`A B C` is an isosceles triangle with `A B=A C` and `D` is a point on `A C` such that `B C^2=A CxC Ddot` Prove that `B D=B C`

Explanation

To prove that \( BD = BC \) in the isosceles triangle \( ABC \) where \( AB = AC \) and \( D \) is a point on \( AC \) such that \( BC^2 = AC \cdot CD \), we can follow these steps:

### Step-by-Step Solution

1. **Given Information**:
- Triangle \( ABC \) is isosceles with \( AB = AC \).
- Point \( D \) is on line segment \( AC \).
- The relation \( BC^2 = AC \cdot CD \) holds.
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