RO-NMO 2004 Problem 93

Let $H$ be the orthocenter of the acute triangle $ABC$ . Let $BB'$ and $CC'$ be altitudes of the triangle ( $B^{\prime} \in AC$ , $C^{\prime} \in AB$ ). A variable line $\ell$ passing through $H$ intersects the segments $[BC']$ and $[CB']$ in $M$ and $N$ . The perpendicular lines of $\ell$ from $M$ and $N$ intersect $BB'$ and $CC'$ in $P$ and $Q$ . Determine the locus of the midpoint of the segment $[ PQ]$ .

Gheorghe Szolosy