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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.

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.

Grade:12

1 Answers

rahul
15 Points
5 years ago
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,

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