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WAEC Mathematics 1996 Question 34

Question 34

Circle Theorems

In the diagram below, PQ is a tangent to the circle MTN at T. What is the size of <MTN?

Diagram for this question
  1. A.52°
  2. B.54°
  3. C.66°
  4. D.72°
  5. E.128°
Show the answer and explanation

Answer: C (66°)

Explanation

By the alternate segment theorem, <TMN equals the angle between the tangent and chord TN, 62°. In triangle MTN, <MTN = 180° − 52° − 62° = 66°.