Ab And Ac Are Two Equal Chords Of Circle

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]