Two chords `A B` and `A C` of a circle are equal. Prove that the centre of the circle lies on the angle bisector of `/_B A Cdot`

Explanation

To prove that the center of the circle lies on the angle bisector of angle BAC when two chords AB and AC are equal, we can follow these steps:

### Step-by-Step Solution:

1. **Draw the Circle and Chords**:
- Let O be the center of the circle. Draw a circle with center O and two equal chords AB and AC such that AB = AC.

2. **Identify the Angle Bisector**:
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