Question 79
Points $X$ and $Y$ are located on sides $AB$ and $AC$ of triangle $ABC$ ($X, Y \neq A$) such that the reflection of line $BC$ with respect to $XY$ is tangent to the circumcircle of triangle $AXY$. If $O$ denotes the circumcenter of triangle $ABC$, prove that the circumcircle of triangle $AXY$ is tangent to the circumcircle of triangle $BOC$.