JournalsemVol. 63 , No. 1DOI 10.4171/em/82

Erdös–Mordell-type inequalities

  • Zhiqin Lu

    University of California, Irvine, United States
Erdös–Mordell-type inequalities cover


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

p+q+r2(x+y+z).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 ABCABC. In this note, we give a more algebraic proof of the Erd\"os-Mordell inequality.