MathDB
Problem 2 Day1

Source: 2011 Armenian Republican Olympiad

August 1, 2016
geometryhexagonrhombus

Problem Statement

Let a hexagone with a diameter DD be given and let d>D2.d>\frac D 2. On each side of the hexagon one constructs a isosceles triangle with two equal sides of length dd. Prove that the sum of the areas of those isoscele triangles is greater than the area of a rhombus with side lengths dd and a diagonal of length DD.
(The diameter of a polygon is the maximum of the lengths of all its sides and diagonals.)