MathDB

Let

ABCD

be a convex quadrilateral with

\angle ABC>90

CDA>90

and

\angle DAB=\angle BCD

. Denote by

E

and

F

the reflections of

A

in lines

BC

and

CD

, respectively. Suppose that the segments

AE

and

AF

meet the line

BD

K

and

L

, respectively. Prove that the circumcircles of triangles

BEK

and

DFL

are tangent to each other.
\emph{Slovakia}

Problem Statement