Question 46
Given triangle $ABC$ and line $\ell$ passing through point $A$, point $X$ on $\ell$ is considered to be variable. Circles $\omega_b$ and $\omega_c$ pass through both of the points $A$ and $X$ and are tangent to sides $AB$ and $AC$, respectively. Tangents $BY$ and $CZ$ are drawn from vertices $B$ and $C$ to circles $\omega_b$ and $\omega_c$ respectively. Prove that as $X$ varies, the circumcircle of triangle $ZXY$ passes through two fixed points.