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WAEC Mathematics 1999 Question 29

Question 29

Circle Theorems

From the diagram below. ABC is a triangle inscribed in a circle centre O. ∠ACB = 40° and |AB| = x cm. Calculate the radius of the circle.

Diagram for this question
  1. A.x/sin 40°
  2. B.x/cos 40°
  3. C.x/(2 sin 40°)
  4. D.x/(2 cos 40°)
Show the answer and explanation

Answer: C (x/(2 sin 40°))

Explanation

By the sine rule, AB/sin C = 2R (the diameter). So 2R = x/sin 40° and R = x/(2 sin 40°).