I read that in a 2D space, the two points farthest away must be in the convex hull (CH).
Intuitively, I can see why. If the two farthest points are not in the convex hull, then there must be a point that is outside the convex hull (contradiction). I know that a vertex of CH has two adjacent edges that converge at that point, which is of further distance from any other vertex or point within CH, than the non-vertices beside it. What I mean is shown in the image below: a vertex (p) with two adjacent edges,
Problem is, I don't see how I can prove this more formally. I am looking for a more concrete proof.
Thank you in advance.