MathDB

On a spherical surface there is a set

M{}

with

n{}

points with the property: for every point

A{}

from

M{}

there exist points

B

and

C

from

M{}

such that the triangle

ABC

is equilateral. For every equilateral triangle with vertexes in

M{}

the perpendicular on its plane that goes through the geometric center of the other points from

M{}

. Prove that all these perpendiculars are concurrent.

Problem Statement