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WAEC Mathematics 1991 (August) Question 46

Question 46

Circle Theorems

In the diagram below, O is the centre of the circle, |SQ| = |QR| and ∠PQR = 68°. Calculate ∠PRS.

Diagram for this question
  1. A.34°
  2. B.45°
  3. C.56°
  4. D.62°
  5. E.68°
Show the answer and explanation

Answer: A (34°)

Explanation

PQ is a diameter, so ∠PRQ = 90°. Triangle SQR is isosceles with apex angle 68°, so ∠QRS = (180° − 68°)/2 = 56°. ∠PRS = 90° − 56° = 34°.