1997 OIM Problems/Problem 6

Revision as of 06:54, 26 December 2023 by Tomasdiaz (talk | contribs) (Problem)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $\textbf{P}  = {P_1, P_2, \cdots , P_{1997}}$ be a set of 1997 points inside a circle of radius 1, with $P_1$ being the center of the circle. For each $k = 1, \cdots , 1997$ let $x_k$ be the distance from $P_k$ to the point of $\textbf{P}$ closest to $P_k$ and different from $P_k$. Show that

\[(x_1)^2 + (x_2)^2 + \cdots + (x_{1997})^2 \le 9\]

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also

https://www.oma.org.ar/enunciados/ibe12.htm