IR-TST 2023 Problem 4

line $l$ through the point $A$ from triangle $ABC$ . Point $X$ is on line $l$ . ${\omega}_b$ and ${\omega}_c$ are circles that through points $X,A$ and respectively tanget to $AB$ adn $AC$ . tangets from $B,C$ respectively to ${\omega}_b$ and ${\omega}_c$ meet them in $Y,Z$ . Prove that by changing $X$ , the circumcircle of the circle $XYZ$ passes through two fixed points.

Proposed by Ali Zamani