Geometry Triangle inequality
Source: Irish MO
May 10, 2012
geometryinequalitiestrigonometry
Problem Statement
Suppose P is a point in the interior of a triangle ABC, that x; y; z are
the distances from P to A; B; C, respectively, and that p; q; r are the per-
pendicular distances from P to the sides BC; CA; AB, respectively. Prove
that
xyz \geq 8pqr;
with equality implying that the triangle ABC is equilateral.