geometric and harmonic mean of distances of sides of triangle, max values
Source: 2010 XIII All-Ukrainian Tournament of Young Mathematicians, Qualifying p6
May 18, 2021
geometrymaxgeometric inequalityUkrainian TYM
Problem Statement
Find inside the triangle , points and for which, respectively, the geometric mean and the harmonic mean of the distances to the sides of the triangle acquire maximum values. In which cases is the segment parallel to one of the sides of the triangle? Find the length of such a segment .