0580/22 May/Jun 2025, Question 12: Combining Circle Theorems
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 2 marks
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The question, in short
P, Q and R are points on a circle with QR as a diameter and angle PQR = 74°. Find angle PRQ, giving geometrical reasons.
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Solution · 2 marks
- 1Angle QPR = 90°, because the angle in a semicircle = 90°
- 2Angle PRQ = 180 − 90 − 74, because the angle sum of a triangle = 180°
- 3Angle PRQ = 16°
Answer16
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