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GCE Mathematics 1989 Question 43

Question 43

Circle Theorems

In the diagram below, O is the centre of the circle. If ∠POR = 114°, calculate ∠PQR.

Diagram for this question
  1. A.123°
  2. B.118.5°
  3. C.117°
  4. D.114°
  5. E.54°
Show the answer and explanation

Answer: A (123°)

Explanation

∠PQR stands on the major arc PR, whose angle at the centre is the reflex angle 360° − 114° = 246°. So ∠PQR = 246° ÷ 2 = 123°.