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concyclic points on a sphere

Source: Polish MO second round 1967 p6

August 28, 2024
geometryConcyclicsphere3D geometry

Problem Statement

Prove that the points A1,A2,…,An A_1, A_2, \ldots, A_n (n≥7 n \geq 7 ) located on the surface of the sphere lie on a circle if and only if the planes tangent to the surface of the sphere at these points have a common point or are parallel to one straight line.
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