Question 88
The medians $AA'$, $BB'$, $CC'$ of the triangle $ABC$ meet the nine points circle at $D$, $E$, $F$, respectively. The points $L$, $M$, $N$ are the feet of the altitudes of $ABC$ ($L$ belongs to $AA'$, etc). The tangents to the nine points circle at $D$, $E$, $F$ meet the lines $MN$, $LN$ and $LM$ at points $P$, $Q$, $R$. Show that points $P$, $Q$ and $R$ are collinear.