Question 17
G5 (CYP) A line $l$ does not meet a circle $\omega$ with center $O$. $E$ is the point on $l$ such that $OE$ is perpendicular to $l$. $M$ is any point on $l$ other than $E$. The tangents from $M$ to $\omega$ touch it at $A$ and $B$. $C$ is the point on $MA$ such that $EC$ is perpendicular to $MA$. $D$ is the point on $MB$ such that $ED$ is perpendicular to $MB$. The line $CD$ cuts $OE$ at $F$. Prove that the location of $F$ is independent of that of $M$.