Question 84
The four vertices of quadrilateral $ABCD$ lie on the circle with diameter $AB$. The diagonals of $ABCD$ intersect at $E$, and the lines $AD$ and $BC$ intersect at $F$. Line $FE$ meets $AB$ at $K$ and line $DK$ meets the circle again at $L$. Prove that $CL$ is perpendicular to $AB$.