Question 72
Excircle to the side $BC$ of $\triangle ABC$ is tangent to $BC$, $AB$ and $AC$ at points $D$, $E$ and $F$, respectively. Let $P$ be orthogonal projection of $D$ on $EF$. Prove that point $P$ lies on the circumcircle $k$ of $\triangle ABC$ if and only if $k$ passes through the midpoint of $EF$.