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WAEC Mathematics 1994 Question 40

Question 40

Circle Theorems

In the diagram, |PS| is a diameter of circle PQRS. |PQ| = |QR| and ∠RSP = 74°. Find ∠QPS.

Diagram for this question
  1. A.32°
  2. B.37°
  3. C.48°
  4. D.53°
  5. E.74°
Show the answer and explanation

Answer: D (53°)

Explanation

∠PQR = 180° − 74° = 106° (cyclic quadrilateral), so ∠QPR = (180° − 106°)/2 = 37°. ∠PRS = 90° (angle in a semicircle), so ∠RPS = 90° − 74° = 16°. ∠QPS = 37° + 16° = 53°.