Question 92
Let $P$ be a point inside the triangle $ABC$. Let $D$, $E$ and $F$ be the feet of the perpendiculars from point $P$ to $BC$, $CA$, and $AB$ respectively. If the quadrilaterals $AEPF$, $BFPD$, and $CDPE$ are circumscribed, prove that $P$ is the incentre of triangle $ABC$.