KöMaL 2014 B4607

The sides of a triangle are $a$, $b$, $c$. A line passes through the centre of the inscribed circle, and intersects side $c$ at $P$, and side $b$ at $Q$. Let $AP$=$p$and $AQ$=$q$. Prove that $\frac{1}{p} + \frac{1}{q} = \frac{a+b+c}{bc}$ .