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WAEC Mathematics 2006 Question 17

Question 17

Circle Theorems

In the diagram, PR is a diameter of the circle centre O. RS is a tangent at R and QP̂R = 58°. Find ∠QRS.

Diagram for this question
  1. A.112°
  2. B.116°
  3. C.122°
  4. D.148°
Show the answer and explanation

Answer: C (122°)

Explanation

The angle in a semicircle is 90°, so ∠PQR = 90° and ∠QRP = 180° − 90° − 58° = 32°. The tangent is perpendicular to the diameter, so ∠PRS = 90°. ∠QRS = 32° + 90° = 122°.