Computer Investigation of Properties of the Gergonne Point of a Triangle

TL;DR

This paper uses computational methods to explore and catalog properties of the Gergonne point in triangles, enhancing understanding of its geometric characteristics.

Contribution

The study introduces a computer-aided approach to systematically investigate and document properties of the Gergonne point, a classical triangle center.

Findings

Identified new geometric relations involving the Gergonne point

Cataloged properties of the Gergonne point through computational analysis

Enhanced the understanding of the Gergonne point's role in triangle geometry

Abstract

The incircle of a triangle touches the sides of the triangle in three points. It is well known that the lines from these points to the opposite vertices meet at a point known as the Gergonne point of the triangle. We use a computer to discover and catalog properties of the Gergonne point.