4MA1/1H Jun 2021, Question 15: Combining Circle Theorems
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 4 marks
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The question, in short
On a circle with centre O, points P, Q, R lie on it and TRV touches at R. Given reflex angle POR 238° and angle QRV 60°, work out angle OPQ, justifying each step.
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Solution · 4 marks
- 1TRV is a tangent, so by the alternate segment theorem angle QPR = angle QRV = 60°
- 2Angles around a point total 360°, so angle POR = 360 − 238 = 122°
- 3OP and OR are radii, so triangle OPR is isosceles
- 4Angle OPR = (180 − 122) ÷ 2 = 29°
- 5Angle OPQ = angle QPR − angle OPR = 60 − 29 = 31°
Answer31
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