1993.10.3

Part of Kyiv City MO 1984-93 - geometry

Problems(1)

constant sum of squares of distances, 2n points 1993 Kyiv City MO 10.3

Source:

The diameter of a circle of radius

R

is divided into

2n

equal parts. The point

M

is taken on the circle. Prove that the sum of the squares of the distances from the point

M

to the points of division (together with the ends of the diameter) does not depend on the choice of the point

M

. Calculate this sum.