MathDB
Geometric inequality

Source: Lusophon Math Olympiad 2020 Day 1 #3

November 1, 2020
inequalitiesgeometrygeometric inequality

Problem Statement

Let ABCABC be a triangle and on the sides we draw, externally, the squares BADE,CBFGBADE, CBFG and ACHIACHI. Determine the greatest positive real constant kk such that, for any triangle △ABC\triangle ABC, the following inequality is true: [DEFGHI]≥k⋅[ABC][DEFGHI]\geq k\cdot [ABC] Note: [X][X] denotes the area of polygon XX.
Back to ProblemsView on AoPS