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arXiv · 2604.26035

Conic locus of inversive Poncelet circumcenter and two points of invariant circle power

Ronaldo Garcia·Shmuel Mark Helman·Dan Reznik
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Abstract

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.

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Ronaldo Garcia, Shmuel Mark Helman, Dan Reznik. 2026-04-28. Conic locus of inversive Poncelet circumcenter and two points of invariant circle power. https://arxiv.org/abs/2604.26035

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