BALTIC-WAY 2000 Problem 3

Given a triangle $A B C$ with $\angle A=90^{\circ}$ and $|A B| \neq|A C|$. The points $D, E, F$ lie on the sides $B C, C A, A B$, respectively, in such a way that $A F D E$ is a square. Prove that the line $B C$, the line $F E$ and the line tangent at the point $A$ to the circumcircle of the triangle $A B C$ intersect in one point.