Four special Poncelet triangle families about the incircle

TL;DR

This paper explores four unique families of Poncelet triangles inscribed in ellipses that preserve specific triangle centers and exhibit notable conservation properties related to the incircle.

Contribution

It introduces four special Poncelet triangle families with properties of stationarity and conservation involving the incircle, expanding understanding of geometric invariants.

Findings

Four families of Poncelet triangles with stationary centers

Identification of conservation properties in these triangle families

Enhanced understanding of ellipse-inscribed Poncelet triangles

Abstract

We describe four special families of ellipse-inscribed Poncelet triangles about the incircle which maintain certain triangle centers stationary and which also display interesting conservations.