>If $m \angle AED=95$ and $m \widehat{AD}=120$, what is $m \angle BAC$? | 35 | 1,426 | [
"30",
"35",
"40",
"60"
] | B | [
"Equals(MeasureOf(Angle(D, E, A)), 95)",
"Equals(MeasureOf(Angle(A, F, D)), 120)",
"PointLiesOnLine(E, Line(C, A))",
"PointLiesOnLine(E, Line(B, D))",
"PointLiesOnCircle(C, Circle(F, radius_5_0))",
"PointLiesOnCircle(A, Circle(F, radius_5_0))",
"PointLiesOnCircle(D, Circle(F, radius_5_0))",
"PointLiesOnCircle(B, Circle(F, radius_5_0))"
] |
|
<image>Find $x$. | 3 | 2,002 | [
"1",
"3",
"5",
"7"
] | B | [
"Equals(LengthOf(Line(A, C)), 5x-1)",
"Equals(LengthOf(Line(A, B)), \\frac{10}{3}x+4)",
"Equals(LengthOf(Line(B, C)), 7x-7)",
"Equals(MeasureOf(Angle(B, A, C)), MeasureOf(Angle(A, B, C)))",
"Equals(MeasureOf(Angle(A, C, B)), MeasureOf(Angle(A, B, C)))"
] |
|
<image>Find $m \angle 2$. | 39 | 1,763 | [
"33",
"39",
"51",
"108"
] | B | [
"Equals(MeasureOf(Angle(R, Q, S)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(P, R, Q)), 33)",
"Equals(MeasureOf(Angle(S, Q, P)), 51)",
"Equals(MeasureOf(Angle(Q, S, R)), MeasureOf(angle 1))",
"PointLiesOnLine(S, Line(R, P))",
"Perpendicular(Line(Q, R), Line(Q, P))"
] |
|
<image>Find the length of $\widehat {AB}$. Round to the nearest hundredth. | 2.36 | 34 | [
"1.18",
"2.36",
"3.36",
"4.72"
] | B | [
"Equals(LengthOf(Line(O, A)), 3)",
"Equals(MeasureOf(Angle(A, O, B)), 45)",
"PointLiesOnCircle(A, Circle(O, radius_0_0))",
"PointLiesOnCircle(B, Circle(O, radius_0_0))"
] |
|
<image>Find the perimeter of the given triangle $\triangle D E F,$ if $\triangle A B C \sim \triangle D E F, A B=5$, $B C=6, A C=7,$ and $D E=3$ | 10.8 | 353 | [
"9.2",
"10.8",
"18",
"31.7"
] | B | [
"Equals(LengthOf(Line(A, C)), 7)",
"Equals(LengthOf(Line(A, B)), 5)",
"Equals(LengthOf(Line(B, C)), 6)",
"Equals(LengthOf(Line(D, E)), 3)"
] |
Subsets and Splits