The diameter of a point set is the maximum distance between any pair of points.
A point like $p_i$ in a polygon is called an extreme point if there exists a line containing $p_i$ such that the polygon is completely on one side of $p_i$.
Another definition of extreme point :
The extreme points of a set S of points in the plane are the vertices of the convex hull at which the interior angle is less than π.
Question :
a) Show that the diameter is realized by a pair of extreme points.
b) Give an $O(nlogn)$-time algorithm for computing the diameter of a set of $n$ points in the plane.
Note 1 : About part (a), I observed that the line connecting two random extreme points is not necessarily a diameter. So, For every extreme point like $E_1$, We should find some $E_i$ such that $E_1E_i$ is a diameter.
Note 2: I have no idea about part (b). I think it may be related to part (a) somehow.