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WAEC Mathematics 2018 Question 17

Question 17

Circle Theorems

In the diagram, PS and RS are targents to the circle centre O. ∠PSR = 70°, ∠POR = m and ∠PQR = n. Find (m + n).

Diagram for this question
  1. A.110°
  2. B.135°
  3. C.165°
  4. D.225°
Show the answer and explanation

Answer: C (165°)

Explanation

In quadrilateral OPSR the radii meet the tangents at 90°, so m = 360° − 180° − 70° = 110°. n is the angle at the circumference on the same arc, so n = 55°. m + n = 165°.