OMM 1997 Problem 2

In a triangle $ABC, P$ and $P'$ are points on side $BC, Q$ on side $CA$ , and $R$ on side $AB$ , such that $\frac{AR}{RB}=\frac{BP}{PC}=\frac{CQ}{QA}=\frac{CP'}{P'B}$ . Let $G$ be the centroid of triangle $ABC$ and $K$ be the intersection point of $AP'$ and $RQ$ . Prove that points $P,G,K$ are collinear.