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WAEC Mathematics 2014 Question 44

Question 44

Circle Theorems

In the diagram, O is the centre of the circle, PR is a tangent to the circle at Q and ∠SOQ = 86°. Calculate the value of ∠SQR.

Diagram for this question
  1. A.43°
  2. B.47°
  3. C.54°
  4. D.86°
Show the answer and explanation

Answer: A (43°)

Explanation

OS = OQ, so ∠OQS = (180° − 86°)/2 = 47°. The radius OQ is perpendicular to the tangent, so ∠SQR = 90° − 47° = 43°.