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WAEC Mathematics 2017 Question 22

Question 22

Circle Theorems

In the diagram, PQ and PS are tangents to the circle centre O. If ∠PSQ = m, ∠SPQ = n and ∠SQR = 33°, find the value of (m + n)

Diagram for this question
  1. A.103°
  2. B.123°
  3. C.133°
  4. D.143°
Show the answer and explanation

Answer: B (123°)

Explanation

QR is a diameter, so the tangent PQ ⟂ QR and ∠PQS = 90° − 33° = 57°. Tangents from P are equal, so m = ∠PSQ = 57° and n = 180° − 114° = 66°. m + n = 123°.