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JAMB Mathematics 1998 Question 25

Question 25

Circle Theorems

In the diagram above, PR is a diameter of the circle PQRS. PST and QRT are straight lines. Find ∠QSR

Diagram for this question
  1. A.20°
  2. B.25°
  3. C.30°
  4. D.35°
Show the answer and explanation

Answer: B (25°)

Explanation

∠PSR = 90° (angle in a semicircle), so ∠RST = 90° and ∠SRT = 60°. Then ∠QRS = 120°, so ∠QPS = 60° (cyclic quadrilateral) and ∠QPR = 60° − 35° = 25°. ∠QSR = ∠QPR = 25° (same segment).