image imagewidth (px) 139 1.6k | problem stringlengths 13 234 | 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 | code stringlengths 31 9.49k | rendered_image imagewidth (px) 204 780 |
|---|---|---|---|---|---|---|---|---|---|
<image>Find x. | 3 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(C, F)), x)",
"Equals(LengthOf(Line(F, D)), 6)",
"Equals(LengthOf(Line(F, E)), 4)",
"Equals(LengthOf(Line(B, F)), 8)",
"PointLiesOnLine(F, Line(B, C))",
"PointLiesOnLine(F, Line(E, D))",
"PointLiesOnCircle(B, Circle(A, radius_0_0))",
"PointLiesOnCircle(C, Circle(A, radius_0_0))",
... | [
"BC",
"BF",
"CE",
"CF",
"ED",
"FD",
"FE"
] | {"A": [116.0, 115.0], "B": [214.0, 172.0], "C": [60.0, 14.0], "D": [222.0, 75.0], "E": [21.0, 50.0], "F": [105.0, 61.0]} | [
"A"
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.5687, 0.5967)
B = (1.0596, 0.8822)
C = (0.2933, 0.1000)
D = (1.1000, 0.3962)
E = (0.1000, 0.2760)
F = (0.5145, 0.3258)
# Draw ci... | ||
<image>If $\overline{B E} \cong \overline{E D}$ and $m \widehat{E D}=120,$ find $m \widehat{B E}$ | 120 | [
"Equals(LengthOf(Line(B,E)),Line(E,D))",
"Equals(MeasureOf(Arc(E,D)),120)",
"Find(MeasureOf(Arc(B,E)))"
] | [
"PointLiesOnLine(N, Line(D, A))",
"PointLiesOnCircle(D, Circle(N, radius_0_0))",
"PointLiesOnCircle(A, Circle(N, radius_0_0))",
"PointLiesOnCircle(B, Circle(N, radius_0_0))",
"PointLiesOnCircle(C, Circle(N, radius_0_0))",
"PointLiesOnCircle(E, Circle(N, radius_0_0))"
] | [
"BC",
"DA",
"DE",
"NA",
"NB",
"NC",
"ND"
] | {"A": [13.0, 25.0], "B": [80.0, 8.0], "C": [109.0, 28.0], "D": [115.0, 102.0], "E": [20.0, 96.0], "N": [66.0, 63.0]} | [
"N"
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.1119, 0.3253)
B = (0.7648, 0.1000)
C = (1.0836, 0.3045)
D = (1.1000, 1.0715)
E = (0.1000, 1.0551)
N = (0.6060, 0.6984)
# Draw ci... | ||
<image>Find x. | 2 \sqrt { 221 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), x)",
"Equals(LengthOf(Line(B, C)), 22)",
"Equals(LengthOf(Line(A, C)), 20)",
"Perpendicular(Line(B, C), Line(A, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [197.42274978466838, 216.00247631352283], "B": [0.6666666666666572, 0.6984924623115489], "C": [0.6666666666666572, 217.32994923857868]} | [] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (1.0836, 1.0934)
B = (0.1000, 0.1000)
C = (0.1000, 1.1000)
# Draw line segments
ax.plot([A[0], B[0]], [A[1], B[1]], 'k-', linewidth... | ||
<image>Find $x$ so that $m || n$. | 27 | [
"Parallel(Line(m),Line(n))",
"Find(x)"
] | [
"Equals(MeasureOf(Angle(D, B, N)), 2x+45)",
"Equals(LengthOf(Line(E, F)), x)",
"Equals(MeasureOf(Angle(A, E, D)), 3x)",
"PointLiesOnLine(E, Line(A, T))",
"PointLiesOnLine(B, Line(E, F))",
"PointLiesOnLine(E, Line(B, D))",
"PointLiesOnLine(B, Line(C, N))",
"PointLiesOnLine(B, Line(D, F))",
"PointLies... | [
"AE",
"AT",
"BC",
"BD",
"BF",
"BN",
"CN",
"DF",
"EB",
"ED",
"EF",
"TE"
] | {"A": [92.0, 259.0], "B": [286.0, 102.0], "C": [279.0, 258.0], "D": [0.0, 200.0], "E": [92.0, 168.0], "F": [327.0, 88.0], "N": [290.0, 5.0], "T": [92.0, 1.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.3813, 0.8890)
B = (0.9739, 0.4092)
C = (0.9532, 0.8859)
D = (0.1000, 0.7086)
E = (0.3813, 0.6122)
F = (1.1000, 0.3661)
N = (0.986... | ||
<image>GRID IN In the figure, the radius of circle $A$ is twice the radius of circle $B$ and four times the radius of circle $C .$ If the sum of the circumferences of the three circles is $42 \pi,$ find the measure of $\overline{A C}$ | 27 | [
"Equals(RadiusOf(Circle(A)),Mul(RadiusOf(Circle(B)),2))",
"Equals(RadiusOf(Circle(A)),Mul(RadiusOf(Circle(C)),4))",
"Equals(SumOf(CircumferenceOf(Circle($1)),CircumferenceOf(Circle($2)),CircumferenceOf(Circle($3))),42\\pi)",
"Find(LengthOf(Line(A,C)))"
] | [
"PointLiesOnLine(E, Line(D, A))",
"PointLiesOnLine(B, Line(D, A))",
"PointLiesOnLine(B, Line(D, E))",
"PointLiesOnLine(E, Line(A, B))",
"PointLiesOnLine(D, Line(A, C))",
"PointLiesOnLine(E, Line(A, C))",
"PointLiesOnLine(B, Line(A, C))",
"PointLiesOnLine(D, Line(E, C))",
"PointLiesOnLine(B, Line(E, ... | [
"AB",
"AC",
"AE",
"BC",
"DA",
"DB",
"DC",
"DE",
"EB",
"EC"
] | {"A": [268.0, 104.0], "B": [109.0, 105.0], "C": [27.0, 103.0], "D": [57.0, 102.0], "E": [161.0, 103.0]} | [
"A",
"B",
"C"
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (1.1000, 0.1041)
B = (0.4403, 0.1014)
C = (0.1000, 0.1000)
D = (0.2245, 0.1005)
E = (0.6561, 0.1023)
# Draw circles
circle_A = plt.... | ||
<image>Find $m \angle 2$. | 34 | [
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(B, D, A)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(B, C, A)), 42)",
"Equals(MeasureOf(Angle(A, B, C)), 38)",
"Equals(MeasureOf(Angle(A, D, C)), 72)",
"Equals(MeasureOf(Angle(D, A, B)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(C, A, D)), MeasureOf(angle 3))",
"PointLies... | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [202.0, 184.0], "B": [434.0, 2.0], "C": [-0.0, 1.0], "D": [262.0, 2.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.5654, 0.5217)
B = (1.1000, 0.1023)
C = (0.1000, 0.1000)
D = (0.7037, 0.1014)
# Draw line segments
ax.plot([A[0], B[0]], [A[1], B... | ||
<image>Find the area of a regular hexagon with a perimeter of 72 feet. | 374.1 | [
"Equals(PerimeterOf(Regular(Hexagon($))),72)",
"Find(AreaOf(Regular(Hexagon($))))"
] | [
"Equals(LengthOf(Line(G, H)), a)",
"Equals(LengthOf(Line(A, F)), 12)",
"Equals(LengthOf(Line(D, G)), 12)",
"Equals(LengthOf(Line(A, D)), 12)",
"Equals(LengthOf(Line(D, H)), 6)",
"Equals(MeasureOf(Angle(G, D, H)), 60)",
"PointLiesOnLine(H, Line(A, D))",
"Perpendicular(Line(G, H), Line(D, H))"
] | [
"AD",
"AE",
"AF",
"AG",
"AH",
"DB",
"DC",
"DG",
"DH",
"EB",
"EC",
"FC",
"GH"
] | {"A": [57.0, 192.0], "B": [221.0, 97.0], "C": [55.0, 2.0], "D": [166.0, 191.0], "E": [167.0, 2.0], "F": [2.0, 96.0], "G": [111.0, 104.0], "H": [113.0, 192.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.3511, 0.9676)
B = (1.1000, 0.5338)
C = (0.3420, 0.1000)
D = (0.8489, 0.9630)
E = (0.8534, 0.1000)
F = (0.1000, 0.5292)
G = (0.597... | ||
<image>Find the area of the parallelogram. Round to the nearest tenth if necessary. | 420 | [
"Find(AreaOf(Parallelogram($)))"
] | [
"Equals(LengthOf(Line(O, B)), 20)",
"Equals(LengthOf(Line(A, C)), 25)",
"Equals(LengthOf(Line(A, N)), 21)",
"PointLiesOnLine(N, Line(A, O))",
"Perpendicular(Line(B, O), Line(N, O))"
] | [
"AC",
"AN",
"AO",
"BO",
"CB",
"NB",
"NO"
] | {"A": [1.0, 137.0], "B": [229.0, 1.0], "C": [93.0, 2.0], "N": [134.0, 137.0], "O": [149.0, 137.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.1000, 0.6965)
B = (1.1000, 0.1000)
C = (0.5035, 0.1044)
N = (0.5606, 0.8892)
O = (0.6212, 0.9139)
# Draw line segments
ax.plot([... | ||
<image>Find the area of the shaded region. Round to the nearest tenth if necessary. | 108.5 | [
"Find(AreaOf(Shaded(Shape($))))"
] | [
"Equals(LengthOf(Line(D, C)), 17)",
"Equals(LengthOf(Line(E, C)), 92)",
"Equals(LengthOf(Line(D, C)), 92)",
"Equals(LengthOf(Line(B, F)), 108)",
"Equals(LengthOf(Line(A, D)), 31)",
"Equals(LengthOf(Line(F, A)), 31)"
] | [
"AD",
"BE",
"BF",
"DC",
"EC",
"FA"
] | {"A": [298.0, 139.0], "B": [139.0, 91.0], "C": [0.0, 0.0], "D": [1.0, 138.0], "E": [137.0, 1.0], "F": [299.0, 93.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (1.0967, 0.5649)
B = (0.5649, 0.4043)
C = (0.1000, 0.1000)
D = (0.1033, 0.5615)
E = (0.5582, 0.1033)
F = (1.1000, 0.4110)
# Draw li... | ||
<image>The triangle is inscribed into the circle. Find the exact circumference of the circle. | 12 \pi | [
"InscribedIn(Triangle($),Circle($))",
"Find(CircumferenceOf(Circle($)))"
] | [
"PointLiesOnLine(I, Line(B, C))",
"PointLiesOnCircle(A, Circle(I, radius_8_0))",
"PointLiesOnCircle(B, Circle(I, radius_8_0))",
"PointLiesOnCircle(C, Circle(I, radius_8_0))",
"Perpendicular(Line(A, C), Line(A, B))",
"Equals(LengthOf(Line(A, C)), LengthOf(Line(A, B)))",
"Equals(LengthOf(Line(A, B)), 6\\s... | [
"AB",
"AC",
"BC",
"BI",
"CI"
] | {"A": [170.0, 4.0], "B": [26.0, 196.0], "C": [362.0, 147.0], "I": [197.0, 172.0]} | [
"I"
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.5244, 0.1000)
B = (0.1000, 0.6756)
C = (1.1000, 0.5244)
I = (0.6000, 0.6000)
# Draw circles
circle_I = plt.Circle(I, 0.5057, fil... | ||
<image>Find x | 4 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(C, B)), x+3)",
"Equals(LengthOf(Line(D, C)), 6)",
"Equals(LengthOf(Line(C, A)), 1)",
"Equals(LengthOf(Line(E, C)), 11x-2)",
"PointLiesOnLine(C, Line(E, B))",
"PointLiesOnLine(C, Line(D, A))"
] | [
"BA",
"CA",
"CB",
"DA",
"DC",
"EB",
"EC",
"ED"
] | {"A": [14.0, 127.0], "B": [0.0, 0.0], "C": [118.0, 78.0], "D": [234.0, 23.0], "E": [250.0, 166.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.1560, 0.6080)
B = (0.1000, 0.1000)
C = (0.5702, 0.4122)
D = (1.0360, 0.1920)
E = (1.1000, 0.7640)
# Draw line segments
ax.plot([... | ||
<image>Find the area of the shaded sector. Round to the nearest tenth. | 311.5 | [
"Find(AreaOf(Shaded(Sector($))))"
] | [
"Equals(LengthOf(Line(K, J)), 11)",
"Equals(MeasureOf(Angle(J, K, L)), 65)",
"PointLiesOnCircle(L, Circle(K, radius_0_0))",
"PointLiesOnCircle(J, Circle(K, radius_0_0))"
] | [
"KJ",
"KL"
] | {"J": [150.0, 11.0], "K": [103.0, 106.0], "L": [210.0, 106.0]} | [
"K"
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
J = (0.5434, 0.1000)
K = (0.1000, 0.9963)
L = (1.1000, 0.9963)
# Draw circles
circle_K = plt.Circle(K, 1.0000, fill=False, color='black... | ||
<image>Find $x$ in the figure. | 16 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(D, G, C)), 3x)",
"Equals(MeasureOf(Angle(C, G, H)), 42)",
"Equals(MeasureOf(Angle(G, C, D)), z)",
"Equals(MeasureOf(Angle(G, C, H)), 48)",
"Equals(MeasureOf(Angle(G, H, C)), y)",
"Parallel(Line(G,D), Line(H,C))",
""
] | [
"GD",
"DC",
"HC",
"HG",
"GC"
] | {"A": [203.0, 109.0], "B": [7.0, 133.0], "C": [197.0, 218.0], "D": [196.0, 8.0], "E": [98.0, 8.0], "F": [97.0, 217.0], "G": [8.0, 9.0], "H": [8.0, 217.0], "I": [8.0, 171.0], "J": [8.0, 58.0], "K": [198.0, 65.0], "L": [11.0, 101.0], "M": [196.0, 192.0], "N": [196.0, 120.0], "O": [196.0, 84.0], "P": [7.0, 115.0], "Q": [1... | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (1.0333, 0.5809)
B = (0.1000, 0.6952)
C = (1.0047, 1.0952)
D = (1.0000, 0.1000)
E = (0.5333, 0.1000)
F = (0.5286, 1.0952)
G = (0.104... | ||
<image>Find $x$. | 35 | [
"Find(x)"
] | [
"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))"
] | [
"BC",
"BE",
"CD",
"CE",
"ED",
"FB",
"FD",
"FE"
] | {"B": [357.0, 133.0], "C": [360.0, 3.0], "D": [1.0, 132.0], "E": [181.0, 67.0], "F": [4.0, 2.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
B = (1.0916, 0.4649)
C = (1.1000, 0.1028)
D = (0.1000, 0.4621)
E = (0.6000, 0.2825)
F = (0.1084, 0.1000)
# Draw line segments
ax.plot([... | ||
<image>In the figure, square $WXYZ$ is inscribed in $\odot R$. Find the measure of a central angle. | 90 | [
"InscribedIn(Square(W,X,Y,Z),Circle(R))",
"Find(MeasureOf(Angle($)))"
] | [
"PointLiesOnLine(S, Line(X, Y))",
"PointLiesOnLine(R, Line(X, Z))",
"PointLiesOnLine(R, Line(Y, W))",
"PointLiesOnCircle(X, Circle(R, radius_2_0))",
"PointLiesOnCircle(Y, Circle(R, radius_2_0))",
"PointLiesOnCircle(W, Circle(R, radius_2_0))",
"PointLiesOnCircle(Z, Circle(R, radius_2_0))",
"Perpendicul... | [
"RS",
"WZ",
"XR",
"XS",
"XW",
"XY",
"XZ",
"YR",
"YS",
"YW",
"YZ"
] | {"R": [86.0, 88.0], "S": [149.0, 90.0], "W": [26.0, 28.0], "X": [147.0, 28.0], "Y": [148.0, 151.0], "Z": [26.0, 150.0]} | [
"R"
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
R = (0.5960, 0.6000)
S = (1.0919, 0.6000)
W = (0.1000, 0.1000)
X = (1.0919, 0.1000)
Y = (1.0919, 1.1000)
Z = (0.1000, 1.1000)
# Draw ci... | ||
<image>Find y. | 45 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(Y, A)), 8)",
"Equals(LengthOf(Line(A, B)), x)",
"Perpendicular(Line(A, B), Line(Y, B))",
"Equals(LengthOf(Line(A, B)), LengthOf(Line(Y, B)))"
] | [
"YA",
"YB",
"AB"
] | {"Y": [239.0, 240.0], "A": [1.0, 0.0], "B": [2.6583676196504484, 238.00411435805466]} | [] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.1276, 0.1000)
B = (0.1000, 1.0660)
Y = (1.0632, 1.1000)
# Draw line segments
ax.plot([Y[0], A[0]], [Y[1], A[1]], 'k-', linewidth... | ||
<image>Find $\angle D$ of quadrilateral ABCD | 45 | [
"Quadrilateral(A,B,C,D)",
"Find(MeasureOf(Angle(D)))"
] | [
"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))"
] | [
"CD",
"CB",
"DA",
"BA"
] | {"C": [399.33517037528145, 180.3341620740618], "D": [0.0, 181.0], "A": [130.5985267034991, 2.0], "B": [399.9944751381215, 2.0]} | [] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.4327, 0.1000)
B = (1.1000, 0.1000)
C = (1.0986, 0.4868)
D = (0.1000, 0.4885)
# Draw line segments
ax.plot([C[0], D[0]], [C[1], D... | ||
<image>Find $x$. | 70 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(G, F)), 4)",
"",
"Equals(LengthOf(Line(G, H)), 4)",
"Equals(MeasureOf(Angle(F, O, G)), x)",
"",
"PointLiesOnCircle(H, Circle(O, radius_4_0))",
"PointLiesOnCircle(G, Circle(O, radius_4_0))",
"PointLiesOnCircle(F, Circle(O, radius_4_0))"
] | [
"GF",
"GH"
] | {"F": [96.0, 9.0], "G": [289.0, 145.0], "H": [93.0, 281.0], "O": [144.0, 146.0]} | [
"O"
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
F = (0.1121, 0.1000)
G = (0.8202, 0.5985)
H = (0.1000, 1.1000)
O = (0.2881, 0.6022)
# Draw circles
circle_O = plt.Circle(O, 0.5321, fil... | ||
<image>The diagonals of rhombus FGHJ intersect at K.
If $m\angle FJH = 82$, find $m\angle KHJ$. | 49 | [
"Rhombus(F,G,H,J)",
"IsDiagonalOf(Line(F,H),Rhombus(F,G,H,J))",
"IsDiagonalOf(Line(G,J),Rhombus(F,G,H,J))",
"IntersectAt(Line(F,H),Line(G,J),Point(K))",
"Equals(MeasureOf(Angle(F,J,H)),82)",
"Find(MeasureOf(Angle(K,H,J)))"
] | [
"PointLiesOnLine(K, Line(G, J))",
"PointLiesOnLine(K, Line(H, F))"
] | [
"KG",
"KJ",
"KH",
"KF",
"GJ",
"GH",
"GF",
"JH",
"JF",
"HF"
] | {"K": [67.70719983978104, 96.38158817049968], "G": [100.10869006580022, 0.7673305491067879], "J": [35.853372721431825, 193.00860047182562], "H": [134.8349455483649, 124.3883276204112], "F": [0.19455558364815317, 69.36708578938888]} | [] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
F = (0.1000, 0.4568)
G = (0.6197, 0.1000)
H = (0.8004, 0.7431)
J = (0.2855, 1.1000)
K = (0.4523, 0.6008)
# Draw line segments
ax.plot([... | ||
<image>Find $y$ in the given parallelogram | 15 | [
"Parallelogram($)",
"Find(y)"
] | [
"Equals(LengthOf(Line(T, Q)), 8)",
"Equals(LengthOf(Line(S, T)), y-4)",
"Equals(LengthOf(Line(R, Q)), 11)"
] | [
"RQ",
"SR",
"ST",
"TQ"
] | {"Q": [29.0, 45.0], "R": [0.0, 249.0], "S": [179.0, 199.0], "T": [203.0, 1.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
Q = (0.2169, 0.2774)
R = (0.1000, 1.1000)
S = (0.8218, 0.8984)
T = (0.9185, 0.1000)
# Draw line segments
ax.plot([R[0], Q[0]], [R[1], Q... | ||
<image>Find $HK$. | 10 | [
"Find(LengthOf(Line(H,K)))"
] | [
"Equals(LengthOf(Line(P, N)), 8)",
"Equals(LengthOf(Line(N, Q)), 12)",
"Equals(LengthOf(Line(P, Q)), 20)",
"Equals(LengthOf(Line(J, H)), 4x+7)",
"Equals(LengthOf(Line(J, K)), 25)",
"Equals(LengthOf(Line(K, H)), 6x-2)",
"Equals(MeasureOf(Angle(H, J, K)), MeasureOf(Angle(P, Q, N)))",
"Equals(MeasureOf(A... | [
"JH",
"JK",
"KH",
"NQ",
"PN",
"PQ"
] | {"H": [2.0, 271.0], "J": [100.0, 0.0], "K": [253.0, 272.0], "N": [400.0, 80.0], "P": [253.0, 80.0], "Q": [330.0, 220.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
H = (0.1000, 0.7809)
J = (0.3462, 0.1000)
K = (0.7307, 0.7834)
N = (1.1000, 0.3010)
P = (0.7307, 0.3010)
Q = (0.9241, 0.6528)
# Draw li... | ||
<image>$\triangle RST \cong \triangle XYZ$. Find $y$. | 15 | [
"Congruent(Triangle(R,S,T),Triangle(X,Y,Z))",
"Find(y)"
] | [
"Equals(LengthOf(Line(T, R)), x+21)",
"Equals(MeasureOf(Angle(T, R, S)), 4y-10)",
"Equals(MeasureOf(Angle(Z, X, Y)), 3y+5)",
"Equals(LengthOf(Line(Z, X)), 2x-14)"
] | [
"SR",
"ST",
"TR",
"XY",
"XZ",
"ZY"
] | {"R": [2.0, 56.0], "S": [55.0, 223.0], "T": [321.0, 3.0], "X": [600.0, 120.0], "Y": [550.0, -30.0], "Z": [321.0, 180.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
R = (0.1000, 0.2438)
S = (0.1886, 0.5231)
T = (0.6334, 0.1552)
X = (1.1000, 0.3508)
Y = (1.0164, 0.1000)
Z = (0.6334, 0.4512)
# Draw li... | ||
<image>Find x. Round to the nearest tenth. | 24.7 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(C, B)), 8)",
"Equals(MeasureOf(Angle(C, B, A)), 140)",
"Equals(LengthOf(Line(A, B)), 18)",
"Equals(LengthOf(Line(C, A)), x)"
] | [
"CA",
"CB",
"AB"
] | {"C": [292.29583785278294, 84.80365384206385], "A": [0.0, 141.0], "B": [180.78661274400534, 0.7568915920984267]} | [] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.1000, 0.5798)
B = (0.7185, 0.1000)
C = (1.1000, 0.3875)
# Draw line segments
ax.plot([C[0], A[0]], [C[1], A[1]], 'k-', linewidth... | ||
<image>Find DX if $E X=24$ and $D E=7$ | 25 | [
"Equals(LengthOf(Line(E,X)),24)",
"Equals(LengthOf(Line(D,E)),7)",
"Find(LengthOf(Line(D,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"
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.9350, 0.1000)
D = (0.9600, 0.2325)
E = (0.9200, 0.3750)
Q = (0.8200, 0.2375)
T = (1.1000, 0.2400)
X = (0.1000, 0.2325)
# Draw ci... | ||
<image>Find $TR$. | 4 | [
"Find(LengthOf(Line(T,R)))"
] | [
"Equals(MeasureOf(Angle(R, P, T)), 60)",
"Equals(LengthOf(Line(P, T)), 4)",
"Equals(LengthOf(Line(R, P)), 4)"
] | [
"RP",
"RT",
"PT"
] | {"R": [273.7379557680813, 259.62363020522014], "P": [178.43508290041999, 1.2755717441929733], "T": [0.0, 214.0]} | [] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
P = (0.7518, 0.1000)
R = (1.1000, 1.0438)
T = (0.1000, 0.8771)
# Draw line segments
ax.plot([R[0], P[0]], [R[1], P[1]], 'k-', linewidth... | ||
<image>Find z | 2 \sqrt { 6 } | [
"Find(z)"
] | [
"Equals(LengthOf(Line(X, W)), 4)",
"Equals(MeasureOf(Angle(X, Y, W)), 23)",
"Equals(LengthOf(Line(W, Z)), 4)",
"Perpendicular(Line(Y, X), Line(X, W))",
"Perpendicular(Line(W, Z), Line(Y, Z))"
] | [
"WZ",
"XW",
"YE",
"YF",
"YG",
"YW",
"YX"
] | {"Z": [86.0, 230.0], "W": [47.0, 132.0], "X": [86.0, 30.0], "Y": [343.0, 133.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
W = (0.1000, 0.4446)
X = (0.2318, 0.1000)
Y = (1.1000, 0.4480)
Z = (0.2318, 0.7757)
# Draw line segments
ax.plot([W[0], Z[0]], [W[1], Z... | ||
<image>Find the measure of $\angle 4$ if $m∠4= m∠5$. | 32 | [
"Equals(MeasureOf(Angle(4)),MeasureOf(Angle(5)))",
"Find(MeasureOf(Angle(4)))"
] | [
"Equals(MeasureOf(Angle(C, E, D)), MeasureOf(angle 7))",
"Equals(MeasureOf(Angle(D, F, B)), 63)",
"Equals(MeasureOf(Angle(F, D, E)), 69)",
"Equals(MeasureOf(Angle(F, B, D)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(B, D, F)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(E, D, G)), 47)",
"Equals(Me... | [
"AB",
"AD",
"AF",
"BC",
"BD",
"BF",
"BG",
"CE",
"CG",
"DC",
"DE",
"DF",
"DG"
] | {"A": [226.0, 268.0], "B": [0.0, 139.0], "C": [438.0, 139.0], "D": [161.0, 139.0], "E": [292.0, 1.0], "F": [96.0, 8.0], "G": [570.0, 139.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.4965, 0.5684)
B = (0.1000, 0.3421)
C = (0.8684, 0.3421)
D = (0.3833, 0.3421)
E = (0.6123, 0.1000)
F = (0.2684, 0.1123)
G = (1.100... | ||
<image>Find the perimeter of the triangle. Round to the nearest tenth if necessary. | 43.5 | [
"Find(PerimeterOf(Triangle($)))"
] | [
"Equals(LengthOf(Line(A, B)), 5)",
"Equals(LengthOf(Line(O, B)), 21.5)",
"Equals(LengthOf(Line(O, C)), 8)",
"Equals(LengthOf(Line(A, C)), 15)",
"PointLiesOnLine(A, Line(C, B))",
"Perpendicular(Line(O, C), Line(C, A))"
] | [
"AB",
"AC",
"AO",
"BC",
"OB",
"OC"
] | {"A": [227.0, 121.0], "B": [300.0, 121.0], "C": [2.0, 120.0], "O": [2.0, 2.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.8550, 0.4993)
B = (1.1000, 0.4993)
C = (0.1000, 0.4960)
O = (0.1000, 0.1000)
# Draw line segments
ax.plot([A[0], B[0]], [A[1], B... | ||
<image>If $\overline{QR} \| \overline{XY}, XQ=15, QZ=12$, and $YR=20$, what is the length of $\overline{RZ}$. | 16 | [
"Parallel(Line(Q,R),Line(X,Y))",
"Equals(LengthOf(Line(X,Q)),15)",
"Equals(LengthOf(Line(Q,Z)),12)",
"Equals(LengthOf(Line(Y,R)),20)",
"Find(LengthOf(Line(R,Z)))"
] | [
"PointLiesOnLine(R, Line(Z, Y))",
"PointLiesOnLine(Q, Line(Z, X))"
] | [
"QX",
"QZ",
"RQ",
"RY",
"RZ",
"YX",
"ZX",
"ZY"
] | {"Q": [21.0, 128.0], "R": [215.0, 158.0], "X": [2.0, 2.0], "Y": [364.0, 61.0], "Z": [42.0, 269.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
Q = (0.1522, 0.4481)
R = (0.6875, 0.5295)
X = (0.1000, 0.1000)
Y = (1.1000, 0.2630)
Z = (0.2105, 0.8376)
# Draw line segments
ax.plot([... | ||
<image>Find $x$. | 13.9 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), y)",
"Equals(MeasureOf(Angle(B, A, C)), 60)",
"Equals(LengthOf(Line(A, C)), 8)",
"Equals(LengthOf(Line(B, C)), x)",
"Perpendicular(Line(A, C), Line(B, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [1.0, 1.0], "B": [251.0, 9.0], "C": [71.0, 116.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.1000, 0.1000)
B = (1.1000, 0.1320)
C = (0.3800, 0.5600)
# Draw line segments
ax.plot([A[0], B[0]], [A[1], B[1]], 'k-', linewidth... | ||
<image>In $\odot P$, $PS=4$, find the length of $\widehat {QR}$. Round to the nearest hundredth. | 4.75 | [
"Circle(P)",
"Equals(LengthOf(Line(P,S)),4)",
"Find(LengthOf(Arc(Q,R)))"
] | [
"Equals(MeasureOf(Angle(R, P, S)), 130)",
"Equals(MeasureOf(Angle(T, P, Q)), 112)",
"PointLiesOnLine(P, Line(T, R))",
"PointLiesOnCircle(S, Circle(P, radius_5_0))",
"PointLiesOnCircle(T, Circle(P, radius_5_0))",
"PointLiesOnCircle(R, Circle(P, radius_5_0))",
"PointLiesOnCircle(Q, Circle(P, radius_5_0))"... | [
"PQ",
"PR",
"PT",
"SP",
"TR"
] | {"P": [152.0, 155.0], "Q": [1.0, 132.0], "R": [119.0, 4.0], "S": [288.0, 222.0], "T": [188.0, 301.0]} | [
"P"
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
P = (0.6078, 0.6000)
Q = (0.1000, 0.5252)
R = (0.4916, 0.1000)
S = (1.0664, 0.8308)
T = (0.7240, 1.1000)
# Draw circles
circle_P = plt.... | ||
<image>Find $y$ if $\triangle JLM \sim \triangle QST$. | 4 | [
"Similar(Triangle(J,L,M),Triangle(Q,S,T))",
"Find(y)"
] | [
"Equals(MeasureOf(Angle(L, J, M)), MeasureOf(Angle(T, Q, S)))",
"Equals(MeasureOf(Angle(J, M, L)), MeasureOf(Angle(S, T, Q)))",
"Equals(LengthOf(Line(M, J)), 4)",
"Equals(LengthOf(Line(S, T)), 3)",
"Equals(LengthOf(Line(T, Q)), 2)",
"Equals(LengthOf(Line(S, Q)), 5)",
"Equals(LengthOf(Line(M, L)), 6x-3)"... | [
"JL",
"JM",
"ML",
"SQ",
"ST",
"TQ"
] | {"J": [0.0, 1.0], "L": [1.0, 279.0], "M": [274.0, 83.0], "Q": [450.0, 200.0], "S": [470.0, 1.0], "T": [320.0, 120.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
J = (0.1000, 0.1000)
L = (0.1021, 0.6915)
M = (0.6830, 0.2745)
Q = (1.0574, 0.5234)
S = (1.1000, 0.1000)
T = (0.7809, 0.3532)
# Draw li... | ||
<image>Find $MP$. | 8 | [
"Find(LengthOf(Line(M,P)))"
] | [
"Equals(LengthOf(Line(M, Q)), 5)",
"Equals(LengthOf(Line(O, N)), 3+\\frac{3}{5})",
"Equals(LengthOf(Line(M, N)), 6)",
"PointLiesOnLine(N, Line(O, M))",
"PointLiesOnLine(Q, Line(M, P))",
"Parallel(Line(N, Q), Line(O, P))"
] | [
"MN",
"MP",
"MQ",
"NQ",
"OM",
"ON",
"OP",
"PQ"
] | {"M": [123.0, 4.0], "N": [258.0, 217.0], "O": [303.0, 293.0], "P": [2.0, 308.0], "Q": [33.0, 227.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
M = (0.5001, 0.1000)
N = (0.9393, 0.8084)
O = (1.0952, 1.0600)
P = (0.1000, 1.1000)
Q = (0.2049, 0.8379)
# Draw line segments
ax.plot([... | ||
<image>Find x. | 24 \sqrt { 2 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, C)), x)",
"Equals(LengthOf(Line(C, D)), y)",
"Equals(LengthOf(Line(A, D)), z)",
"Equals(LengthOf(Line(B, C)), 12)",
"Equals(LengthOf(Line(B, D)), 4)",
"PointLiesOnLine(D, Line(A, B))",
"Perpendicular(Line(C, D), Line(B, D))",
"Perpendicular(Line(A, C), Line(B, C))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [256.0, 1.0], "B": [1.0, 0.0], "C": [256.0, 234.0], "D": [140.0, 128.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (1.1000, 0.1039)
B = (0.1000, 0.1000)
C = (1.1000, 1.0176)
D = (0.6451, 0.6020)
# Draw line segments
ax.plot([A[0], B[0]], [A[1], B... | ||
<image>For the pair of similar figures, use the given areas to find $x$. | 10.4 | [
"Similar(Shape($1),Shape($2))",
"Find(x)"
] | [
"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)"
] | [
"AB",
"AC",
"BX",
"CX"
] | {"A": [257.0, 61.0], "B": [89.0, 106.0], "C": [90.0, 1.0], "X": [1.0, 51.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (1.1000, 0.3344)
B = (0.4437, 0.5102)
C = (0.4477, 0.1000)
X = (0.1000, 0.2953)
# Draw line segments
ax.plot([A[0], B[0]], [A[1], B... | ||
<image>Find the length of $\widehat {ZY}$. Round to the nearest hundredth. | 5.24 | [
"Find(LengthOf(Arc(Z,Y)))"
] | [
"Equals(LengthOf(Line(X, Y)), 4)",
"PointLiesOnCircle(Z, Circle(X, radius_0_0))",
"PointLiesOnCircle(Y, Circle(X, radius_0_0))",
"Equals(MeasureOf(Angle(X, Y)), 4)",
""
] | [
"XY",
"XZ"
] | {"X": [128.0, 128.0], "Y": [97.0, 5.0], "Z": [2.0, 127.0]} | [
"X"
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
X = (1.1000, 1.0697)
Y = (0.8556, 0.1000)
Z = (0.1000, 1.0618)
# Draw circles
circle_X = plt.Circle(X, 1.0000, fill=False, color='black... | ||
<image>Find the value of x. | 130 | [
"Find(x)"
] | [
"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... | [
"AB",
"AE",
"BC",
"BD",
"BE"
] | {"A": [168.30712454533213, 12.385750909335755], "B": [117.40138436884067, 115.47190744524228], "C": [222.99371704358114, 166.5060065486671], "D": [33.536117346541275, 197.47042066987996], "E": [105.18081665559488, 1.470642132171676]} | [
"B"
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.7876, 0.1557)
B = (0.5279, 0.6816)
C = (1.0666, 0.9420)
D = (0.1000, 1.1000)
E = (0.4655, 0.1000)
# Draw circles
circle_B = plt.... | ||
<image>Find $m \angle A B C$ if $m \widehat{A B}=102$ | 129 | [
"Equals(MeasureOf(Arc(A,B)),102)",
"Find(MeasureOf(Angle(A,B,C)))"
] | [
"Equals(MeasureOf(Arc(A,B)),102)",
"PointLiesOnLine(C, Line(B, F))",
"PointLiesOnLine(A, Line(B, H))",
"PointLiesOnCircle(B, Circle(G, radius_3_0))",
"PointLiesOnCircle(A, Circle(G, radius_3_0))"
] | [
"BA",
"BC",
"BF",
"BH",
"FC",
"HA"
] | {"A": [40.0, 95.0], "B": [153.0, 181.0], "C": [219.0, 167.0], "F": [258.0, 160.0], "G": [132.0, 93.0], "H": [0.0, 64.0]} | [
"G"
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.2576, 0.2213)
B = (0.6938, 0.5569)
C = (0.9497, 0.5035)
F = (1.1000, 0.4721)
G = (0.6116, 0.2124)
H = (0.1000, 0.1000)
# Draw ci... | ||
<image>If $R T=15, Q P=21,$ and $P T=8,$ find $T S$ | 20 | [
"Equals(LengthOf(Line(R,T)),15)",
"Equals(LengthOf(Line(Q,P)),21)",
"Equals(LengthOf(Line(P,T)),8)",
"Find(LengthOf(Line(T,S)))"
] | [
"PointLiesOnLine(T, Line(P, S))",
"PointLiesOnLine(R, Line(Q, S))",
"Parallel(Line(P, Q), Line(T, R))"
] | [
"PQ",
"PS",
"PT",
"QR",
"QS",
"RS",
"TS"
] | {"P": [0.0, 148.0], "Q": [49.0, 8.0], "R": [96.0, 46.0], "S": [209.0, 149.0], "T": [59.0, 148.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
P = (0.1000, 0.7699)
Q = (0.3344, 0.1000)
R = (0.5509, 0.2907)
S = (1.1000, 0.7746)
T = (0.3827, 0.7712)
# Draw line segments
ax.plot([... | ||
<image>$\triangle K L N$ and $\triangle L M N$ are isosceles and $m \angle J K N=130$. Find the measure of $\angle LKN$. | 81 | [
"Isosceles(Triangle(K,L,N))",
"Isosceles(Triangle(L,M,N))",
"Equals(MeasureOf(Angle(J,K,N)),130)",
"Find(MeasureOf(Angle(L,K,N)))"
] | [
"Equals(MeasureOf(Angle(K, L, N)), 18)",
"Equals(MeasureOf(Angle(J, L, K)), 25)",
"Equals(MeasureOf(Angle(N, L, M)), 20)",
"Equals(LengthOf(Line(K, L)), LengthOf(Line(N, L)))",
"Equals(LengthOf(Line(N, M)), LengthOf(Line(M, L)))"
] | [
"JK",
"KL",
"KN",
"LJ",
"ML",
"NL",
"NM"
] | {"J": [5.0, 94.0], "K": [69.0, 3.0], "L": [55.0, 219.0], "M": [133.0, 134.0], "N": [138.0, 18.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
J = (0.1000, 0.5225)
K = (0.3958, 0.1000)
L = (0.3314, 1.1000)
M = (0.6917, 0.7067)
N = (0.7137, 0.1737)
# Draw line segments
ax.plot([... | ||
<image>Find x. Round the side measure to the nearest tenth. | 34.8 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(B, C, A)), 87)",
"Equals(LengthOf(Line(A, C)), 21)",
"Equals(MeasureOf(Angle(A, B, C)), 37)",
"Equals(LengthOf(Line(A, B)), x)"
] | [
"AB",
"AC",
"BC"
] | {"A": [0.6624724919093978, 164.00636893203884], "B": [318.70485866229535, 162.00280197472503], "C": [108.0, 0.0]} | [] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.1000, 0.6157)
B = (1.1000, 0.6094)
C = (0.4375, 0.1000)
# Draw line segments
ax.plot([A[0], B[0]], [A[1], B[1]], 'k-', linewidth... | ||
<image>Find sinA | \sqrt { 26 } / 26 | [
"Find(SinOf(Angle(A)))"
] | [
"Equals(LengthOf(Line(A, C)), 5\\sqrt{26})",
"Equals(MeasureOf(Angle(D, C, A)), x)",
"Equals(LengthOf(Line(C, D)), 5)",
"Equals(LengthOf(Line(C, B)), \\sqrt{26})",
"Equals(LengthOf(Line(A, D)), 25)",
"Equals(LengthOf(Line(D, B)), 1)",
"PointLiesOnLine(D, Line(A, B))",
"Perpendicular(Line(A, C), Line(C... | [
"AC",
"BC",
"CD",
"AD",
"AB",
"BD"
] | {"A": [0.0, 132.0], "B": [683.0, 135.0], "D": [652.0, 135.0], "C": [649.0, 1.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.1000, 0.2918)
B = (1.1000, 0.2962)
C = (1.0502, 0.1000)
D = (1.0546, 0.2962)
# Draw line segments
ax.plot([A[0], C[0]], [A[1], C... | ||
<image>If XM = 4, XN = 6, and NZ = 9, find XY. | 10 | [
"Equals(LengthOf(Line(X,M)),4)",
"Equals(LengthOf(Line(X,N)),6)",
"Equals(LengthOf(Line(N,Z)),9)",
"Find(LengthOf(Line(X,Y)))"
] | [
"PointLiesOnLine(M, Line(X, Y))",
"PointLiesOnLine(N, Line(X, Z))",
"Parallel(Line(M, N), Line(Y, Z))"
] | [
"MN",
"XM",
"XY",
"YM",
"ZX",
"ZY",
"NX",
"NZ"
] | {"M": [63.0, 81.0], "N": [78.0, 126.0], "X": [2.0, 127.0], "Y": [167.0, 1.0], "Z": [210.0, 126.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
M = (0.3932, 0.4857)
N = (0.4667, 0.7078)
X = (0.1000, 0.7091)
Y = (0.8996, 0.1000)
Z = (1.1000, 0.7055)
# Draw line segments
ax.plot([... | ||
<image>Find x. Round to the nearest tenth if necessary. Assume that segments that appear
to be tangent are tangent. | 8 | [
"Tangent(Line($),Circle($))",
"Find(x)"
] | [
"Equals(LengthOf(Line(X, B)), x+16)",
"Equals(LengthOf(Line(A, C)), 16)",
"Equals(LengthOf(Line(X, C)), x)",
"PointLiesOnLine(X, Line(C, B))",
"PointLiesOnCircle(A, Circle(D, radius_3_0))",
"PointLiesOnCircle(B, Circle(D, radius_3_0))",
"PointLiesOnCircle(X, Circle(D, radius_3_0))"
] | [
"AC",
"AX",
"CB",
"CX",
"XB"
] | {"A": [157.0, 143.0], "B": [7.0, 117.0], "C": [253.0, 93.0], "D": [88.0, 86.0], "X": [171.0, 100.0]} | [
"D"
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.7015, 0.3247)
B = (0.1000, 0.2261)
C = (1.1000, 0.1284)
D = (0.4295, 0.1000)
X = (0.7772, 0.1600)
# Draw circles
circle_D = plt.... | ||
<image>Find $x$. | \frac { 26 } { 3 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(B, C)), 43)",
"Equals(LengthOf(Line(A, C)), x)",
"Equals(LengthOf(Line(A, D)), 4)",
"Equals(LengthOf(Line(B, D)), 6)",
"PointLiesOnLine(D, Line(A, B))",
"Equals(MeasureOf(Angle(A, C, D)), MeasureOf(Angle(D, C, B)))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [0.0, 203.0], "B": [373.0, 204.0], "C": [103.0, 0.0], "D": [154.0, 204.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.1000, 0.6442)
B = (1.1000, 0.6469)
C = (0.3761, 0.1000)
D = (0.5129, 0.6453)
# Draw line segments
ax.plot([A[0], B[0]], [A[1], B... | ||
<image>In the figure, $m∠1 = 50$ and $m∠3 = 60$. Find the measure of $\angle 2$. | 110 | [
"Equals(MeasureOf(Angle(1)),50)",
"Equals(MeasureOf(Angle(3)),60)",
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(M, J, B)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(E, P, C)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(A, G, K)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(P, O, R)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(P, R, O)), MeasureOf(angle 5))",
"Equals(MeasureOf(Ang... | [
"AB",
"AF",
"AG",
"AH",
"AJ",
"AN",
"AQ",
"AR",
"AS",
"AT",
"AU",
"BF",
"BG",
"BJ",
"BT",
"CI",
"CK",
"CM",
"CP",
"DO",
"DW",
"EL",
"FE",
"FG",
"FJ",
"FL",
"FN",
"FO",
"FP",
"FS",
"FT",
"GC",
"GI",
"GJ",
"GK",
"GP",
"GQ",
"GR",
"GT",
"HC"... | {"A": [324.0, 147.0], "B": [0.0, 146.0], "C": [183.0, 39.0], "D": [490.0, 123.0], "E": [66.0, 226.0], "F": [135.0, 146.0], "G": [279.0, 147.0], "H": [211.0, 7.0], "I": [151.0, 2.0], "J": [89.0, 146.0], "K": [347.0, 224.0], "L": [262.0, 1.0], "M": [20.0, 226.0], "N": [229.0, 39.0], "O": [156.0, 123.0], "P": [206.0, 65.0... | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.7683, 0.3969)
B = (0.1000, 0.3969)
C = (0.4727, 0.1787)
D = (1.1000, 0.3490)
E = (0.2347, 0.5592)
F = (0.3760, 0.3969)
G = (0.656... | ||
<image>Find the measure of $∠A$ to the nearest tenth. | 16.7 | [
"Find(MeasureOf(Angle(A)))"
] | [
"Equals(LengthOf(Line(C, B)), 6)",
"Equals(LengthOf(Line(C, A)), 20)",
"Perpendicular(Line(C, B), Line(C, A))"
] | [
"CA",
"CB",
"AB"
] | {"C": [0.022724892658914086, 131.00010472300764], "A": [434.0, 132.0], "B": [2.000658761528342, 0.6376811594202962]} | [] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (1.1000, 0.5635)
B = (0.1070, 0.1000)
C = (0.1000, 0.5612)
# Draw line segments
ax.plot([C[0], A[0]], [C[1], A[1]], 'k-', linewidth... | ||
<image>Find x. | 2 \sqrt { 13 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(C, D)), 4)",
"Equals(LengthOf(Line(B, D)), 9)",
"Equals(LengthOf(Line(A, C)), x)",
"Equals(LengthOf(Line(A, D)), z)",
"Equals(LengthOf(Line(A, B)), y)",
"PointLiesOnLine(D, Line(B, C))",
"Perpendicular(Line(B, D), Line(A, D))",
"Perpendicular(Line(A, C), Line(A, B))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [2.0, 139.0], "B": [287.0, 140.0], "C": [1.0, 1.0], "D": [57.0, 28.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.1035, 0.5825)
B = (1.1000, 0.5860)
C = (0.1000, 0.1000)
D = (0.2958, 0.1944)
# Draw line segments
ax.plot([A[0], B[0]], [A[1], B... | ||
<image>Find $ m ∠RSU $ so that $ m \parallel n $. | 124 | [
"Parallel(Line(m),Line(n))",
"Find(MeasureOf(Angle(R,S,U)))"
] | [
"Equals(MeasureOf(Angle(F, E, U)), 8x+4)",
"Equals(MeasureOf(Angle(F, T, V)), 9x-11)",
"Equals(LengthOf(Line(A, D)), 5)",
"PointLiesOnLine(T, Line(R, B))",
"PointLiesOnLine(E, Line(R, B))",
"PointLiesOnLine(E, Line(R, T))",
"PointLiesOnLine(T, Line(B, E))",
"PointLiesOnLine(R, Line(B, F))",
"PointLi... | [
"AD",
"AU",
"BE",
"BF",
"BT",
"CV",
"DU",
"EA",
"ED",
"EF",
"EU",
"RB",
"RE",
"RF",
"RT",
"TC",
"TE",
"TF",
"TV"
] | {"A": [301.0, 1.0], "B": [443.0, 196.0], "C": [154.0, 201.0], "D": [0.0, 151.0], "E": [155.0, 74.0], "F": [1.0, 6.0], "R": [44.0, 27.0], "T": [292.0, 132.0], "U": [253.0, 22.0], "V": [444.0, 57.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.7779, 0.1000)
B = (1.0977, 0.5392)
C = (0.4468, 0.5505)
D = (0.1000, 0.4378)
E = (0.4529, 0.2620)
F = (0.1023, 0.1113)
R = (0.201... | ||
<image>Find tanB | 5 | [
"Find(TanOf(Angle(B)))"
] | [
"Equals(LengthOf(Line(A, C)), 5\\sqrt{26})",
"Equals(MeasureOf(Angle(D, C, A)), x)",
"Equals(LengthOf(Line(C, D)), 5)",
"Equals(LengthOf(Line(C, B)), \\sqrt{26})",
"Equals(LengthOf(Line(A, D)), 25)",
"Equals(LengthOf(Line(D, B)), 1)",
"PointLiesOnLine(D, Line(A, B))",
"Perpendicular(Line(A, C), Line(C... | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [0.0, 132.0], "B": [683.0, 135.0], "C": [649.0, 1.0], "D": [652.0, 135.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.1000, 0.2918)
B = (1.1000, 0.2962)
C = (1.0502, 0.1000)
D = (1.0546, 0.2962)
# Draw line segments
ax.plot([A[0], B[0]], [A[1], B... | ||
<image>$RP=3.5$ and $JP=9$. Find $PL$. | 7 | [
"Equals(LengthOf(Line(R,P)),3.5)",
"Equals(LengthOf(Line(J,P)),9)",
"Find(LengthOf(Line(P,L)))"
] | [
"PointLiesOnLine(T, Line(J, L))",
"PointLiesOnLine(R, Line(J, K))",
"PointLiesOnLine(P, Line(J, S))",
"PointLiesOnLine(S, Line(L, K))",
"PointLiesOnLine(P, Line(L, R))",
"PointLiesOnLine(P, Line(K, T))",
"Equals(LengthOf(Line(K, R)), LengthOf(Line(R, J)))",
"Equals(LengthOf(Line(L, T)), LengthOf(Line(... | [
"JC",
"JK",
"JL",
"JR",
"JS",
"JT",
"KR",
"KS",
"KT",
"LC",
"LK",
"LR",
"LS",
"LT",
"PJ",
"PK",
"PL",
"PR",
"PS",
"PT",
"TC"
] | {"C": [151.0, 284.0], "J": [1.0, 374.0], "K": [202.0, 4.0], "L": [541.0, 62.0], "P": [248.0, 143.0], "R": [105.0, 182.0], "S": [365.0, 33.0], "T": [271.0, 218.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
C = (0.3773, 0.6280)
J = (0.1000, 0.7911)
K = (0.4705, 0.1000)
L = (1.1000, 0.2133)
P = (0.5568, 0.3681)
R = (0.2853, 0.4455)
S = (0.785... | ||
<image>If PR || WX, WX = 10, XY = 6, WY = 8, RY = 5, and PS = 3, find SY | 4 | [
"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(S,Y)))"
] | [
"PointLiesOnLine(S, Line(W, Y))",
"PointLiesOnLine(S, Line(Q, P))",
"PointLiesOnLine(Q, Line(W, X))",
"PointLiesOnLine(B, Line(Y, X))",
"PointLiesOnLine(B, Line(Q, R))",
"PointLiesOnLine(B, Line(Q, R))",
"PointLiesOnLine(Y, Line(P, R))",
"Perpendicular(Line(C, P), Line(Y, S))",
"Perpendicular(Line(Y... | [
"PR",
"QB",
"QP",
"QR",
"QS",
"QX",
"RB",
"SP",
"WQ",
"WS",
"WX",
"WY",
"XB",
"YB",
"YP",
"YR",
"YS",
"YX"
] | {"B": [120.0, 130.0], "P": [290.0, 0.0], "Q": [291.0, 133.0], "R": [3.0, 131.0], "S": [291.0, 82.0], "W": [409.0, 81.0], "X": [121.0, 212.0], "Y": [119.0, 80.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
B = (0.3882, 0.4202)
P = (0.8069, 0.1000)
Q = (0.8094, 0.4276)
R = (0.1000, 0.4227)
S = (0.8094, 0.3020)
W = (1.1000, 0.2995)
X = (0.390... | ||
<image>Find x. | 2 \sqrt { 5 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, D)), 3\\sqrt{2})",
"Equals(LengthOf(Line(C, D)), z)",
"Equals(LengthOf(Line(B, D)), \\sqrt{2})",
"Equals(LengthOf(Line(B, C)), y)",
"Equals(LengthOf(Line(A, B)), x)",
"PointLiesOnLine(D, Line(A, C))",
"Perpendicular(Line(C, D), Line(B, D))",
"Perpendicular(Line(B, C), Line(A, ... | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [0.0, 0.0], "B": [224.0, 178.0], "C": [365.0, 0.0], "D": [222.0, 0.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.1000, 0.1000)
B = (0.7137, 0.5877)
C = (1.1000, 0.1000)
D = (0.7082, 0.1000)
# Draw line segments
ax.plot([A[0], B[0]], [A[1], B... | ||
<image>The sum of the circumference of circles $H,J,K$ is $56 \pi$ units. Find $KJ$. | 24 | [
"Equals(SumOf(CircumferenceOf(Circle(H)),Circle(J),Circle(K)),56\\pi)",
"Find(LengthOf(Line(K,J)))"
] | [
"Equals(LengthOf(Line(K, A)), 4x)",
"Equals(LengthOf(Line(C, G)), 2x)",
"Equals(LengthOf(Line(H, A)), x)",
"Equals(LengthOf(Line(H, C)), x)",
"PointLiesOnLine(C, Line(J, H))",
"PointLiesOnLine(B, Line(J, K))",
"PointLiesOnLine(A, Line(K, H))",
"PointLiesOnCircle(B, Circle(J, radius_0_0))",
"PointLie... | [
"HA",
"HC",
"JB",
"JC",
"JH",
"JK",
"KA",
"KB",
"KH"
] | {"A": [380.0, 160.0], "B": [359.0, 281.0], "C": [452.0, 213.0], "H": [445.0, 150.0], "J": [465.0, 334.0], "K": [196.0, 191.0]} | [
"J",
"K",
"H"
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.7821, 0.1401)
B = (0.7104, 0.5769)
C = (1.0523, 0.3454)
H = (1.0257, 0.1000)
J = (1.1000, 0.7840)
K = (0.1000, 0.2524)
# Draw ci... | ||
<image>Solve for x in the figure below. | 7 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(H, E, G)), 6x+2)",
"Equals(MeasureOf(Angle(H, F, G)), 3x+23)",
"PointLiesOnLine(I, Line(H, F))",
"PointLiesOnLine(I, Line(E, G))",
"PointLiesOnCircle(E, Circle(B, radius_4_0))",
"PointLiesOnCircle(G, Circle(B, radius_4_0))",
"PointLiesOnCircle(H, Circle(B, radius_4_0))",
"Point... | [
"HE",
"HF",
"GE",
"GF",
"EI",
"IG",
"HI",
"IF"
] | {"E": [115.0, 1.0], "F": [221.0, 65.0], "G": [179.0, 219.0], "H": [12.0, 167.0], "I": [144.0, 102.0]} | [
"B"
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
E = (0.5725, 0.1000)
F = (1.0587, 0.3936)
G = (0.8661, 1.1000)
H = (0.1000, 0.8615)
I = (0.7088, 0.5644)
# Draw circles
# Draw line se... | ||
<image>Find the measure of $\angle 2$ if $m \angle D G F=53$ and $m \angle A G C=40$. | 50 | [
"Equals(MeasureOf(Angle(D,G,F)),53)",
"Equals(MeasureOf(Angle(A,G,C)),40)",
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(B, A, D)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(A, D, G)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(F, G, B)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(G, C, B)), MeasureOf(angle 3))",
"PointLiesOnLine(B, Line(G, A))",
"PointLiesOnLine(F, Line(A, D))",
"Perpend... | [
"CG",
"CA",
"CB",
"GD",
"GA",
"GF",
"GB",
"AD",
"AF",
"AB",
"DF"
] | {"C": [467.3028007071389, 179.32857098008682], "G": [245.71043804039223, 179.38710896331065], "D": [0.0, 1.0], "A": [464.76705978377527, 1.2643739086495174], "F": [244.00841171251108, 0.761259982253776], "B": [372.8431907794965, 75.82984531392174]} | [] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (1.0946, 0.1011)
B = (0.8979, 0.2606)
C = (1.1000, 0.4821)
D = (0.1000, 0.1005)
F = (0.6222, 0.1000)
G = (0.6258, 0.4822)
# Draw li... | ||
<image>Find $x$. | 4 | [
"Find(x)"
] | [
"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",
"KL",
"MP",
"PQ",
"MQ",
"JM",
"KP",
"LQ"
] | {"L": [538.0, 78.0], "J": [100.0, 152.0], "K": [321.0, 114.0], "M": [129.0, 254.0], "P": [364.0, 262.0], "Q": [589.0, 262.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
J = (0.1000, 0.2513)
K = (0.5519, 0.1736)
L = (0.9957, 0.1000)
M = (0.1593, 0.4599)
P = (0.6399, 0.4763)
Q = (1.1000, 0.4763)
# Draw li... | ||
<image>Find $m \angle D G E$ | 30 | [
"Find(MeasureOf(Angle(D,G,E)))"
] | [
"Equals(MeasureOf(Angle(A, G, C)), 60)",
"PointLiesOnLine(G, Line(E, C))",
"PointLiesOnLine(G, Line(A, B))",
"PointLiesOnCircle(E, Circle(G, radius_0_0))",
"PointLiesOnCircle(C, Circle(G, radius_0_0))",
"PointLiesOnCircle(A, Circle(G, radius_0_0))",
"PointLiesOnCircle(D, Circle(G, radius_0_0))",
"Poin... | [
"AB",
"EC",
"GA",
"GB",
"GC",
"GD",
"GE"
] | {"A": [1.0, 82.0], "B": [169.0, 86.0], "C": [44.0, 12.0], "D": [85.0, 159.0], "E": [126.0, 158.0], "G": [86.0, 85.0]} | [
"G"
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.1000, 0.5242)
B = (1.1000, 0.5480)
C = (0.3551, 0.1000)
D = (0.5881, 1.0361)
E = (0.8449, 0.9722)
G = (0.6000, 0.5361)
# Draw ci... | ||
<image>Refer to the figure at the right. Find the value of $x$ if $ p \parallel q $. | 45 | [
"Shape($)",
"Parallel(Line(p),Line(q))",
"Find(x)"
] | [
"Equals(LengthOf(Line(P, O)), p)",
"Equals(LengthOf(Line(M, N)), q)",
"Equals(MeasureOf(Angle(A, B, D)), 3x-60)",
"Equals(MeasureOf(Angle(D, B, C)), y)",
"Equals(MeasureOf(Angle(E, C, F)), 2x+15)",
"PointLiesOnLine(A, Line(B, I))",
"PointLiesOnLine(A, Line(C, I))",
"PointLiesOnLine(A, Line(F, I))",
... | [
"AF",
"BA",
"BD",
"BF",
"BG",
"BH",
"BO",
"BP",
"BQ",
"BR",
"BU",
"CA",
"CB",
"CE",
"CF",
"CI",
"CJ",
"CK",
"CL",
"CM",
"CN",
"CS",
"CT",
"CV",
"DO",
"DP",
"DQ",
"DR",
"DU",
"ES",
"ET",
"EV",
"GD",
"GH",
"GO",
"GP",
"GQ",
"GR",
"GU",
"HD"... | {"A": [195.0, 31.0], "B": [192.0, 79.0], "C": [181.0, 162.0], "D": [315.0, 57.0], "E": [335.0, 132.0], "F": [178.0, 203.0], "G": [380.0, 45.0], "H": [44.0, 108.0], "I": [202.0, 1.0], "J": [67.0, 182.0], "K": [358.0, 129.0], "L": [172.0, 236.0], "M": [425.0, 116.0], "N": [25.0, 191.0], "O": [1.0, 116.0], "P": [403.0, 39... | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.5649, 0.1717)
B = (0.5504, 0.2849)
C = (0.5257, 0.4789)
D = (0.8401, 0.2295)
E = (0.8881, 0.4110)
F = (0.5133, 0.5759)
G = (0.993... | ||
<image>Find the length of $WY$ | 9 | [
"Find(LengthOf(Line(W,Y)))"
] | [
"Equals(LengthOf(Line(Y, X)), 4x+5)",
"Equals(LengthOf(Line(W, Y)), 6x+3)",
"Equals(LengthOf(Line(W, X)), 9x)",
"Equals(LengthOf(Line(X, x)), LengthOf(Line(W, Y)))",
"Equals(LengthOf(Line(W, Y)), LengthOf(Line(Y, X)))"
] | [
"WX",
"WY",
"YX"
] | {"W": [0.0, 155.0], "X": [92.0, 1.0], "Y": [180.0, 156.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
W = (0.1000, 0.9622)
X = (0.6082, 0.1000)
Y = (1.1000, 0.9708)
# Draw line segments
ax.plot([W[0], X[0]], [W[1], X[1]], 'k-', linewidth... | ||
<image>Find $m\angle U$ | 134 | [
"Find(MeasureOf(Angle(W)))"
] | [
"Equals(MeasureOf(Angle(V, U, T)), 3x-4)",
"Equals(MeasureOf(Angle(W, V, U)), x)",
"Equals(MeasureOf(Angle(T, W, V)), 3x-4)",
"Equals(MeasureOf(Angle(U, T, W)), x)"
] | [
"WV",
"WT",
"VU",
"TU"
] | {"W": [245.66261808367074, 112.33738191632929], "U": [110.00892057464263, 1.9999283487980506], "V": [356.9946018893387, 0.6720647773279325], "T": [0.0, 113.0]} | [] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
T = (0.1000, 0.4146)
U = (0.4082, 0.1037)
V = (1.1000, 0.1000)
W = (0.7881, 0.4128)
# Draw line segments
ax.plot([W[0], V[0]], [W[1], V... | ||
<image>$\Delta DFG$ and $\Delta F G H$ are isosceles, $m \angle FDH=28$ and$\overline{DG} \cong \overline{FG} \cong \overline{FH}$. Find the measure of $\angle GFH$. | 68 | [
"Isosceles(Triangle(D,F,G))",
"Isosceles(Triangle(F,G,H))",
"Equals(MeasureOf(Angle(F,D,H)),28)",
"Equals(LengthOf(Line(D,G)),Line(F,G))",
"Equals(LengthOf(Line(F,G)),Line(F,H))",
"Find(MeasureOf(Angle(G,F,H)))"
] | [
"Equals(MeasureOf(Angle(F, D, H)), 28)",
"PointLiesOnLine(G, Line(D, H))",
"Equals(LengthOf(Line(F, G)), LengthOf(Line(H, F)))",
"Equals(LengthOf(Line(H, A)), LengthOf(Line(D, G)))"
] | [
"DG",
"DH",
"FD",
"FG",
"FH",
"HG"
] | {"D": [1.0, 105.0], "F": [193.0, 2.0], "G": [160.0, 106.0], "H": [227.0, 106.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
D = (0.1000, 0.5554)
F = (0.9522, 0.1000)
G = (0.8033, 0.5564)
H = (1.1000, 0.5568)
# Draw line segments
ax.plot([D[0], G[0]], [D[1], G... | ||
<image>Find y. | 1.5 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(I, J)), \\frac{4}{2}y+1)",
"Equals(LengthOf(Line(H, A)), 6-x)",
"Equals(LengthOf(Line(E, N)), 2y)",
"Equals(LengthOf(Line(B, H)), 2x+3)",
"PointLiesOnLine(H, Line(A, B))",
"PointLiesOnLine(B, Line(A, G))",
"PointLiesOnLine(H, Line(A, G))",
"PointLiesOnLine(E, Line(A, N))",
"Poi... | [
"AB",
"AE",
"AG",
"AH",
"AK",
"AM",
"AN",
"BG",
"BH",
"BI",
"BK",
"BL",
"BO",
"CF",
"CJ",
"DP",
"ED",
"EI",
"EJ",
"EM",
"EN",
"EP",
"FJ",
"GH",
"GK",
"HC",
"HF",
"HJ",
"HK",
"ID",
"IJ",
"IL",
"IO",
"IP",
"JD",
"JP",
"LO",
"MN"
] | {"A": [98.0, 186.0], "B": [49.0, 72.0], "C": [222.0, 128.0], "D": [147.0, 0.0], "E": [172.0, 187.0], "F": [0.0, 129.0], "G": [24.0, 15.0], "H": [73.0, 129.0], "I": [157.0, 72.0], "J": [164.0, 128.0], "K": [118.0, 233.0], "L": [224.0, 72.0], "M": [0.0, 185.0], "N": [222.0, 187.0], "O": [1.0, 72.0], "P": [177.0, 226.0]} | [
""
] | import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import Arc
import numpy as np
fig, ax = plt.subplots(figsize=(5, 5))
# Define key points
A = (0.5206, 0.8983)
B = (0.3103, 0.4090)
C = (1.0528, 0.6494)
D = (0.7309, 0.1000)
E = (0.8382, 0.9026)
F = (0.1000, 0.6536)
G = (0.203... |
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