Erdös–Mordell-type inequalities

  • Zhiqin Lu

    University of California, Irvine, United States


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.

Cite this article

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

DOI 10.4171/EM/82