OBM 2017 Problem 3

A quadrilateral $ABCD$ has the incircle $\omega$ and is such that the semi-lines $AB$ and $DC$ intersect at point $P$ and the semi-lines $AD$ and $BC$ intersect at point $Q$ . The lines $AC$ and $PQ$ intersect at point $R$ . Let $T$ be the point of $\omega$ closest from line $PQ$ . Prove that the line $RT$ passes through the incenter of triangle $PQC$ .