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arXiv · 2503.05435

The excenters of bicentric polygons are concyclic

Norbert Hungerbühler·Clemens Pohle·Yun Zhang
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Abstract

We show that the centers of the excircles of a bicentric polygon $B$ are concyclic on a circle $E$. The center of the circumscribed circle $K$ of $B$ is the midpoint of the center of $E$ and the center of the inscribed circle $C$ of $B$. The radius of $E$ is given by a simple formula in terms of the radii of $C$ and $K$ and the distance between their centers.

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Norbert Hungerbühler, Clemens Pohle, Yun Zhang. 2025-03-07. The excenters of bicentric polygons are concyclic. https://arxiv.org/abs/2503.05435

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