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0580/22 Oct/Nov 2021, Question 14: Alternate Segment Theorem

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 3 marks

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The question, in short

Circle with points P, Q, R; tangent ST at R; angle P 55°, Q 65°, PRQ 60°; find x between RQ and RS, then explain why triangle SVR is isosceles with second tangent SV.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

State the size of angle x and justify it using a circle tangent theorem.

  1. 1x = angle QPR = 55
  2. 2Reason: alternate segment theorem (angle between tangent and chord equals angle in the alternate segment)

Answer55, alternate segment theorem

Part (b) · 1 mark

Explain, using tangent properties, why triangle SVR has two equal sides.

  1. 1SV and SR are tangents from the same external point S
  2. 2Tangents from an external point are equal in length, so SV = SR and triangle SVR is isosceles

AnswerTangents from an external point are equal in length

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Also searched as: 0580/22/O/N/21 · 0580_w21_qp_22 · 0580 w21 22 · question 14.
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