Question 5
Let $AD$, $BE$ and $CF$ be respectively the altitudes of $\triangle ABC$. Let $P$, $Q$ and $R$ be points on the lines $BC$, $CA$ and $AB$ respectively such that $AP$ is perpendicular to $EF$, $BQ$ is perpendicular to $FD$ and $CR$ is perpendicular to $DE$. Show that $AP$, $BQ$ and $CR$ are concurrent.