IMO Shortlist 1987 problem 5


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2. travnja 2012.
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Find, with proof, the point P in the interior of an acute-angled triangle ABC for which BL^2+CM^2+AN^2 is a minimum, where L,M,N are the feet of the perpendiculars from P to BC,CA,AB respectively.

Proposed by United Kingdom.
Izvor: Međunarodna matematička olimpijada, shortlist 1987