A One-Line Proof of Leversha's "Quartet of Isogonal Conjugates" Theorem

TL;DR

This paper presents a concise and insightful proof of Leversha's theorem on isogonal conjugates in non-cyclic quadrilaterals, utilizing computational tools to simplify the geometric argument.

Contribution

It provides the first short proof of Leversha's theorem, enhancing understanding and accessibility of this geometric result.

Findings

Proof simplifies understanding of Leversha's theorem

Utilizes computational tools for geometric proofs

Clarifies properties of isogonal conjugates in quadrilaterals

Abstract

We give a short and insightful proof of Gerry Leversha's elegant theorem regarding the isogonal conjugates of each of the vertices of a non-cyclic quadrilateral with respect to the triangle formed by the other three. It uses the Maple package RENE.txt, available from . http://www.math.rutgers.edu/~zeilberg/tokhniot/RENE.txt