KöMaL 2006 B3877

The centroid of the triangle ABC is $S$, and the midpoint of $AB$ is $F$. For an interior point $P$ of the line segment $AF$, consider that point $Q$ of the line $PS$ for which $QC$and $AB$ are parallel. Let $R$ be the intersection of the lines $QA$ and $BC$. Prove that the line segment $PR$ halves the area of the triangle ABC .