Circle theorems
10th grade (Year 11 in England) · 16 questions · Common Core: HSG.C.A.2 · England: GCSE Higher Geometry
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Question 1
A tangent touches a circle at A. Chord AB makes an angle of 76° with the tangent. C is a point on the circle in the other segment. Find ∠ACB.
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Question 2
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 73°, and ∠ABC = 68°. Find ∠BAC.
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Question 3
A tangent touches a circle at A. Chord AB makes an angle of 36° with the tangent. C is a point on the circle in the other segment. Find ∠ACB.
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Question 4
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 53°, and ∠ABC = 48°. Find ∠BAC.
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Question 5
A tangent touches a circle at A. Chord AB makes an angle of 35° with the tangent. C is a point on the circle in the other segment. Find ∠ACB.
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Question 6
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 46°, and ∠ABC = 69°. Find ∠BAC.
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Question 7
A tangent touches a circle at A. Chord AB makes an angle of 55° with the tangent. C is a point on the circle in the other segment. Find ∠ACB.
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Question 8
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 73°, and ∠ABC = 56°. Find ∠BAC.
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Question 9
A tangent touches a circle at A. Chord AB makes an angle of 55° with the tangent. C is a point on the circle in the other segment. Find ∠ACB.
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Question 10
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 31°, and ∠ABC = 42°. Find ∠BAC.
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Question 11
A tangent touches a circle at A. Chord AB makes an angle of 49° with the tangent. C is a point on the circle in the other segment. Find ∠ACB.
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Question 12
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 69°, and ∠ABC = 37°. Find ∠BAC.
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Question 13
A tangent touches a circle at A. Chord AB makes an angle of 56° with the tangent. C is a point on the circle in the other segment. Find ∠ACB.
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Question 14
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 66°, and ∠ABC = 52°. Find ∠BAC.
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Question 15
A tangent touches a circle at A. Chord AB makes an angle of 53° with the tangent. C is a point on the circle in the other segment. Find ∠ACB.
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Question 16
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 70°, and ∠ABC = 69°. Find ∠BAC.
Answer
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