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0580/23 May/Jun 2025, Question 13: Cyclic Quadrilaterals

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 4 marks

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The question, in short

On a circle with tangent EF at A and AB parallel to DC, use angle EAD = 35° and angle DAB = 60° to work out two angles at B and C.

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

Part (a) · 2 marks

Work out the size of angle DCB and state a geometrical reason for your result.

  1. 1Angle DCB = 180 − 60 = 120°
  2. 2because opposite angles of a cyclic quadrilateral sum to 180°

Answer120 and opposite angles of a cyclic quadrilateral sum to 180°

Part (b) · 2 marks

Work out the size of angle DBC.

  1. 1Angle DCB = 180 − 60 = 120° (opposite angles of a cyclic quadrilateral)
  2. 2Angle ABC = 180 − 120 = 60° (co-interior angles, AB parallel to DC)
  3. 3Angle ABD = angle EAD = 35° (alternate segment theorem)
  4. 4Angle DBC = 60 − 35 = 25

Answer25

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Also searched as: 0580/23/M/J/25 · 0580_s25_qp_23 · 0580 s25 23 · question 13.
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