Question 33
Let $\omega_{1}$ and $\omega_{2}$ be two circles intersecting at distinct points $A$ and $B$. Point $X$ varies along $\omega_{1}$, and point $Y$ on $\omega_{2}$ is chosen such that $AB$ bisects the angle $\angle XAY$. Prove that as $X$ varies along $\omega_{1}$, the circumcenter of $\triangle AXY$ (if it exists) varies along a fixed line.