Question 79
The points $P$ and $Q$ lie in the interior of $\triangle ABC$, $\angle ACP = \angle BCQ$ and $\angle CAP = \angle BAQ$. The feet of the perpendiculars from $P$ to the lines $BC$, $CA$ and $AB$ are denoted by $D$, $E$ and $F$, respectively. Prove that if $\angle DEF = 90^{\circ}$, then $Q$ is the orthocenter of $\triangle BDF$.