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A sphere, a plane and tangent circles with a cone

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

October 1, 2005
geometry3D geometryspheregeometric transformationrotationgeometry unsolved

Problem Statement

Consider a sphere and a plane π\pi. For a variable point M∈πM \in \pi, exterior to the sphere, one considers the circular cone with vertex in MM 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
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