The excenters of bicentric polygons are concyclic
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916646417858560 |
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| author | Hungerbühler, Norbert Pohle, Clemens Zhang, Yun |
| author_facet | Hungerbühler, Norbert Pohle, Clemens Zhang, Yun |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_05435 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The excenters of bicentric polygons are concyclic Hungerbühler, Norbert Pohle, Clemens Zhang, Yun Metric Geometry 51M04, 51M15 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. |
| title | The excenters of bicentric polygons are concyclic |
| topic | Metric Geometry 51M04, 51M15 |
| url | https://arxiv.org/abs/2503.05435 |