MathDB

5

Part of 1987 IMO Shortlist

Problems(1)

Find the point P (IMO SL 1987-P5)

Source:

8/19/2010
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.
geometrycircumcircleTriangleminimizationCircumcenterIMO Shortlist