A Generalization of Certain Remarkable Points of the Triangle Geometry

TL;DR

This paper generalizes key theorems in triangle geometry, unifying several notable points such as Franke's and Kariya's points through a new theorem.

Contribution

It introduces a new theorem that extends existing concurrence theorems, connecting multiple remarkable points in triangle geometry.

Findings

Unified framework for notable triangle points

Generalized theorem encompassing Franke's and Kariya's points

Enhanced understanding of triangle geometry relationships

Abstract

In this article we prove a theorem that will generalize the concurrence theorems that are leading to the Franke's point, Kariya's point, and to other remarkable points from the triangle geometry.