Conic locus of inversive Poncelet circumcenter and two points of invariant circle power
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911634861064192 |
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| author | Garcia, Ronaldo Helman, Shmuel Mark Reznik, Dan |
| author_facet | Garcia, Ronaldo Helman, Shmuel Mark Reznik, Dan |
| contents | We prove that over a generic Poncelet triangle family, the locus of the circumcenter of an inversive triangle is a conic. Additionally, we prove an earlier conjecture: over generic Poncelet triangles, two unique points exist which maintain constant power with respect to the circumcircle and Euler's circle of the family, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26035 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Conic locus of inversive Poncelet circumcenter and two points of invariant circle power Garcia, Ronaldo Helman, Shmuel Mark Reznik, Dan Metric Geometry Computational Geometry 51M04, 51N20, 51N35 We prove that over a generic Poncelet triangle family, the locus of the circumcenter of an inversive triangle is a conic. Additionally, we prove an earlier conjecture: over generic Poncelet triangles, two unique points exist which maintain constant power with respect to the circumcircle and Euler's circle of the family, respectively. |
| title | Conic locus of inversive Poncelet circumcenter and two points of invariant circle power |
| topic | Metric Geometry Computational Geometry 51M04, 51N20, 51N35 |
| url | https://arxiv.org/abs/2604.26035 |