Question 92
In any triangle $ABC$, in which the median from $C$ is not perpendicular to any of the sides $CA$ nor $CB$, let us denote $X$ and $Y$ intersections of this median's axis with lines $CA$ and $CB$. Find all such triangles $ABC$ for which points $A, B, X, Y$ lie on the same circle. (Ján Mazák)