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WAEC Mathematics 1988 Question 28

Question 28

Circle Theorems

In the diagram below, O is the centre of the circle, BOC is a diameter and angle ADC is 37°. What is ACB?

Diagram for this question
  1. A.14.7°
  2. B.127°
  3. C.65°
  4. D.53°
  5. E.37°
Show the answer and explanation

Answer: D (53°)

Explanation

∠ABC = ∠ADC = 37° (angles on the same arc AC). ∠BAC = 90° (angle in a semicircle), so ∠ACB = 180° − 90° − 37° = 53°.