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0580/23 May/Jun 2026, Question 13: Chord Properties

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 3 marks

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The question, in short

Circle centre O with AOC a diameter, M midpoint of chord AB, AB = 6 cm and OM = 4 cm. Find OA, then justify why angle ABC is 90°.

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

Part (a) · 2 marks

Using AB = 6 cm, M as midpoint, and OM = 4 cm, calculate the radius OA.

  1. 1AM = 6 ÷ 2 = 3 cm and angle AMO = 90° (perpendicular from centre to chord)
  2. 2OA² = 3² + 4² = 25
  3. 3OA = 5 cm

Answer5

Part (b) · 1 mark

State a geometrical reason why angle ABC equals 90° given AOC is a diameter.

  1. 1AC is a diameter, so the angle in a semicircle is 90°

AnswerAngle in a semicircle

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Also searched as: 0580/23/M/J/26 · 0580_s26_qp_23 · 0580 s26 23 · question 13.
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