1997 OIM Problems/Problem 6
Problem
Let 
be a set of 1997 points inside a circle of radius 1, with 
being the center of the circle. For each 
let 
be the distance from 
to the point of 
closest to and different from . Show that
![\[(x_1)^2 + (x_2)^2 + \cdots + (x_{1997})^2 \le 9\]](http://latex.artofproblemsolving.com/d/0/7/d073e37edb14bff92b025b159a8d973da115e443.png)
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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