IMO 1989/3
Posted: Sat Jan 03, 2015 11:42 am
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 $k<\frac{1}{2}+\sqrt{2n}$
(I think this is easy for a IMO 3)
(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 $k<\frac{1}{2}+\sqrt{2n}$
(I think this is easy for a IMO 3)