If Ar, r°1,2,3,.....,n be points on a circle of unit radius then prove that the sum of thair mutual distance is less than n².

Imagine it this way, the maximum distance between any two points in the circle is equal to its diameter.So if n=2 then the maximum distance between the points is 2, which is less than n² = (4).

Now imagine that there is an n-sided polygon inscribed in a circle of unit radius,then the maximum sum of all distances between them would be ⁿC₂ *2 =n(n-1)=n²-1², for all n,