Loci of Poncelet Triangles with Multiple Caustics

08/11/2021

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by   Ronaldo Garcia, et al.

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We analyze loci of triangles centers over variants of two-well known triangle porisms: the bicentric family and the confocal family. Specifically, we evoke a more general version of Poncelet's closure theorem whereby individual sides can be made tangent to separate caustics. We show that despite a more complicated dynamic geometry, the locus of certain triangle centers and associated points remain conics and/or circles.