constant sum of squares of distances, 2n points 1993 Kyiv City MO 10.3
Source:
July 20, 2021
geometry
Problem Statement
The diameter of a circle of radius is divided into equal parts. The point is taken on the circle. Prove that the sum of the squares of the distances from the point to the points of division (together with the ends of the diameter) does not depend on the choice of the point . Calculate this sum.