Question 30
Let $ABC$ be a triangle with circumcenter $O$ and incenter $I$. The points $D$, $E$ and $F$ on the sides $BC$, $CA$ and $AB$ respectively are such that $BD + BF = CA$ and $CD + CE = AB$. The circumcircles of the triangles $BFD$ and $CDE$ intersect at $P \neq D$. Prove that $OP = OI$.