Question 98
Let $ABC$ be a triangle with $\angle BAC = 30^\circ$ and $\angle ABC = 45^\circ$. Consider all pairs of points $X$ and $Y$ such that $X$ and $Y$ lie on the rays $AC^{\rightarrow}$ and $BC^{\rightarrow}$, respectively, and $OX = BY$, where $O$ is the circumcenter of $\triangle ABC$. Prove that the perpendicular bisectors of the segments $XY$ pass through a fixed point.