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0606/23 Oct/Nov 2025, Question 8: Radians, Arcs and Sectors

Cambridge IGCSE Additional Mathematics 0606 · Paper 23 (Calculator) · Calculator · 8 marks

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The question, in short

Circle centre O radius 2, chord AB length 2√3, Q on circle with AQ = BQ; arc APB centred at Q. Find angle AQB in radians, then the shaded area in terms of π.

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Part (a) · 2 marks

Find the exact size of angle AQB, in radians.

  1. 1In triangle AOB: sin(½ angle AOB) = √3/2, so angle AOB = 2π/3
  2. 2Angle at the circumference is half the angle at the centre: angle AQB = π/3

Answerπ/3

Part (b) · 6 marks

Using your angle, calculate the shaded region's area, giving it in terms of π.

  1. 1Segment of circle O: sector AOB − triangle AOB = ½ × 2² × 2π/3 − ½ × 2² × sin(2π/3) = 4π/3 − √3
  2. 2AQ = 2√3 (equilateral triangle AQB since angle AQB = π/3 and AQ = BQ)
  3. 3Segment of circle Q: ½ × (2√3)² × π/3 − ½ × (2√3)² × sin(π/3) = 2π − 3√3
  4. 4Shaded area = (4π/3 − √3) − (2π − 3√3)
  5. 5= 2√3 − 2π/3

Answer2√3 − 2π/3 or (6√3 − 2π)/3

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Also searched as: 0606/23/O/N/25 · 0606_w25_qp_23 · 0606 w25 23 · question 8.
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