CAPS 1999 Problem 2

The altitudes through the vertices $A,B,C$ of an acute-angled triangle $ABC$ meet the opposite sides at $D,E,F,$ respectively. The line through $D$ parallel to $EF$ meets the lines $AC$ and $AB$ at $Q$ and $R$ , respectively. The line $EF$ meets $BC$ at $P$ . Prove that the circumcircle of the triangle $PQR$ passes through the midpoint of $BC$ .