44. Exemplar exercise problems XVIII

Let \(s\) denote the semi-perimeter of a triangle \(ABC\) in which \(BC = a\), \(CA = b\), \(AB = c\). If a circle touches the sides \(BC\), \(CA\), \(AB\) at \(D\), \(E\), \(F\), respectively, prove that \(BD = s - b\).