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4024/22 May/Jun 2026, Question 18: Angle at the Centre

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 4 marks

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The question, in short

Circle with centre O, tangent DE at A, angle BAC = 80° and angle BAD = 55°. Find x with a geometrical reason, then find y.

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

Part (a) · 2 marks

Find x, the angle BOC at the centre, and give a geometrical reason for the value.

  1. 1x = 2 × angle BAC
  2. 2x = 2 × 80 = 160
  3. 3The angle at the centre is twice the angle at the circumference

Answer160, angle at the centre is twice the angle at the circumference

Part (b) · 2 marks

Find y, the angle ABO in triangle AOB.

  1. 1Angle OAD = 90° (tangent ⟂ radius)
  2. 2Angle BAO = 90 − 55 = 35°
  3. 3OA = OB, so triangle AOB is isosceles
  4. 4y = angle BAO = 35

Answer35

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