Largest area implies orthocenter
Source: 10th Brazilian Math Olympiad - Problem 2
December 27, 2017
Brazilian Math Olympiad 1988Brazilian Math OlympiadorthocentergeometryPlane Geometry
Problem Statement
Show that, among all triangles whose vertices are at distances 3,5,7 respectively from a given point P, the ones with largest area have P as orthocenter.(You can suppose, without demonstration, the existence of a triangle with maximal area in this question.)