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4024/12 May/Jun 2024, Question 17: Combining Circle Theorems

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Circle with centre O and points A, B, C, D on the circumference; angle BAD = 120° and angle OBC = 20°. Find x and y.

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

Part (a) · 2 marks

Find the value of x, the angle OCD.

  1. 1Angle BCD = 180 − 120 = 60° (opposite angles of a cyclic quadrilateral)
  2. 2OB = OC (radii), so angle OCB = angle OBC = 20°
  3. 3x = angle OCD = 60 − 20 = 40

Answer40

Part (b) · 2 marks

Find the value of y, the angle BDC.

  1. 1OB = OC (radii), so angle OCB = 20°
  2. 2Angle BOC = 180 − 20 − 20 = 140°
  3. 3Angle at circumference is half the angle at centre: y = 140 ÷ 2 = 70

Answer70

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