Let $ABC$ be a triangle. Construct point $X$ such that $BX=BA$ and $X$ and $C$ lies on the same side of line $AB$. Construct point $Y$ such that $CY=CA$ and $Y$ and $B$ lies on different sides of line $AC$. Suppose that triangle $BAX$ and triangle $CAY$ are similar, prove that the circumcenter of triangle $AXY$ lies on the circumcircle of triangle $ABC$.