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0606/12 May/Jun 2026, Question 6: Radians, Arcs and Sectors

Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 8 marks

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The question, in short

Circle centre O radius r, points A, B, C on circumference, angle AOB = α radians, shaded minor sector AOB. Find α from a perimeter condition, then find r from a given sector area.

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

Part (a) · 4 marks

Shaded sector perimeter equals major arc ACB length. Find the exact value of α.

  1. 1Perimeter of shaded sector = 2r + rα
  2. 2Major arc ACB = r(2π − α)
  3. 32r + rα = 2πr − rα
  4. 42α = 2π − 2
  5. 5α = π − 1

Answerα = π − 1

Part (b) · 4 marks

Shaded sector area is 18(π² − 1). Find the exact value of r, simplified.

  1. 1(1/2)r²(π − 1) = 18(π² − 1)
  2. 2r² = 36(π² − 1)/(π − 1)
  3. 3π² − 1 = (π − 1)(π + 1), so r² = 36(π + 1)
  4. 4r = 6√(π + 1)

Answerr = 6√(π + 1)

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Also searched as: 0606/12/M/J/26 · 0606_s26_qp_12 · 0606 s26 12 · question 6.
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