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0580/12 Feb/Mar 2023, Question 15: Angle in a Semicircle

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Calculator · 4 marks

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The question, in short

Circle with centre O and diameter AC; points A, B, C, D, E on the circumference. Angle BCA = 65°, angle ODE = 46°. Find x = angle BAC and y = angle OED, giving reasons.

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

Part (a) · 2 marks

Find x, the size of angle BAC, and state a reason for your answer.

  1. 1Angle ABC = 90° (angle in a semicircle)
  2. 2x = 180 − 90 − 65
  3. 3x = 25, because angle in a semicircle = 90°

Answer25, because angle in a semicircle = 90°

Part (b) · 2 marks

Find y, the size of angle OED, and state a reason for your answer.

  1. 1OD = OE (radii), so triangle ODE is isosceles
  2. 2y = 46, because base angles of an isosceles triangle are equal

Answer46, because base angles of an isosceles triangle are equal

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