A regular tetrahedron with unit edge length is given. Prove that:(a) There exist four points on the surface S of the tetrahedron, such that the distance from any point of the surface to one of these four points does not exceed 1/2;(b) There do not exist three points with this property.The distance between two points on surface S is defined as the length of the shortest polygonal line going over S and connecting the two points.
geometry3D geometrycombinatoricscombinatorial geometrytetrahedron