Question 10
Let $\Gamma$ be a circle with centre $S$ and radius $r$, and let $A$ be a point outside the circle. Let $BC$ be a diameter of $\Gamma$ such that $B$ does not lie on the line $AS$, and consider the point $O$ where the perpendicular bisectors of triangle $ABC$ meet, that is, the circumcentre of $ABC$.
Determine all possible positions of the point $O$ as $B$ varies on the circle $\Gamma$.
Determine all possible positions of the point $O$ as $B$ varies on the circle $\Gamma$.