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JAMB Mathematics 1987 Question 31

Question 31

Circle Theorems

In the diagram above, POQ is a diameter, O is the centre of the circle and TP is a tangent. Find the value of x.

Diagram for this question
  1. A.30°
  2. B.40°
  3. C.45°
  4. D.50°
Show the answer and explanation

Answer: A (30°)

Explanation

OP is perpendicular to the tangent TP, so in triangle OPT angle POT = 180° − 90° − 30° = 60°. The angle x at Q stands on the same arc PR, so it is half of 60°, i.e. 30°.