Question

In the given figure, AB is the diameter of a circle with centre O. A circle is drawn with AO as diameter. A chord AD of the larger circle intersects the smaller circle at C. Show that:

AC = CD

Answer 1

Since AO is the diameter of the smaller circle,

∠ACO = 90°

Thus OC ⊥ AD.

In any circle, a radius perpendicular to a chord bisects the chord.

Here, OC is a radius of the smaller circle, and AD is a chord passing through it.

Therefore, OC bisects AD, giving

AC = CD