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<p>We tour several Euclidean properties of Poncelet triangles inscribed in an ellipse and circumscribing the incircle, including loci of triangle centers and envelopes of key objects. We also show that a number of degenerate behaviors are triggered by the presence of an equilateral triangle in the family.</p>

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Graceful loci of Poncelet triangles about the incircle and their degeneracies

  • 期刊论文

  • 发表日期：

    2026年3月6日

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  • Ronaldo A. Garcia,
  • Mark Helman,
  • Dan Reznik

摘要

We tour several Euclidean properties of Poncelet triangles inscribed in an ellipse and circumscribing the incircle, including loci of triangle centers and envelopes of key objects. We also show that a number of degenerate behaviors are triggered by the presence of an equilateral triangle in the family.