Let $\Gamma$ be a circle of center $S$ and radius $r$ and $A$ a point outside the circle. Let $BC$ be a diameter of $\Gamma$ such that $B$ does not belong to the line $AS$, and we consider the point $O$ where the perpendicular bisectors of triangle $ABC$ intersect, that is, the circumcenter of $ABC$. Determine all possible locations of point $O$ when $B$ varies in circle $\Gamma$.