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Omni-MATH / Find, with proof, the point P in the interior of an acute-angled triangle ABC for which BL²+CM²+AN² is a minimum, where L,M,N are the feet of the perpendiculars from P to BC,CA,AB …

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problem

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. [i]
Plain-text mathematical notation (without MathML)
Find, with proof, the point P in the interior of an acute-angled triangle ABC for which BL²+CM²+AN² is a minimum, where L,M,N are the feet of the perpendiculars from P to BC,CA,AB respectively.

[i]
Original LaTeX notation
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.

[i]

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Source and history

task_id
f1aff3e0-a8b3-5c89-9ae5-a290e766daee
task_key
test--f1aff3e0-a8b3-5c89-9ae5-a290e766daee
task_revision_id
1
config / split
/ test

Official source

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