Conjecture for the locus of X1 (incenter) over Poncelet triangles: a conic iff the pair is confocal
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- Опубликовано: 25 авг 2024
- While researchers (Olga Romaskevich, Ronaldo Garcia) have proven that for Poncelet triangles interscribed between two confocal caustics (elliptic billiard) the locus of the incenter X1 is a conic (see [1] for bibliography), we conjecture that this can only be the case if the pair is confocal. Proofs?
[1] D. Reznik, R. Garcia, J. Koiller, "Can the Elliptic Billiard Still Surprise Us?",
Mathematical Gems and Curiosities ,Math. Intellig. v. 42, Sergei Tabachnikov (ed.), 2020, p. 6--17.