Question 197
Let $ABC$ be a triangle with incenter $I$. The incircle of $ABC$ is tangent to sides $BC$, $CA$, $AB$ at $D$, $E$, $F$. Let $H$ denote the orthocenter of triangle $BIC$, and let $P$ denote the midpoint of the altitude from $D$ to $EF$. Prove that $HP$ bisects $EF$.