BALTIC-WAY 2002 Problem 13

Let $A B C$ be an acute triangle with $\angle B A C>\angle B C A$, and let $D$ be a point on side $A C$ such that $|A B|=|B D|$. Furthermore, let $F$ be a point on the circumcircle of triangle $A B C$ such that line $F D$ is perpendicular to side $B C$ and points $F, B$ lie on different sides of line $A C$. Prove that line $F B$ is perpendicular to side $A C$.