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WAEC Mathematics 1997 Question 33

Question 33

Circle Theorems

TR is the tangent to the circle PQR with centre O. Find the size of ∠PRT

Diagram for this question
  1. A.44°
  2. B.46°
  3. C.60°
  4. D.74°
  5. E.118°.
Show the answer and explanation

Answer: C (60°)

Explanation

∠QOR = 2 × 74° = 148°, so in isosceles triangle OQR ∠OQR = 16°. ∠PQR = 44 + 16 = 60°, and the tangent–chord angle ∠PRT equals ∠PQR in the alternate segment: 60°.