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another 3d locus, cone and sphere

Source: Polish MO Finals 1956 p6

August 29, 2024
3D geometrygeometrysphere

Problem Statement

Given a sphere of radius R R and a plane α \alpha having no common points with this sphere. A point S S moves in the plane α \alpha , which is the vertex of a cone tangent to the sphere along a circle with center C C . Find the locus of point C C .
[hide=another is Polish MO 1967 p6] [url=https://artofproblemsolving.com/community/c6h3388032p31769739]here
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