The incircle of a $\Delta ABC$, touches the side $BC$, $CA$ and $AB$ at $D, E$ and $F$ respectively. If $AF + BD + CE = AE + BF + CD +$ __________ perimeter of $\Delta ABC$

Question

$\begin{array}{1 1} (a)\;2 \\ (b)\;\large\frac{1}{2} \\ (c)\;1 \\(d)\;\text{none of the above} \end{array}$