# The Number of Halving Circles

```@article{Ardila2004TheNO,
title={The Number of Halving Circles},
author={Federico Ardila},
journal={The American Mathematical Monthly},
year={2004},
volume={111},
pages={586-591}
}```
1. INTRODUCTION. We say that a set S of 2n + 1 points in the plane is in general position if no three of the points are collinear and no four are concyclic. We call a circle 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. The goal of this paper is to prove the following surprising fact: any set of 2n + 1 points in general position in the plane has exactly n 2 halving circles. Our starting point is the following… CONTINUE READING

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