Problem

Source: Romanian IMO Team Selection Test TST 1988, problem 1

Tags: geometry, 3D geometry, sphere, geometric transformation, rotation, geometry unsolved



Consider a sphere and a plane $\pi$. For a variable point $M \in \pi$, exterior to the sphere, one considers the circular cone with vertex in $M$ and tangent to the sphere. Find the locus of the centers of all circles which appear as tangent points between the sphere and the cone. Octavian Stanasila