Question 76
Points $M$, $N$ and $P$ lie on the sides $BC$, $CA$, $AB$ of triangle $ABC$. Triangles $CNM$, $APN$ and $BMP$ are acute and let $H_C$, $H_A$ and $H_B$ be their respective orthocenters. Prove that if the three lines $AH_A$, $BH_B$ and $CH_C$ are concurrent then $MH_A$, $NH_B$ and $PH_C$ are also concurrent.
