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[
{
"content": "<image>\nQuestion: What is the measure of angle BAC if AB is the diameter of circle O, C is a point on the circle, and the tangent passing through point C intersects with the extension of diameter AB at point D, with angle ADC measuring 20°?\nChoices:\nA: 45°\nB: 40°\nC: 35°\nD: 30°",
"role": "user"
}
] |
C
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, circle O is intersected by the extension of line segment PO at point B, and PA serves as a tangent at point A. If the measure of angle BAP is 116 degrees, what is the measure of angle P? \nChoices:\nA: 64°\nB: 26°\nC: 52°\nD: 38°",
"role": "user"
}
] |
D
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Math
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[
{
"content": "<image>\nQuestion: In the given illustration, AB and AC serve as tangents to circle O, intersecting at points B and C. Point D lies on circle O, and DC and BD are connected. If angle A measures 50°, what is the measure of angle D?\nChoices:\nA: 50°\nB: 65°\nC: 75°\nD: 130°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: What is the value of angle ADC if it is given that BC is the diameter of circle O, and points A and D lie on circle O, and angle ACB measures 32°?\nChoices:\nA: 68°\nB: 62°\nC: 58°\nD: 52°",
"role": "user"
}
] |
C
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Math
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[
{
"content": "<image>\nQuestion: What is the measure of angle C in triangle ABC, where point O lies on side BC, and the circle with center O and radius BO intersects side AC at point A, and point D lies on the major arc AB with angle ADB measuring 60 degrees?\nChoices:\nA: 65°\nB: 50°\nC: 40°\nD: 30°",
"role": "user"
}
] |
D
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, quadrilateral ABCD is inscribed in circle O. If angle BOD measures 140°, what is the degree measure of angle BCD?\nChoices:\nA: 100°\nB: 110°\nC: 120°\nD: 140°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, tangents PA and PB intersect at circle O, with A and B as the points of tangency. If point C is situated on circle O and angle ACB measures 52°, what is the measure of angle APB?\nChoices:\nA: 104°\nB: 76°\nC: 128°\nD: 63°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: If CD is the diameter of circle O and points A and B lie on circle O such that AC = AB, and angle BCD measures 26°, what is the degree measure of angle ABC?\nChoices:\nA: 26°\nB: 27°\nC: 28°\nD: 32°",
"role": "user"
}
] |
D
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, if PA and PB are tangents to circle O at points A and B, and C is a point on circle O, with angle P measuring 40 degrees, what is the measure of angle ACB?\nChoices:\nA: 80°\nB: 70°\nC: 60°\nD: 50°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, circle O intersects the x-axis at points A and B, and intersects the positive y-axis at point C. If angle DAB measures 25°, what is the degree measure of angle OCD at point C on the circle in the first quadrant?\nChoices:\nA: 50°\nB: 60°\nC: 65°\nD: 70°",
"role": "user"
}
] |
D
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, circle O has diameter AB, with perpendicular chord CD. If chord AF is extended and it intersects DC at point E, what is the measure of angle CFE if angle DFC is 48 degrees?\nChoices:\nA: 60°\nB: 66°\nC: 68°\nD: 72°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: If quadrilateral ABCD is inscribed in circle O and AB is the diameter of the circle, with angle AOD measuring 40 degrees and chord AC bisecting angle DAB, what is the measure of angle ADC?\nChoices:\nA: 140°\nB: 125°\nC: 110°\nD: 105°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, quadrilateral ABCD is inscribed in circle O with diagonals AC and BD intersecting at point E, and BD serving as the diameter of circle O. If the measure of angle BDC is 40° and angle AEB is 110°, what is the measure of angle ABC?\nChoices:\nA: 65°\nB: 70°\nC: 75°\nD: 80°",
"role": "user"
}
] |
D
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Math
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[
{
"content": "<image>\nQuestion: As shown in the diagram, AB is the tangent line of circle O. Point A is the point of tangency. Line OB intersects circle O at point C. Point D is on circle O. Connect AD, CD, OA. If angle B = 20°, then the degree measure of angle ADC is ().\nChoices:\nA: 40°\nB: 35°\nC: 30°\nD: 20°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: As shown in the figure, quadrilateral ABCD is inscribed in circle O. AB = CD, A is the midpoint of BD, and angle BDC = 54°. Then, angle ADB is equal to ()\nChoices:\nA: 42°\nB: 46°\nC: 50°\nD: 54°",
"role": "user"
}
] |
A
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, points A, B, and C lie on circle O. If the measure of angle BAC is 26° and a tangent line to circle O passing through point C intersects the extension of OB at point D, what is the measure of angle D?\nChoices:\nA: 26°\nB: 38°\nC: 48°\nD: 52°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, circle O has a diameter AB, with points C and D positioned on the circle. If OD is perpendicular to AC and DC is connected, and angle COB measures 30 degrees, what is the measure of angle ACD?\nChoices:\nA: 30°\nB: 37.5°\nC: 45°\nD: 60°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: What is the measure of angle BDC if points D and A are situated on the minor arc BC and major arc BC of circle O respectively, and angle BOC measures 110°?\nChoices:\nA: 55°\nB: 70°\nC: 80°\nD: 125°",
"role": "user"
}
] |
D
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Math
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[
{
"content": "<image>\nQuestion: If point B lies on AC in circle O and the measure of angle AOC is 100 degrees, what is the degree measure of angle ABC?\nChoices:\nA: 80°\nB: 100°\nC: 120°\nD: 130°",
"role": "user"
}
] |
D
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Math
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[
{
"content": "<image>\nQuestion: What is the measure of angle ACB if angle ABO is 36 degrees and points A, B, and C lie on circle O?\nChoices:\nA: 54°\nB: 27°\nC: 36°\nD: 108°",
"role": "user"
}
] |
A
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Math
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[
{
"content": "<image>\nQuestion: If AB is the diameter of circle O and point D is located on circle O, with angle AOC measuring 130°, what is the measure of angle BDC?\nChoices:\nA: 70°\nB: 50°\nC: 25°\nD: 40°",
"role": "user"
}
] |
C
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Math
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[
{
"content": "<image>\nQuestion: What is the measure of angle A if AB is the diameter of circle O, and points C and D lie on circle O, with OC being parallel to DB and AD and CD are connected?\nChoices:\nA: 30°\nB: 28°\nC: 24°\nD: 34°",
"role": "user"
}
] |
D
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Math
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[
{
"content": "<image>\nQuestion: If angle BAO measures 32 degrees in the given diagram where points A, B, and C lie on circle O, what is the measure of angle ACB?\nChoices:\nA: 32°\nB: 45°\nC: 58°\nD: 64°",
"role": "user"
}
] |
C
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Math
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[
{
"content": "<image>\nQuestion: As shown in the figure, points A, B, C are on circle O. The extension of CO intersects AB at point D. angle A = 50° and angle ADC = 110°. The degree measure of angle B is ()\nChoices:\nA: 30°\nB: 40°\nC: 45°\nD: 50°",
"role": "user"
}
] |
A
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Math
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[
{
"content": "<image>\nQuestion: As shown in the diagram, quadrilateral ABCD is an inscribed quadrilateral of circle O, and angle A = 60°. The degree measure of angle DCE is ().\nChoices:\nA: 60°\nB: 120°\nC: 90°\nD: 0°",
"role": "user"
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] |
A
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, triangle ABC is inscribed in circle O with angle A measuring 40° and angle ABC measuring 70°. If BD is the diameter of circle O, and it intersects AC at point E, what is the degree measure of angle AEB?\nChoices:\nA: 70°\nB: 90°\nC: 110°\nD: 120°",
"role": "user"
}
] |
D
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Math
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[
{
"content": "<image>\nQuestion: As shown in the figure, AB is the diameter of circle O, C and D are two points on circle O. Given that angle CDB = 20°, the measure of angle ABC is ().\nChoices:\nA: 20°\nB: 40°\nC: 70°\nD: 90°",
"role": "user"
}
] |
C
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Math
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[
{
"content": "<image>\nQuestion: Given that AB is the diameter of semicircle O and points C and D trisect AE. If the measure of angle COD is 50 degrees, what is the degree measure of angle BOE?\nChoices:\nA: 25°\nB: 30°\nC: 50°\nD: 60°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: What is the measure of angle AOB in circle O, where chord AC intersects radius OB at point D, and angle B measures 60 degrees while angle ADB measures 116 degrees?\nChoices:\nA: 132°\nB: 120°\nC: 112°\nD: 110°",
"role": "user"
}
] |
C
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Math
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[
{
"content": "<image>\nQuestion: If angle 1 measures 20.0 degrees and the ruler and triangle ruler with a 30.0 degree angle are placed together as shown in the diagram, what is the measure of angle 2?\nChoices:\nA: 30°\nB: 40°\nC: 50°\nD: 60°",
"role": "user"
}
] |
C
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, circle O contains points A, B, and C. If BC is parallel to OA and angle A measures 20°, what is the measure of angle B?\nChoices:\nA: 10°\nB: 20°\nC: 40°\nD: 50°",
"role": "user"
}
] |
C
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Math
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[
{
"content": "<image>\nQuestion: In the given figure, circle O has AB as its diameter, and triangle ABC is inscribed in the circle. D is a point on AB such that BC=BD. If CD is extended to intersect circle O at point E, and AE is connected, what is the measure of angle CAE if angle B is 70 degrees?\nChoices:\nA: 60°\nB: 65°\nC: 70°\nD: 75°",
"role": "user"
}
] |
D
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Math
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[
{
"content": "<image>\nQuestion: What is the measure of angle B if points A, B, and C lie on circle O, AB is parallel to OC, and angle A is 70 degrees?\nChoices:\nA: 110°\nB: 125°\nC: 135°\nD: 165°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: As shown in the diagram, AB is the diameter of circle O, C and D are points on circle O. Angle DOB is 64° and angle D is equal to angle B. The value of angle B is ().\nChoices:\nA: 13°\nB: 14°\nC: 15°\nD: 16°",
"role": "user"
}
] |
D
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Math
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[
{
"content": "<image>\nQuestion: What is the measure of angle D in the given diagram of circle O, where points A, B, and C are connected by line segments AB, AC, OB, and OC, and the tangent line BD intersects the extension of line OC at point D when angle A measures 25 degrees?\nChoices:\nA: 20°\nB: 30°\nC: 40°\nD: 50°",
"role": "user"
}
] |
C
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Math
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[
{
"content": "<image>\nQuestion: Triangle ADC is inscribed in circle O, with BC as the diameter of the circle. Given that the measure of angle A is 66 degrees, what is the measure of angle BCD?\nChoices:\nA: 14°\nB: 24°\nC: 34°\nD: 66°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: As shown in the figure, PA and PB are tangents to circle O, with points of tangency A and B respectively. The extension of line PO intersects circle O at point C. OA, OB, and BC are then connected. If AO = 2 and OP = 4, the measure of angle C is _______.\nChoices:\nA: 20°\nB: 30°\nC: 45°\nD: 60°",
"role": "user"
}
] |
B
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Math
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{
"content": "<image>\nQuestion: In the given illustration, triangle ABC is depicted with angle ACB measuring 90°. A circle O is drawn with AC as the diameter, intersecting AB at point D. If CD equals OD, what is the degree measure of angle B?\nChoices:\nA: 30°\nB: 45°\nC: 60°\nD: 70°",
"role": "user"
}
] |
C
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, if AB is the diameter of circle O and CD is a chord such that point C does not coincide with point A or point B and point C and point D are on opposite sides of diameter AB, what is the measure of angle BCD if angle AOD equals 110 degrees?\nChoices:\nA: 25°\nB: 35°\nC: 55°\nD: 70°",
"role": "user"
}
] |
B
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Math
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{
"content": "<image>\nQuestion: In the given illustration, circle O has diameter AB, with points C and D located on AB. The intersection of AC and BD occurs at point E. If angle BEC measures 58°, what is the degree measure of angle DOC?\nChoices:\nA: 32°\nB: 64°\nC: 61°\nD: 58°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, circle O has AB as its diameter and CD as a chord. If angle CDB measures 26°, what is the measure of angle ABC?\nChoices:\nA: 26°\nB: 52°\nC: 64°\nD: 74°",
"role": "user"
}
] |
C
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Math
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{
"content": "<image>\nQuestion: In the given diagram, circle O has diameter AB. A tangent line is drawn from point C on the circle to intersect the extension of AB at point D. If angle A measures 35 degrees, what is the measure of angle D?\nChoices:\nA: 15°\nB: 20°\nC: 25°\nD: 30°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: In the given illustration, circle O has AB as the diameter, with points C and D positioned on the circle. C serves as the midpoint of arc BAD. When connecting CD, CB, and OD, CD intersects with AB at point F. If angle AOD is 100 degrees, what is the measure of angle ABC?\nChoices:\nA: 15°\nB: 20°\nC: 25°\nD: 30°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: In the given illustration, circle O has chord AB, and point C is situated on the tangent passing through point B. OC is perpendicular to OA, and it intersects AB at point P. If angle OAB measures 22°, what is the measure of angle OCB?\nChoices:\nA: 22°\nB: 44°\nC: 48°\nD: 68°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: In the given semicircle O with diameter AB, where AC equals BC, and D is a point on AC, how much is the measure of angle DOC if angle DEC measures 65 degrees and BD intersects OC at point E? \nChoices:\nA: 25°\nB: 32.5°\nC: 35°\nD: 40°",
"role": "user"
}
] |
D
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Math
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[
{
"content": "<image>\nQuestion: In the given illustration, point P is located outside circle O, and tangent lines PA and PB intersect the circle at points A and B respectively. Point C lies to the left of circle O, above line AB. If angle P measures 50°, what is the measure of angle ACB?\nChoices:\nA: 50°\nB: 55°\nC: 60°\nD: 65°",
"role": "user"
}
] |
D
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Math
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[
{
"content": "<image>\nQuestion: As shown in the figure, AB is the diameter of circle O. Point C is a point outside circle O. CA and CD are tangent to circle O at points A and D respectively. Connect BD and AD. If angle ACD = 50°, then the degree of angle DBA is ().\nChoices:\nA: 15°\nB: 35°\nC: 65°\nD: 75°",
"role": "user"
}
] |
C
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, circle O has diameter AB, with point C lying on the circle. A tangent passing through C intersects the extended line of AB at E, and point D lies on AC but does not coincide with points A and C. If angle D measures 110°, what is the degree measure of angle AEC?\nChoices:\nA: 55°\nB: 50°\nC: 45°\nD: 40°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: As shown in the figure, AB is the diameter of circle O. Chord CD is perpendicular to AB, and DE is parallel to CB. DE intersects circle O at point E. If angle CBA = 20°, then the degree measure of angle AOE is ().\nChoices:\nA: 120°\nB: 80°\nC: 110°\nD: 100°",
"role": "user"
}
] |
D
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram of circle O, if angle OAC plus angle C equals 50 degrees, what is the measure of angle BAC?\nChoices:\nA: 30°\nB: 35°\nC: 40°\nD: 45°",
"role": "user"
}
] |
C
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, line BC is a tangent to circle O at point B. Line CO intersects and extends circle O at point A, and AB is connected. If angle BAC measures 36°, what is the measure of angle C? \nChoices:\nA: 36°\nB: 24°\nC: 18°\nD: 15°",
"role": "user"
}
] |
C
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram of the cyclic quadrilateral ABDE within circle O, where AB is the diameter, and angle E measures 106°, if the tangent line DC passing through point D intersects the extension of AB at point C, what is the measure of angle C?\nChoices:\nA: 58°\nB: 32°\nC: 74°\nD: 48°",
"role": "user"
}
] |
A
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, triangle ABC is inscribed within circle O, and D is the midpoint of side BC. If OD is extended to intersect circle O at point E, and EC is then connected, what is the measure of angle A if angle OEC is 65°?\nChoices:\nA: 50°\nB: 55°\nC: 60°\nD: 65°",
"role": "user"
}
] |
A
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Math
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[
{
"content": "<image>\nQuestion: In the triangle ABC shown in the diagram, AB = 6. A circle with center A and a radius of 3 is tangent to the side BC at point D. It intersects AC and AB at points E and G, respectively. Point F is a point on arc GE. angle CDE = 18°. The measure of angle GFE is ()\nChoices:\nA: 50°\nB: 48°\nC: 45°\nD: 36°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, chord AB of circle O is both perpendicular to and bisects radius OC. Furthermore, AE is a tangent to circle O and intersects the extension of OC at point E. What is the measure of angle CAE?\nChoices:\nA: 25°\nB: 30°\nC: 35°\nD: 40°",
"role": "user"
}
] |
B
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Math
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{
"content": "<image>\nQuestion: What is the measure of angle D if points A, B, and C lie on circle O, and angle ABC is 28 degrees? \nChoices:\nA: 30°\nB: 56°\nC: 28°\nD: 34°",
"role": "user"
}
] |
D
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, circle O is intersected by the extension of line AO at point C, and line AB is a tangent to the circle at point B. If the measure of angle A is 26 degrees, what is the measure of angle C?\nChoices:\nA: 26°\nB: 32°\nC: 52°\nD: 64°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, triangle ABC is inscribed in circle O, with angle ACB measuring 40° and AC being equal to BC. The midpoint of BC is E. If we connect OE and extend it to intersect circle O at point D, what is the measure of angle ADO? \nChoices:\nA: 35°\nB: 25°\nC: 20°\nD: 15°",
"role": "user"
}
] |
D
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, circle O has AB as its diameter. The line PA is tangent to circle O at point A, and PO intersects circle O at point C. If angle BCO measures 10 degrees, what is the measure of angle P?\nChoices:\nA: 20\nB: 70°\nC: 25°\nD: 65°",
"role": "user"
}
] |
B
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, if AB is the diameter of circle O and point C lies on the extension of AB, with CD being tangent to circle O at point D, what is the measure of angle C if angle CDA is 118°?\nChoices:\nA: 32°\nB: 33°\nC: 34°\nD: 44°",
"role": "user"
}
] |
C
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Math
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[
{
"content": "<image>\nQuestion: Given triangle ABC circumscribes circle O, connect AO and extend it to intersect BC at point D. If angle C = 50°, then the degree of angle BAD is ()\nChoices:\nA: 40°\nB: 45°\nC: 50°\nD: 55°",
"role": "user"
}
] |
A
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, triangle ABG is circumscribed in circle O. When AO is connected and extended to intersect with BC at point D, and if angle B is 70 degrees and angle C is 50 degrees, what is the degree measure of angle ADB?\nChoices:\nA: 70°\nB: 80°\nC: 82°\nD: 84°",
"role": "user"
}
] |
A
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Math
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[
{
"content": "<image>\nQuestion: In the given illustration, points PA and PB are tangents to circle O at points A and B respectively. If point C lies on circle O and lines AC and BC are connected, what is the measure of angle ACB if angle P is 50 degrees?\nChoices:\nA: 115°\nB: 130°\nC: 65°\nD: 75°",
"role": "user"
}
] |
A
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Math
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[
{
"content": "<image>\nQuestion: As shown in the diagram, points A and B are both on circle O. Line PC is tangent to circle O at point C. If angle CAP = 35°, then the size of angle APC is ()\nChoices:\nA: 20°\nB: 25°\nC: 30°\nD: 35°",
"role": "user"
}
] |
A
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Math
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[
{
"content": "<image>\nQuestion: In the given diagram, line PA is a tangent to circle O at point A. The extension of PO intersects circle O at point B. If angle P measures 38 degrees, what is the measure of angle B?\nChoices:\nA: 22°\nB: 24°\nC: 26°\nD: 28°",
"role": "user"
}
] |
C
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Math
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{
"content": "<image>\nQuestion: In the given diagram of triangle ABC, where angle A is 80 degrees, if point O serves as the incenter of the triangle, what is the measure of angle BOC?\nChoices:\nA: 100°\nB: 160°\nC: 80°\nD: 130°",
"role": "user"
}
] |
D
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given figure, AB is a tangent to circle O, AC is a chord, and CB intersects circle O at point D. If CB passes through the center O and angle ACB measures 28°, what is the measure of angle B?\nChoices:\nA: 33°\nB: 34°\nC: 56°\nD: 28°",
"role": "user"
}
] |
B
|
Math
|
|
[
{
"content": "<image>\nQuestion: If triangle ABC is inscribed in circle O, with AB equal to AC, angle ACB measuring 65 degrees, and point C being the midpoint of arc BD, what is the measure of angle ACD?\nChoices:\nA: 12°\nB: 15°\nC: 18°\nD: 20°",
"role": "user"
}
] |
B
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given diagram, lines a and b are intersected by line l, where a is parallel to b. If angle 1 measures 60°, what is the degree measure of angle 2?\nChoices:\nA: 140°\nB: 120°\nC: 60°\nD: 30°",
"role": "user"
}
] |
B
|
Math
|
|
[
{
"content": "<image>\nQuestion: If a rectangular piece of paper is folded according to the provided diagram, and angle 1 measures 40 degrees, what is the measure of angle 2?\nChoices:\nA: 40°\nB: 50°\nC: 60°\nD: 70°",
"role": "user"
}
] |
D
|
Math
|
|
[
{
"content": "<image>\nQuestion: What is the degree measure of angle ACB if angle CAB is 40 degrees and a rectangular piece of paper is folded into the shape depicted in the figure?\nChoices:\nA: 40°\nB: 50°\nC: 60°\nD: 70°",
"role": "user"
}
] |
D
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given illustration, a configuration of triangular boards is set up where the oblique sides of the two boards are parallel. The right-angle vertices of each board coincide with the oblique sides of the other. If angle C is 45°, what is the degree measure of angle α in the illustration?\nChoices:\nA: 45°\nB: 60°\nC: 75°\nD: 85°",
"role": "user"
}
] |
C
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given diagram, point D lies in the interior of angle EAB, with CD being parallel to AB and DF parallel to AE. Line segment DH is perpendicular to AB and intersects AB at point H. If angle A measures 40°, what is the measure of angle FDH?\nChoices:\nA: 180°\nB: 130°\nC: 135°\nD: 140°",
"role": "user"
}
] |
B
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given diagram, a regular ruler intersects with a right angle triangle ruler at points D and E, while the other side of the regular ruler passes through point A and intersects with the right angle side BC of the triangle ruler at point F. If the measure of angle CAF is 42°, what is the degree measure of angle CDE?\nChoices:\nA: 62°\nB: 48°\nC: 58°\nD: 72°",
"role": "user"
}
] |
B
|
Math
|
|
[
{
"content": "<image>\nQuestion: Given that line l1 is parallel to line l2, and line l3 intersects l1 at point A and intersects l2 at point B, with the line l4 passing through point B and intersecting l1 at point C, if angle 3 is 50° and the sum of angles 1, 2, and 3 is 240°, what is the measure of angle 4?\nChoices:\nA: 80°\nB: 70°\nC: 60°\nD: 50°",
"role": "user"
}
] |
B
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given triangle ABC, angle B measures 50° and angle C measures 70°. Line DE intersects at point A, and angle DAB measures 50°. What is the measure of angle EAC?\nChoices:\nA: 40°\nB: 50°\nC: 60°\nD: 70°",
"role": "user"
}
] |
D
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given diagram, if AB is parallel to CD and angle B measures 75 degrees while angle D measures 35 degrees, what is the measure of angle E?\nChoices:\nA: 75°\nB: 35°\nC: 110°\nD: 40°",
"role": "user"
}
] |
D
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given diagram, line a is parallel to line b and angle 1 measures 60°. What is the measure of angle 2?\nChoices:\nA: 90°\nB: 100°\nC: 110°\nD: 120°",
"role": "user"
}
] |
D
|
Math
|
|
[
{
"content": "<image>\nQuestion: Triangle ABC is depicted in the figure, where point D lies on the extension of side BC and point E is an arbitrary point on side AC. Line EF is drawn parallel to side BC, intersecting side AB at point F. Given that angle ACD measures 50 degrees and angle BAC measures 15 degrees, what is the measure of angle AFE?\nChoices:\nA: 15°\nB: 25°\nC: 35°\nD: 45°",
"role": "user"
}
] |
C
|
Math
|
|
[
{
"content": "<image>\nQuestion: Place a right-angled triangle ruler ABC with an angle of 30° as shown in the figure. Point A and C are located on lines a and b respectively. If a is parallel to b, and angle 1 = 40°, then the degree of angle 2 is ().\nChoices:\nA: 40°\nB: 30°\nC: 20°\nD: 10°",
"role": "user"
}
] |
C
|
Math
|
|
[
{
"content": "<image>\nQuestion: If the measure of angle 1 is 47 degrees, what is the degree measure of angle 2? \nChoices:\nA: 43°\nB: 47°\nC: 133°\nD: 137°",
"role": "user"
}
] |
D
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the provided diagram, line AB is parallel to line CD. Points E and F are located on the side AC. If angle CED measures 70 degrees and angle BFC measures 130 degrees, what is the combined measurement of angle B and angle D?\nChoices:\nA: 40°\nB: 50°\nC: 60°\nD: 70°",
"role": "user"
}
] |
C
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given figure, point D is the intersection of the perpendicular bisectors of AB and AC in triangle ABC, while point E is the intersection of the perpendicular bisectors of AB and AC in the same triangle. If the measure of angle BAC is 110 degrees, what is the measure of angle DAE?\nChoices:\nA: 40\nB: 45\nC: 50\nD: 55",
"role": "user"
}
] |
A
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given triangle ABC, if the measure of angle B is 40°, and the perpendicular bisector of side AC intersects AC at point D and BC at point E, with the angle EAB to CAE ratio being 3, what is the measure of angle C?\nChoices:\nA: 28°\nB: 25°\nC: 22.5°\nD: 20°",
"role": "user"
}
] |
A
|
Math
|
|
[
{
"content": "<image>\nQuestion: As shown in the diagram, in triangle ABC, AB = AC. Point P is a point inside triangle ABC, and angle PBC = angle PCA. If angle BPC = 115°, then the degree measure of angle A is ().\nChoices:\nA: 50°\nB: 55°\nC: 60°\nD: 65°",
"role": "user"
}
] |
A
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given diagram, lines a and b pass through the vertices A and C of equilateral triangle ABC, and line b is parallel to line a. If angle 1 measures 42 degrees, what is the degree measure of angle 2?\nChoices:\nA: 18°\nB: 42°\nC: 60°\nD: 102°",
"role": "user"
}
] |
D
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given diagram of triangle ABC, where AC is equal to BC, point D lies on side AC, and point E is located on the extension of CB. If angle C measures 50° and angle E measures 25°, what is the measure of angle BFE?\nChoices:\nA: 30°\nB: 40°\nC: 50°\nD: 60°",
"role": "user"
}
] |
B
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given diagram, line m is parallel to line n, and the vertex B of equilateral triangle ABC lies on line n. If angle 1 is 25 degrees, what is the measure of angle 2?\nChoices:\nA: 25°\nB: 35°\nC: 45°\nD: 55°",
"role": "user"
}
] |
B
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given diagram, triangle ABC is depicted, and the perpendicular bisectors of AB and AC intersect BC at points E and F respectively. What is the measure of angle EAF if angle BAC is 102 degrees?\nChoices:\nA: 38°\nB: 40°\nC: 24°\nD: 44°",
"role": "user"
}
] |
C
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given diagram, if triangle ABC is depicted with AB equal to AC and the perpendicular bisector of AC intersecting BC at point D, and angle BAD measures 78 degrees, then what is the degree measure of angle B? \nChoices:\nA: 34°\nB: 30°\nC: 28°\nD: 26°",
"role": "user"
}
] |
A
|
Math
|
|
[
{
"content": "<image>\nQuestion: Given a triangle ABC where AB = AD = CD, and angle C measures 38.5 degrees, what is the measure of angle BAD?\nChoices:\nA: 26°\nB: 28°\nC: 36°\nD: 38.5°",
"role": "user"
}
] |
A
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given figure, if angle ABC measures 40 degrees and BD bisects angle ABC, and DE is parallel to AB passing through D and intersecting BC at point E, then what is the degree measure of angle DFB if point F lies on AB and satisfies DF = DE?\nChoices:\nA: 20°\nB: 140°\nC: 140°\nD: 40°",
"role": "user"
}
] |
D
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given illustration, if in the isosceles triangle ABC, AB is equal to AC and angle A measures 50°, and line MN is perpendicular to and bisects side AC at points D and E, then what is the measure of angle BCD?\nChoices:\nA: 10°\nB: 15°\nC: 20°\nD: 25°",
"role": "user"
}
] |
B
|
Math
|
|
[
{
"content": "<image>\nQuestion: If in triangle ABC, angle ABC is equal to angle ACB and angle A measures 50 degrees, and P is a point inside the triangle with angle PBC equal to angle PCA, what is the measure of angle BPC?\nChoices:\nA: 115°\nB: 100°\nC: 130°\nD: 140°",
"role": "user"
}
] |
A
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given triangle ABC, if point D lies on the perpendicular bisector of AB and angle CAD measures 80 degrees while angle C measures 50 degrees, what is the measure of angle B?\nChoices:\nA: 25°\nB: 30°\nC: 40°\nD: 50°",
"role": "user"
}
] |
A
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given diagram of triangle ABC, where AB is equal to AC and angle A measures 40 degrees, if DE is the perpendicular bisector of AB, what is the degree measure of angle DBC?\nChoices:\nA: 30°\nB: 20°\nC: 15°\nD: 10°",
"role": "user"
}
] |
A
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given diagram, if angle E in triangle ABE measures 25°, and the perpendicular bisector of AE labeled MN intersects BE at point C, and AB is equal to AC, what is the measure of angle BAE?\nChoices:\nA: 100°\nB: 105°\nC: 110°\nD: 120°",
"role": "user"
}
] |
B
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given diagram, point O lies on the side AC of angle BAC, and circle O tangentially touches side AB at point D. The circle also intersects the line segment AO at point E. If point P is located on circle O and angle EPD measures 35.0 degrees, then what is the measure of angle BAC?\nChoices:\nA: 20°\nB: 35°\nC: 55°\nD: 70°",
"role": "user"
}
] |
A
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given diagram, AF bisects angle BAC and intersects BC at point E. A perpendicular line FD passes through point F and intersects BC at point D. If the measure of angle B is 20 degrees more than angle C, what is the degree measure of angle F?\nChoices:\nA: 10°\nB: 15°\nC: 20°\nD: 0",
"role": "user"
}
] |
A
|
Math
|
|
[
{
"content": "<image>\nQuestion: In the given diagram, line AB is parallel to line CD. If angle CAB is bisected by line AE and intersects CD at point E, and angle C measures 100 degrees, what is the measure of angle AED?\nChoices:\nA: 110°\nB: 125°\nC: 135°\nD: 140°",
"role": "user"
}
] |
D
|
Math
|
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