0580/31 May/Jun 2026, Question 19: Angle in a Semicircle
Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 3 marks
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The question, in short
On a circle centred at O, points A, B, C, D lie on the circumference, BD is a diameter, AB equals AD, and angle BDC is 52°. Work out the size of angle ABC.
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Solution · 3 marks
- 1Angle BCD = 90° (angle in a semicircle)
- 2Angle DBC = 180 − 90 − 52 = 38°
- 3Angle BAD = 90° (angle in a semicircle) and AB = AD, so angle ABD = (180 − 90) ÷ 2 = 45°
- 4Angle ABC = 45 + 38 = 83°
Answer83
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