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0580/42 Oct/Nov 2025, Question 12: Angle at the Centre

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 4 marks

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The question, in short

Circle with centre O, points A, B, C on circumference, tangent DE at C; angle ABC = 52°, angle BCE = 65°. Find x and y with reasons.

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

Part (a) · 2 marks

Find x, the marked angle AOC, and give a geometrical reason for the value.

  1. 1Angle AOC = 2 × angle ABC = 2 × 52 = 104°
  2. 2because the angle at the centre is twice the angle at the circumference
  3. 3x = 104

Answer104 and angle at the centre is twice the angle at the circumference

Part (b) · 2 marks

Find y, the marked angle BAO.

  1. 1Angle BAC = angle BCE = 65° (alternate segment theorem)
  2. 2OA = OC (radii), so angle OAC = (180 − 104) ÷ 2 = 38°
  3. 3y = angle BAC − angle OAC = 65 − 38 = 27

Answer27

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Also searched as: 0580/42/O/N/25 · 0580_w25_qp_42 · 0580 w25 42 · question 12.
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