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WAEC Mathematics 2016 Question 22

Question 22

Circle Theorems

In the diagram, TS is a tangent to the circle at S, |PR| = |RS| and ∠PQR = 117°. Calculate ∠PST.

Diagram for this question
  1. A.54°
  2. B.44°
  3. C.34°
  4. D.27°
Show the answer and explanation

Answer: A (54°)

Explanation

∠PSR = 180° − 117° = 63° (cyclic quadrilateral). Triangle PRS is isosceles so ∠RPS = 63° and ∠PRS = 54°; ∠PST = ∠PRS = 54° (alternate segment).