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
Two tangents are drawn from point P to a circle, touching it at A and B. PA = (5x + 31) cm and PB = (6x + 20) cm. Find x.
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Question 2
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 3
PA and PB are tangents from P to a circle with centre O, touching it at A and B. ∠APB = 30°. Find ∠AOB.
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Question 4
Two tangents are drawn from point P to a circle, touching it at A and B. PA = (1x + 16) cm and PB = (5x + 8) cm. Find x.
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Question 5
A tangent from P touches a circle with centre O at T. The radius is 7 cm and OP = 25 cm. Find the length PT.
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Question 6
PA and PB are tangents from P to a circle with centre O, touching it at A and B. ∠APB = 21°. Find ∠AOB.
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Question 7
Two tangents are drawn from point P to a circle, touching it at A and B. PA = (2x + 29) cm and PB = (7x + 4) cm. Find x.
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Question 8
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 9
PA and PB are tangents from P to a circle with centre O, touching it at A and B. ∠APB = 50°. Find ∠AOB.
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Question 10
Two tangents are drawn from point P to a circle, touching it at A and B. PA = (3x + 7) cm and PB = (4x + 4) cm. Find x.
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Question 11
A tangent from P touches a circle with centre O at T. The radius is 9 cm and OP = 15 cm. Find the length PT.
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Question 12
PA and PB are tangents from P to a circle with centre O, touching it at A and B. ∠APB = 53°. Find ∠AOB.
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Question 13
Two tangents are drawn from point P to a circle, touching it at A and B. PA = (3x + 56) cm and PB = (6x + 20) cm. Find x.
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Question 14
A tangent from P touches a circle with centre O at T. The radius is 7 cm and OP = 25 cm. Find the length PT.
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Question 15
PA and PB are tangents from P to a circle with centre O, touching it at A and B. ∠APB = 46°. Find ∠AOB.
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Question 16
Two tangents are drawn from point P to a circle, touching it at A and B. PA = (5x + 19) cm and PB = (7x + 13) cm. Find x.
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