`DeltaABC` is a right triangle right angled at A such that `AB = AC` and bisector of `/_C` intersects the side `AB` at `D`. Prove that `AC + AD = BC`.

Explanation

To solve the problem, we need to prove that in triangle \( \Delta ABC \), where \( A \) is the right angle, \( AB = AC \), and the angle bisector of \( \angle C \) intersects \( AB \) at \( D \), the relation \( AC + AD = BC \) holds true.

### Step-by-Step Solution:

1. **Draw the Triangle**:
- Draw triangle \( ABC \) such that \( \angle A = 90^\circ \), \( AB = AC \), and \( D \) is the point where the bisector of \( \angle C \) intersects \( AB \).

2. **Assign Lengths**:
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