4MA1/1HR Jun 2022, Question 15: Combining Circle Theorems
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 3 marks
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The question, in short
A circle centred at O has points P, Q, R, S on it, with PS as a diameter and angle PQR = 136°. Calculate the size of angle RPS.
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Solution · 3 marks
- 1PS is a diameter, so angle PRS = 90° (angle in a semicircle).
- 2PQRS is a cyclic quadrilateral, so angle PQR + angle PSR = 180°.
- 3Angle PSR = 180° − 136° = 44°
- 4The angles of triangle PRS add up to 180°.
- 5Angle RPS = 180° − 90° − 44° = 46°
- 6Angle RPS = 46°
Answer46
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