37th Iranian Mathematical Olympiad

Consider a triangle $△ABC$ with circumcenter $O$ and incenter $I$. The incircle touches sides $BC$, $CA$ and $AB$ at $D$, $E$ and $F$, respectively. Let $K$ be a point such that $KF$ is tangent to circumcircle of $△BFD$ and $KE$ is tangent to circumcircle of $△CED$. Prove that $BC$, $OI$ and $AK$ are concurrent.