In a given set of points, Prove that the two farthest points are the vertices of the convex hull,
How can i get the accurate proof, so that the question can be explained in the class
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I'm assuming you asked about points on two-dimensional plane.
Let $P_1$ and $P_2$ are these two points, such that the (Euclidean) distance $D$ between them is maximal over all the pairs of points in the given point set. All the other points must be inside an intersection of two disks with radius $D$ - one disk with center in the $P_1$ and another disk with center in the $P_2$.
So, we have a curvilinear rhombus with diagonal $(P_1, P_2)$ and circular sides with radius $D$, which must contain both all points of the given set and also their convex hull.