SHARYGIN 2006 Problem 17

In two circles intersecting at points $A$ and $B$ , parallel chords $A_1B_1$ and $A_2B_2$ are drawn. The lines $AA_1$ and $BB_2$ intersect at the point $X, AA_2$ and $BB_1$ intersect at the point $Y$ . Prove that $XY // A_1B_1$ .