Question 18
Let $ABC$ be an acute triangle, and let $D, E, F$ be the feet of the altitudes from $A, B, C$, respectively. The lines $BC$ and $EF$ cross at $P$, and the line through $D$ and parallel to $EF$ crosses the lines $AC$ and $AB$ at $Q$ and $R$, respectively. Prove that the circle $PQR$ passes through the midpoint of the side $BC$.