%0 Journal Article
%T The number of point-splitting circles
%A Federico Ardila M
%J Mathematics
%D 2001
%I arXiv
%X Let S be a set of 2n+1 points in the plane such that no three are collinear and no four are concyclic. A circle will be called point-splitting if it has 3 points of S on its circumference, n-1 points in its interior and n-1 in its exterior. We show the surprising property that S always has exactly n^2 point- splitting circles, and prove a more general result.
%U http://arxiv.org/abs/math/0110209v1