IMO Shortlist 2002 problem G2


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2. travnja 2012.
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Let ABC be a triangle for which there exists an interior point F such that \angle AFB=\angle BFC=\angle CFA. Let the lines BF and CF meet the sides AC and AB at D and E respectively. Prove that

AB+AC\geq4DE.
Izvor: Međunarodna matematička olimpijada, shortlist 2002