Question 73
Consider a triangle $\triangle ABC$ with incenter $I$. Let $D$ be the intersection point of $BI$ and $AC$, and let $CI$ intersect the circumcircle of $\triangle ABC$ at $M$. Point $K$ lies on the line $MD$ such that $\angle KIA = 90^\circ$. Let $F$ be the reflection of $B$ with respect to $C$. Prove that $BIKF$ is cyclic.