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GCE Mathematics 1989 Question 38

Question 38

Circle Theorems

In the diagram above, O is the centre of the circle QRT and PT is a tangent to the circle at T. Calculate the angle x.

Diagram for this question
  1. A.55°
  2. B.40°
  3. C.35°
  4. D.25°
  5. E.20°
Show the answer and explanation

Answer: E (20°)

Explanation

QR is a diameter, so ∠QTR = 90°. By the tangent–chord angle, ∠PTQ = ∠QRT = 35°. In △PTR: x = 180° − (35° + 90°) − 35° = 20°.