Two Triangles with the Same Orthocenter and a Vectorial Proof of Stevanovic's Theorem

TL;DR

This paper presents a vectorial proof demonstrating two triangles share the same orthocenter and extends this approach to prove Stevanovic's theorem related to Fuhrmann's triangle, enriching geometric understanding.

Contribution

It introduces a novel vectorial proof technique for the orthocenter coincidence and applies it to establish Stevanovic's theorem.

Findings

Two triangles share the same orthocenter

Vectorial proof of Stevanovic's theorem

Enhanced understanding of Fuhrmann's triangle

Abstract

In this article we'll emphasize on two triangles and provide a vectorial proof of the fact that these triangles have the same orthocenter. This proof will further allow us to develop a vectorial proof of the Stevanovic's theorem relative to the orthocenter of the Fuhrmann's triangle.