MathNet 2022-part-04 — 197 problems (EN–VI) Question 107

Let $O$ be the circumcenter of triangle $ABC$. Points $X$ and $Y$ on side $BC$ are such that $AX = BX$ and $AY = CY$. Prove that the circumcircle of triangle $AXY$ passes through the circumcenters of triangles $AOB$ and $AOC$.