(a) Let P be a given convex polygon with n vertices. The diameter of P is defined as the distance between the two furthest away points. Show that given P, your could find diam(P) in O(n) time. (b) Next let S be a set of n points in the plane. Find in O(nlogn) the diameter of S . Suggest an O(nlogn) time algorithm for finding the two point of S which are furthest away from each other.

diam(P) = max ||91 92|| 91,92EP