Πέμπτη, 12 Οκτωβρίου 2017

2001 JBMO problem 3 (GRE)

proposed by Greece

 Let ${ABC}$ be an equilateral triangle and ${D, E }$  points on the sides ${ [AB]}$ and ${ [AC] }$ respectively. If ${DF, EF }$  (with ${F \in AE, G \in AD }$) are the interior angle bisectors of the angles of the triangle ${ADE }$, prove that the sum of the areas of the triangles ${DEF }$  and ${DEG }$  is at most equal with the area of the triangle ${ABC}$. When does the equality hold?

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