Circle theorems
10th grade (Year 11 in England) · 16 questions · Common Core: HSG.C.A.2, HSG.C.A.4 · England: GCSE Higher Geometry
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Question 1
A tangent from P touches a circle with centre O at T. The radius is 6 cm and OP = 10 cm. Find the length PT.
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Question 2
PA and PB are tangents from P to a circle with centre O, touching it at A and B. ∠APB = 101°. Find ∠AOB.
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Question 3
Two tangents are drawn from point P to a circle, touching it at A and B. PA = (4x + 20) cm and PB = (6x + 10) cm. Find x.
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Question 4
A tangent from P touches a circle with centre O at T. The radius is 14 cm and OP = 50 cm. Find the length PT.
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Question 5
PA and PB are tangents from P to a circle with centre O, touching it at A and B. ∠APB = 90°. Find ∠AOB.
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Question 6
Two tangents are drawn from point P to a circle, touching it at A and B. PA = (4x + 8) cm and PB = (5x + 6) cm. Find x.
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Question 7
A tangent from P touches a circle with centre O at T. The radius is 10 cm and OP = 26 cm. Find the length PT.
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Question 8
PA and PB are tangents from P to a circle with centre O, touching it at A and B. ∠APB = 99°. Find ∠AOB.
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Question 9
Two tangents are drawn from point P to a circle, touching it at A and B. PA = (4x + 17) cm and PB = (6x + 13) cm. Find x.
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Question 10
A tangent from P touches a circle with centre O at T. The radius is 24 cm and OP = 51 cm. Find the length PT.
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Question 11
PA and PB are tangents from P to a circle with centre O, touching it at A and B. ∠APB = 29°. Find ∠AOB.
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Question 12
Two tangents are drawn from point P to a circle, touching it at A and B. PA = (1x + 65) cm and PB = (5x + 17) cm. Find x.
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Question 13
A tangent from P touches a circle with centre O at T. The radius is 15 cm and OP = 39 cm. Find the length PT.
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Question 14
PA and PB are tangents from P to a circle with centre O, touching it at A and B. ∠APB = 62°. Find ∠AOB.
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Question 15
Two tangents are drawn from point P to a circle, touching it at A and B. PA = (5x + 25) cm and PB = (7x + 7) cm. Find x.
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Question 16
A tangent from P touches a circle with centre O at T. The radius is 14 cm and OP = 50 cm. Find the length PT.
Answer
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