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
O is the centre. ∠AOB = 54° and C is on the major arc. Find ∠ACB.
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Question 2
O is the centre of a circle. A, B and C are on the circle, with C on the major arc. ∠ACB = 84°. Find ∠AOB.
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Question 3
AB is a diameter of a circle and C is a point on the circle. ∠CAB = 52°. Find ∠CBA.
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Question 4
O is the centre. ∠AOB = 168° and C is on the major arc. Find ∠ACB.
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Question 5
O is the centre of a circle. A, B and C are on the circle, with C on the major arc. ∠ACB = 71°. Find ∠AOB.
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Question 6
AB is a diameter of a circle and C is a point on the circle. ∠CAB = 19°. Find ∠CBA.
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Question 7
O is the centre. The reflex angle AOB is 204°. C is on the major arc. Find ∠ACB.
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Question 8
O is the centre of a circle. A, B and C are on the circle, with C on the major arc. ∠ACB = 55°. Find ∠AOB.
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Question 9
AB is a diameter of a circle and C is a point on the circle. ∠CAB = 57°. Find ∠CBA.
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Question 10
O is the centre. The reflex angle AOB is 250°. C is on the major arc. Find ∠ACB.
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Question 11
O is the centre of a circle. A, B and C are on the circle, with C on the major arc. ∠ACB = 74°. Find ∠AOB.
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Question 12
AB is a diameter of a circle and C is a point on the circle. ∠CAB = 34°. Find ∠CBA.
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Question 13
O is the centre. ∠AOB = 50° and C is on the major arc. Find ∠ACB.
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Question 14
O is the centre of a circle. A, B and C are on the circle, with C on the major arc. ∠ACB = 36°. Find ∠AOB.
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Question 15
AB is a diameter of a circle and C is a point on the circle. ∠CAB = 18°. Find ∠CBA.
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Question 16
O is the centre. ∠AOB = 96° and C is on the major arc. Find ∠ACB.
Answer
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