Question

Two chords AB and AC of a circle are equal. Prove that the centre of the circle lies on the bisector of angle BAC.

Answer 1

Given: AB and AC are two equal chords of C (O, r).

To prove: Centre, O lies on the bisector of ∠BAC.

Construction: Join BC. Let the bisector of ∠BAC intersects BC in P.

Proof:

In ΔAPB and ΔAPC,

AB = AC (Given)

∠ BAP = ∠CAP (Given)

AP = AP (Common)