Conic locus of inversive Poncelet circumcenter and two points of invariant circle power
arXiv:2604.2603572.0
AI Analysis
For mathematicians studying Poncelet porism and triangle geometry, this resolves a conjecture and provides new geometric loci.
The paper proves that the circumcenter of an inversive triangle traces a conic over a generic Poncelet triangle family, and confirms a conjecture about two points with constant power relative to the circumcircle and Euler's circle.
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.