IR-MO 2002 Problem 8

Circles $C_{1}$ and $C_{2}$ are tangent to each other at $K$ and are tangent to circle $C$ at $M$ and $N$ . External tangent of $C_{1}$ and $C_{2}$ intersect $C$ at $A$ and $B$ . $AK$ and $BK$ intersect with circle $C$ at $E$ and $F$ respectively. If AB is diameter of $C$ , prove that $EF$ and $MN$ and $OK$ are concurrent. ( $O$ is center of circle $C$ .)