# IMO 1983 – Problem 3

Let $N$ and $k$ be positive integers and  let $S$ be a set of  $n$ points in the plane such that

$(i)$ no three points of $S$ are collinear, and
$(ii)$  for any point $P$ of  $S$, there are at least $k$ points of $S$ equidistant from $P$

Prove that  $k$  $<$  $\frac{1}{2}$  $+$  $\sqrt{2n}$

Try the question …
Solution will be updated soon

I am a young student who loves math . I like number theory and inequalities part the most , and preparing for Math Olympiads :)

Posted on Thursday,July 19, 2012, in Combinatorics, Problems and tagged , , , , , , , , , . Bookmark the permalink. 2 Comments.