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0580/43 Oct/Nov 2021, Question 2: Combining Circle Theorems

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 6 marks

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The question, in short

Use circle geometry with centre O and angle OBA = 38° to find angle APB; then use a cyclic quadrilateral CDEF with FC = FE and tangent TCF = 50° to find two angles.

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

Part (a) · 3 marks

Find angle APB using the circle with centre O and angle OBA = 38°.

  1. 1OA = OB, so angle OAB = 38°
  2. 2Angle AOB = 180 − 2 × 38 = 104°
  3. 3Angle APB = 104 ÷ 2 = 52° (angle at centre is twice angle at circumference)

Answer52°

Part (bi) · 2 marks

Find angle EFC in cyclic quadrilateral CDEF, given FC = FE and tangent angle TCF = 50°.

  1. 1Angle FEC = angle TCF = 50° (alternate segment theorem)
  2. 2FC = FE, so angle FCE = 50°
  3. 3Angle EFC = 180 − 50 − 50 = 80°

Answer80°

Part (bii) · 1 mark

Find angle CDE in the cyclic quadrilateral CDEF.

  1. 1Angle CDE = 180 − 80 = 100° (opposite angles of a cyclic quadrilateral add to 180°)

Answer100°

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Also searched as: 0580/43/O/N/21 · 0580_w21_qp_43 · 0580 w21 43 · question 2.
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