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4024/22 May/Jun 2025, Question 14: Combining Circle Theorems

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 3 marks

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The question, in short

In a circle with cyclic quadrilateral PQRS and tangent APB at P, angle SPB = 37° and angle PSQ = 85°; find angle PQS and angle QRS.

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

Part (a) · 1 mark

Find angle PQS using the tangent-chord angle SPB = 37°.

  1. 1Alternate segment theorem: angle between tangent and chord PS = angle in the alternate segment
  2. 2Angle PQS = angle SPB = 37°

Answer37

Part (b) · 2 marks

Find angle QRS using cyclic quadrilateral properties and angle PSQ = 85°.

  1. 1Angle QPS = 180 − 37 − 85 = 58° (angles in triangle PQS)
  2. 2Opposite angles of a cyclic quadrilateral add to 180°
  3. 3Angle QRS = 180 − 58 = 122°

Answer122

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Also searched as: 4024/22/M/J/25 · 4024_s25_qp_22 · 4024 s25 22 · question 14.
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