TUYMAADA 2022 S2

Two circles $w_{1}$ and $w_{2}$ of different radii touch externally at $L$ . A line touches $w_{1}$ at $A$ and $w_{2}$ at $B$ (the points $A$ and $B$ are different from $L$ ). A point $X$ is chosen in the plane. $Y$ and $Z$ are the second points of intersection of the lines $XA$ and $XB$ with $w_{1}$ and $w_{2}$ respectively. Prove that all $X$ such that $AB||Y Z$ belong to one circle.