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JAMB Mathematics 2003 Question 35

Question 35

Circle Theorems

In the diagram above, PQR is a straight line and PS is a tangent to the circle QRS with |PS| = |SR| and ∠SPR = 40°. Find ∠PSQ.

Diagram for this question
  1. A.40°
  2. B.30°
  3. C.20°
  4. D.10°
Show the answer and explanation

Answer: A (40°)

Explanation

Triangle PSR is isosceles, so ∠SRP = 40°. By the alternate segment theorem ∠PSQ = ∠SRQ = 40°.