Let s denotes the semi-perimeter of a `DeltaABC` in which BC=a, CA=b and AB=c. If a circle touches the sides BC, CA, AB, at D, E, F, respectively. Prove that BD=s-b.

Explanation

To prove that \( BD = s - b \) in triangle \( ABC \) where a circle touches the sides \( BC \), \( CA \), and \( AB \) at points \( D \), \( E \), and \( F \) respectively, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Semi-Perimeter**:
The semi-perimeter \( s \) of triangle \( ABC \) is given by:
\[
s = \frac{a + b + c}{2}
...