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3d locus with a sphere

Source: Polish MO Recond Round 1980 p3

September 9, 2024
geometryLocus3D geometrysphere

Problem Statement

There is a sphere K K in space and points A,B A, B outside the sphere such that the segment AB AB intersects the interior of the sphere. Prove that the set of points P P for which the segments AP AP and BP BP are tangent to the sphere K K is contained in a certain plane.
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