Question 38
Let $ABCD$ be a convex quadrilateral with $\angle ABC\gt90^\circ$, $\angle CDA\gt90^\circ$, and $\angle DAB=\angle BCD$. Let $E$ and $F$ be the reflections of $A$ in lines $BC$ and $CD$, respectively. Suppose that the segments $AE$ and $AF$ meet line $BD$ at $K$ and $L$, respectively. Prove that the circumcircles of triangles $BEK$ and $DFL$ are tangent to each other.