KöMaL 2020 C1586

The points $D$ and $E$ divide side $AB$ of triangle $ABC$ into three equal parts. Let $P$ be an arbitrary interior point of line segment $DE$. Draw parallels to line $PC$ through the points $D$ and $E$. These lines intersect sides $AC$ and $BC$ at points $Q$ and $R$, respectively. Show that the area of quadrilateral $PRCQ$ equals the area of triangle $APQ$.