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4024/11 Oct/Nov 2025, Question 16: Combining Circle Theorems

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 6 marks

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The question, in short

Circle with centre O, points Q, R, S, T on it; UV tangent at T; SOQV straight; angle QST = 32°. Find angles QRT, TQS and TVQ, giving a reason for QRT.

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

Part (a) · 2 marks

Find angle QRT and state a geometrical reason for it.

  1. 1Angle QRT = angle QST = 32°
  2. 2Angles in the same segment are equal

Answer32, angles in the same segment are equal

Part (b) · 2 marks

Find angle TQS.

  1. 1Angle STQ = 90° (angle in a semicircle, SQ is a diameter)
  2. 2Angle TQS = 180 − 90 − 32 = 58°

Answer58

Part (c) · 2 marks

Find angle TVQ.

  1. 1Angle QTV = angle QST = 32° (alternate segment theorem)
  2. 2SQ is a diameter, so angle STQ = 90° and angle SQT = 180 − 90 − 32 = 58°
  3. 3Angle TQV = 180 − 58 = 122° (angles on a straight line)
  4. 4Angle TVQ = 180 − 122 − 32 = 26°

Answer26

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Also searched as: 4024/11/O/N/25 · 4024_w25_qp_11 · 4024 w25 11 · question 16.
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