The stationary focus of the Kiepert parabola over a special Poncelet triangle family

TL;DR

This paper proves that the focus of the Kiepert in-parabola remains fixed when considering a special family of Poncelet triangles inscribed in a circle, including an equilateral triangle.

Contribution

It establishes the stationary property of the Kiepert parabola's focus over a specific Poncelet triangle family, extending geometric understanding.

Findings

Focus of Kiepert parabola is stationary in the family

Family includes circle-inscribed Poncelet triangles with an equilateral triangle

Provides geometric insight into Poncelet configurations

Abstract

We show that the focus of the Kiepert in-parabola remains stationary over a family of circle-inscribed Poncelet triangles which contain an equilateral triangle.