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Show that we can always find a circle such that all points lie inside the circle

Source: MTRP 2016 Class 11-Short Answer Type Question: Problem 4 :-

May 31, 2020
geometry

Problem Statement

For any given kk points in a plane, we define the diameter of the points as the maximum distance between any two points among the given points. Suppose nn points are there in a plane with diameter dd. Show that we can always find a circle with radius 32d\frac{\sqrt{3}}{2}d such that all points lie inside the circle.
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