# Erdös–Mordell-type inequalities

### Zhiqin Lu

University of California, Irvine, United States

## Abstract

The famous Erd\"os-Mordell inequality states that, if $P$ is a point in the interior of a triangle $ABC$ whose distances are $p,q,r$ from the vertices of the triangle and $x,y,z$ from its sides, then

$p+q+r\geq 2(x+y+z).$

In the paper by Satnoianu~\cite{Sat}, some generalizations of the above inequality were given. His proof depends heavily on the geometry of the triangle $ABC$. In this note, we give a more algebraic proof of the Erd\"os-Mordell inequality.

## Cite this article

Zhiqin Lu, Erdös–Mordell-type inequalities. Elem. Math. 63 (2008), no. 1, pp. 23–24

DOI 10.4171/EM/82