Find, with proof, the point
in the interior of an acute-angled triangle
for which
is a minimum, where
are the feet of the perpendiculars from
to
respectively.
Proposed by United Kingdom.
%V0
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.
Školjka