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WAEC Mathematics 2010 Question 35

Question 35

Circle Theorems

In the diagram, GI is a tangent to the circle at H. If EF//GI, calculate the size of ∠EHF.

Diagram for this question
  1. A.126°
  2. B.72°
  3. C.54°
  4. D.28°
Show the answer and explanation

Answer: B (72°)

Explanation

∠FHI = 54°. EF ∥ GI gives ∠EFH = 54° (alternate), and the alternate segment theorem gives ∠HEF = 54°. So ∠EHF = 180° − 108° = 72°.