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4024/12 May/Jun 2022, Question 20: Combining Circle Theorems

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks

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The question, in short

Circle with centre O and points A, B, C, D on the circumference; angle AOB = 70° and angle OAD = 25°. Find angles ADB and BCD.

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Part (a) · 1 mark

Find angle ADB using the marked angle AOB = 70° at the centre.

  1. 1Angle at the centre is twice the angle at the circumference
  2. 2Angle ADB = 70 ÷ 2 = 35°

Answer35

Part (b) · 2 marks

Find angle BCD, using the circle geometry and the 25° angle OAD.

  1. 1OA = OB (radii), so angle OAB = (180 − 70) ÷ 2 = 55°
  2. 2Angle DAB = 25 + 55 = 80°
  3. 3Opposite angles of a cyclic quadrilateral add to 180°
  4. 4Angle BCD = 180 − 80 = 100°

Answer100

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Also searched as: 4024/12/M/J/22 · 4024_s22_qp_12 · 4024 s22 12 · question 20.
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