DE-MO 2002 Problem 2

Minimal distance of a finite set of different points in space is length of the shortest segment, whose both ends belong to this set and segment has length greater than $0$ . a) Prove there exist set of $8$ points on sphere with radius $R$ , whose minimal distance is greater than $1,15R$ . b) Does there exist set of $8$ points on sphere with radius $R$ , whose minimal distance is greater than $1,2R$ ?