MathDB

3

Part of 1980 Poland - Second Round

Problems(1)

3d locus with a sphere

Source: Polish MO Recond Round 1980 p3

9/9/2024
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.
geometryLocus3D geometrysphere