constant sum of distances, circle, diameter related 1993 Kyiv City MO 8.4
Source:
July 20, 2021
geometrySumdiameter
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.