(x+y+z)^2 <= (a^2+b^2+c^2)/2 + 2S.sqrt(3), in a triangle?
Source: a Geo book!
August 24, 2004
geometryinequalitiesgeometry solved
Problem Statement
A triangle with sides a, b, c has area S.
The distances of its centroid from the vertices are x, y, z.
Show that:
if (x + y + z)^2 ≤ (a^2 + b^2 + c^2)/2 + 2S√3,
then the triangle is equilateral.