Question

In the given figure, AC is a diameter of a circle, whose centre is 0. 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

Construction: Join OB

Then, in triangle AOB,
∠OBA=90°

[Angle in a semi-circle is a right angle]

That is, OB is perpendicular to AE.

Now, we know that the perpendicular drawn from the centre to a chord bisects the chord.

Therefore, AB=BE.
Hence, proved.