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JAMB Mathematics 1978 Question 20

Question 20

Circle Theorems

In the figure above, O is the centre of the circle ABC <CED = 30°, <EDA = 40°. What is the size of <ABC?

Diagram for this question
  1. A.70°
  2. B.110°
  3. C.130°
  4. D.125°
  5. E.145°
Show the answer and explanation

Answer: D (125°)

Explanation

The lines EC and DA cross at O, so in triangle EOD the angle at O is 180° − 30° − 40° = 110°, and the vertically opposite angle AOC is 110°. The angle at the circumference on the minor arc is 180° − ½(110°) = 125°.