Question 69
Consider an acute triangle $ABC$ with area $S$. Let $CD \perp AB$ ($D \in AB$), $DM \perp AC$ ($M \in AC$) and $EN \perp BC$ ($N \in BC$). Denote by $H_1$ and $H_2$ the orthocentres of the triangles $MNC$ and $MND$ respectively. Find the area of the quadrilateral $AH_1BH_2$ in terms of $S$.
