KöMaL 2012 A568

Given a triangle ABC and a line $\ell$ through its incenter. Denote by $A$', $B$' and $C$' the mirror images of $A$, $B$ and $C$ about $\ell$, respectively. Let the lines through $A$', $B$' and $C$', parallel to $\ell$, meet the lines $BC$, $CA$ and $AB$ at $P$, $Q$ and $R$, respectively. Prove that the points $P$, $Q$ and $R$ lie on a line and this line is tangent to the incircle.