**AB and AC are two equal chords of a circle. Prove that the bisector of the angle BAC passes through the centre of the circle.**

###### Answers:

Given AS and AC are two equal chords whose centre is O.

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

Construction Join SC, draw bisector AD of ∠BAC.

Proof In ΔSAM and ΔCAM,

AS = AC [given]

∠BAM = ∠CAM [given]