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WAEC Mathematics 1995 Question 33

Question 33

Circle Theorems

In the diagram below; O is the centre of the circle and |BD| = |DC|. If ∠DCB = 35°, find ∠BAO.

Diagram for this question
  1. A.20°
  2. B.25°
  3. C.30°
  4. D.35°
  5. E.40°
Show the answer and explanation

Answer: A (20°)

Explanation

∠DBC = 35° (isosceles triangle), so the exterior angle ∠BDA = 35° + 35° = 70°. AD is a diameter, so ∠ABD = 90°. Then ∠BAO = 180° − 90° − 70° = 20°.