If two chords `A B` and `A C` of a circle with centre `O` are such that the centre `O` lies on the bisector of `/_B A C ,` prove that `A B=A C` , i.e. the chords are equal.

Explanation

In `triangle AOB ` and `triangleAOC`
`OA` is common
`angle OAC=angleOAB` [OA is angle bisector of `angleA`]
`OC=OB` [radius]
So,by SAS congruence rule,
`triangle AOBcongtriangleAOC`
By `CPCT, AB=AC`