Question 3
Let $ABCD$ be a convex quadrilateral whose angles at $B$ and $D$ are obtuse and whose angles at $A$ and $C$ are equal. Let $E$ and $F$ be the reflections of $A$ across the lines $BC$ and $CD$, respectively. Let $K$ and $L$ be the intersections of the line $BD$ with the lines $AE$ and $AF$, respectively. Prove that the circumcircles of triangles $BEK$ and $DFL$ are tangent to each other.