Question 184
Let $l$ be the perimeter of an acute triangle $\triangle ABC$ which is not equilateral, $P$ a variable point inside $\triangle ABC$, and $D, E$ and $F$ be projections of $P$ on $BC, CA$ and $AB$ respectively.
Prove that
$$
2(AF + BD + CE) = l,
$$
if and only if $P$ is collinear with the incenter and circumcenter of $\triangle ABC$. (posed by Xiong Bin)
Prove that
$$
2(AF + BD + CE) = l,
$$
if and only if $P$ is collinear with the incenter and circumcenter of $\triangle ABC$. (posed by Xiong Bin)