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WAEC Mathematics 1993 Question 19

Question 19

Circle Theorems

In the diagram, PQR is a tangent to the circle QST at Q. If |QT| = |ST| and ∠SQR = 68°, find ∠PQT

Diagram for this question
  1. A.34°
  2. B.48°
  3. C.56°
  4. D.68°
  5. E.73°
Show the answer and explanation

Answer: C (56°)

Explanation

By the alternate segment theorem ∠QTS = ∠SQR = 68°. Triangle QTS is isosceles (QT = ST), so ∠TQS = (180° − 68°)/2 = 56°. On the straight line PQR: ∠PQT = 180° − 56° − 68° = 56°.