IMO Shortlist 1981 problem 15


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2. travnja 2012.
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Consider a variable point P inside a given triangle ABC. Let D, E, F be the feet of the perpendiculars from the point P to the lines BC, CA, AB, respectively. Find all points P which minimize the sum {BC\over PD}+{CA\over PE}+{AB\over PF}.
Izvor: Međunarodna matematička olimpijada, shortlist 1981