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0606/22 Feb/Mar 2025, Question 1: Radians, Arcs and Sectors

Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 8 marks

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The question, in short

Circle centre O radius 5 cm, A on circle, AB tangent at A, OB = 13 cm. Work out angle AOB in radians, then the perimeter and area of the shaded region between the tangent, OB and the arc.

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Part (a) · 2 marks

Calculate the size of angle AOB, in radians.

  1. 1AB is a tangent, so angle OAB = 90°
  2. 2cos AOB = 5/13
  3. 3AOB = arccos(5/13) = 1.18 radians

Answer1.18

Part (b) · 3 marks

Calculate the total length around the boundary of the shaded region.

  1. 1AB = √(13² − 5²) = 12
  2. 2Arc length = 5 × 1.176… = 5.88…
  3. 3Straight part of OB outside the circle = 13 − 5 = 8
  4. 4Perimeter = 12 + 8 + 5.88… = 25.9 cm

Answer25.9 cm

Part (c) · 3 marks

Calculate the area enclosed by the shaded region.

  1. 1Area of triangle OAB = (1/2)(5)(12) = 30
  2. 2Area of sector = (1/2)(5²)(1.176…) = 14.70…
  3. 3Shaded area = 30 − 14.70… = 15.3 cm²

Answer15.3 cm²

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Also searched as: 0606/22/F/M/25 · 0606_m25_qp_22 · 0606 m25 22 · question 1.
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