IMO 1989/3

Discussion on International Mathematical Olympiad (IMO)
tanmoy
Posts: 305
Joined: Fri Oct 18, 2013 11:56 pm
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 $k<\frac{1}{2}+\sqrt{2n}$