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sum of areas of the triangles DEF and DEG is at most twice

Source: JBMO 2001, Problem 3

October 30, 2005
geometrytrigonometrygeometry proposed

Problem Statement

Let ABCABC be an equilateral triangle and DD, EE points on the sides [AB][AB] and [AC][AC] respectively. If DFDF, EFEF (with F∈AEF\in AE, G∈ADG\in AD) are the interior angle bisectors of the angles of the triangle ADEADE, prove that the sum of the areas of the triangles DEFDEF and DEGDEG is at most equal with the area of the triangle ABCABC. When does the equality hold? Greece
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