%0 Journal Article
%T The number of halving circles
%A Federico Ardila
%J Mathematics
%D 2004
%I arXiv
%X A set S of 2n+1 points in the plane is said to be in general position if no three points of S are collinear and no four are concyclic. A circle is called halving with respect to S if it has three points of S on its circumference, n-1 points in its interior, and n-1 in its exterior. We prove the following surprising result: any set of 2n+1 points in general position in the plane has exactly n^2 halving circles.
%U http://arxiv.org/abs/math/0408354v1