On the product of distances to a point set on a sphere

Let S be the surface of the unit sphere in three-dimensional euclidean space, and let W N =( x 1 x 2 , x N )be an N -tuple of points on S . We consider the product of mutual distances and, for the variable point x on S , the product of distance from x to the points of ω N . We obtain essentially best possible bounds for max ωN p(Ω N ) and for min ω N max x∈s p ( x , ω N ).