Problem

Source: XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade

Tags: geometry, geometric place



Let $k$ be a fixed circle in a given plane and a point $C$ out of the plane. Let $A$ be a random point from $k$ and $B$ be its diametrically opposite one in $k$. Find the geometric place of the center of the circumscribed circle of $ABC$.