Problem

Source: Serbia TST 2021, P2

Tags: geometry



Let $D$ be an arbitrary point on the side $BC$ of triangle $ABC$. Points $E$ and $F$ are on $CA$ and $BA$ are such that $CD=CE$ and $BD=BF$. Lines $BE$ and $CF$ intersect at point $P$. Prove that when point $D$ varies along the line $BC$, $PD$ passes through a fixed point.