Question 112
Let $E$ and $F$ be two points on the side $CD$ of a convex quadrilateral $ABCD$ satisfying $0 \lt DE = FC \lt CD$. Let $K$ be the second point of intersection of the circumcircles of the triangles $ADE$ and $ACF$, and let $L$ be the second point intersection of the circumcircles of the triangles $BDE$ and $BCF$. Show that the points $A$, $B$, $K$, $L$ lie on a circle.