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WAEC Mathematics 2015 Question 17

Question 17

Circle Theorems

In the diagram, PTR is a tangent to the circle centre O. If angle TON = 108°, calculate the size of angle PTN.

Diagram for this question
  1. A.132°
  2. B.126°
  3. C.108°
  4. D.102°
Show the answer and explanation

Answer: B (126°)

Explanation

Triangle TON is isosceles, so ∠OTN = (180° − 108°)/2 = 36°. The radius OT meets the tangent at 90°, so ∠PTN = 90° + 36° = 126°.