6

Part of 1967 Poland - Second Round

Problems(1)

concyclic points on a sphere

Source: Polish MO second round 1967 p6

Prove that the points

A_1, A_2, \ldots, A_n

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.

geometryConcyclicsphere3D geometry