Question

In the given figure, AC is a diameter of a circle, whose centre is O. A circle is described on AO as diameter. AE, a chord of the larger circle, intersects the smaller circle at B. Prove that : AB = BE.

Answer 1

Join OB,

Then ∠OBA = 90°

(Angle in a semicircle is a right angle)

i.e. OB ⊥ AE

We know the perpendicular drawn from the centre to a chord bisects the chord.

Therefore, AB = BE