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4024/21 Oct/Nov 2021, Question 3: Combining Circle Theorems

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 7 marks

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The question, in short

Use circle geometry with centre O, tangent DE at C, angle ABO 34°, and two sectors sharing centre O with OP 7.4 cm, PQ 1.2 cm and angle QOR 96° to answer the parts.

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

Part (ai) · 1 mark

Explain why triangle AOB is isosceles using radii and the given angle.

  1. 1AO and BO are both radii, so the triangle has 2 equal sides: isosceles

AnswerAO and BO are radii, so 2 equal sides

Part (aii) · 3 marks

Find angle BEC using the tangent at C and straight lines AOC and OBE.

  1. 1Angle BAO = 34° (isosceles triangle), so angle AOB = 180 − 34 − 34 = 112°
  2. 2Angle BOC = 180 − 112 = 68° (AOC straight line)
  3. 3Angle OCE = 90° (tangent perpendicular to radius)
  4. 4Angle BEC = 180 − 90 − 68 = 22°

Answer22°

Part (b) · 3 marks

Calculate the shaded area between the arcs of sectors OPS and OQR.

  1. 1OQ = 7.4 + 1.2 = 8.6 cm
  2. 2Shaded area = 96/360 × π × (8.6² − 7.4²)
  3. 3= 96/360 × π × 19.2 = 16.08… ≈ 16.1 cm²

Answer16.1 or 16.08 to 16.09

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Also searched as: 4024/21/O/N/21 · 4024_w21_qp_21 · 4024 w21 21 · question 3.
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