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JAMB Mathematics 1983 Question 36

Question 36

Circle Theorems

PQRS is a cyclic quadrilateral in which PQ = PS. PT is a tangent to the circle and PQ makes an angle of 50° with the tangent as shown in the figure below. What is the size of QRS?

Diagram for this question
  1. A.50°
  2. B.40°
  3. C.110°
  4. D.80°
  5. E.100°.
Show the answer and explanation

Answer: E (100°.)

Explanation

By the alternate segment theorem <PSQ = 50°, and PQ = PS makes <PQS = 50° too, so <QPS = 80°. Opposite angles of a cyclic quadrilateral add to 180°, so <QRS = 100°.