Erdös–Mordell-type inequalities

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

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.