102.53 The excentral triangle and a curious application to inequalities

摘要

Introduction The celebrated Weitzenb?ck's inequality from 1919 is [1] where are sides of a triangle and is its area. Equality holds if, and only if, the triangle is equilateral. The inequality was given as Problem 2 at the third International Mathematical Olympiad held in 1961 in Hungary. One sharpening is the well-known Finsler-Hadwiger inequality from 1937 [2].