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Find the point P (IMO SL 1987-P5)

Source:

August 19, 2010
geometrycircumcircleTriangleminimizationCircumcenterIMO Shortlist

Problem Statement

Find, with proof, the point PP in the interior of an acute-angled triangle ABCABC for which BL2+CM2+AN2BL^2+CM^2+AN^2 is a minimum, where L,M,NL,M,N are the feet of the perpendiculars from PP to BC,CA,ABBC,CA,AB respectively.
Proposed by United Kingdom.
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