Question 17
Let $A$, $B$ and $C$ be three points such that $B$ is the midpoint of segment $AC$, and let $P$ be a point such that $\angle PBC = 60^\circ$. The equilateral triangle $PCQ$ is constructed so that $B$ and $Q$ lie in different half-planes with respect to $PC$, and the equilateral triangle $APR$ so that $B$ and $R$ lie in the same half-plane with respect to $AP$. Let $X$ be the intersection point of the lines $BQ$ and $PC$; let $Y$ be the intersection point of the lines $BR$ and $AP$. Prove that $XY$ and $AC$ are parallel.