TUYMAADA 2006 Problem 3

A line $d$ is given in the plane. Let $B\in d$ and $A$ another point, not on $d$ , and such that $AB$ is not perpendicular on $d$ . Let $\omega$ be a variable circle touching $d$ at $B$ and letting $A$ outside, and $X$ and $Y$ the points on $\omega$ such that $AX$ and $AY$ are tangent to the circle. Prove that the line $XY$ passes through a fixed point.

Proposed by F. Bakharev