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The number of halving circles

Federico Ardila
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Abstract

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.

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Federico Ardila. 2004-08-25. The number of halving circles. https://arxiv.org/abs/math/0408354

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