Circle theorems
10th grade (Year 11 in England) · 16 questions · Common Core: HSG.C.A.2, HSG.C.A.3 · England: GCSE Higher Geometry
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Question 1
Two angles at the circumference stand on the same arc. One is 58°. What is the other?
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Question 2
ABCD is a cyclic quadrilateral. Angle A = 110°. What is angle C?
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Question 3
Two angles at the circumference stand on the same arc. One is 28°. What is the other?
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Question 4
ABCD is a cyclic quadrilateral. Angle A = 100°. What is angle C?
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Question 5
Two angles at the circumference stand on the same arc. One is 51°. What is the other?
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Question 6
A tangent meets a radius at the point of contact. A triangle formed with the centre has an angle of 74° at the centre. What is the angle between the tangent and the line to the centre (the third angle)?
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Question 7
Two angles at the circumference stand on the same arc. One is 25°. What is the other?
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Question 8
ABCD is a cyclic quadrilateral. Angle A = 82°. What is angle C?
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Question 9
Two angles at the circumference stand on the same arc. One is 66°. What is the other?
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Question 10
A tangent meets a radius at the point of contact. A triangle formed with the centre has an angle of 51° at the centre. What is the angle between the tangent and the line to the centre (the third angle)?
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Question 11
Two angles at the circumference stand on the same arc. One is 42°. What is the other?
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Question 12
A triangle is drawn in a semicircle with one side the diameter. One of the other angles is 28°. What is the third angle (not the right angle)?
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Question 13
Two angles at the circumference stand on the same arc. One is 38°. What is the other?
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Question 14
A tangent meets a radius at the point of contact. A triangle formed with the centre has an angle of 20° at the centre. What is the angle between the tangent and the line to the centre (the third angle)?
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Question 15
Two angles at the circumference stand on the same arc. One is 54°. What is the other?
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Question 16
ABCD is a cyclic quadrilateral. Angle A = 93°. What is angle C?
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