One group of inequalities with altitudes and medians in triangle

TL;DR

This paper establishes new inequalities relating altitudes and medians in triangles, including at least one novel inequality and a unique proof of a main theorem, with some immediate corollaries.

Contribution

The paper introduces a previously unconsidered inequality involving altitudes and medians and provides a new proof of a main theorem in this area.

Findings

New inequality relating altitudes and medians

Main theorem proved in a novel form

Immediate corollaries derived from the inequalities

Abstract

In the article we prove some inequalities that contain relations between altitudes and medians in triangle. At least one of these inequalities has not been considered in the literature before and the main theorem has also not been proved elsewhere in that form. Some immediate corollaries have been presented as well.