PL-OM 2014 Problem 6

In an acute triangle $ABC$ point $D$ is the point of intersection of altitude $h_a$ and side $BC$ , and points $M, N$ are orthogonal projections of point $D$ on sides $AB$ and $AC$ . Lines $MN$ and $AD$ cross the circumcircle of triangle $ABC$ at points $P, Q$ and $A, R$ . Prove that point $D$ is the center of the incircle of $PQR$ .