KöMaL 2018 B4967

Let $P$ be an interior point of $\triangle ABC$, and the midpoint of sides $AB$, $BC$ and $CA$ are $C_1$, $A_1$ and $B_1$, respectively. Through the points $A_1$, $B_1$ and $C_1$, draw parallels to the lines $AP$, $BP$ and $CP$, respectively. Show that these three lines are concurrent.