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MATH / Given triangle ABC, there exists a unique point P such that

Problem

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problem

Given triangle ABC,ABC, there exists a unique point PP such that AB2+AP2+BP2=AC2+AP2+CP2=BC2+BP2+CP2.AB^2 + AP^2 + BP^2 = AC^2 + AP^2 + CP^2 = BC^2 + BP^2 + CP^2.Express the common value above in terms of the side lengths a,a, b,b, and c,c, and circumradius RR of triangle ABC.ABC.
Plain-text mathematical notation (without MathML)
Given triangle ABC, there exists a unique point P such that
AB²+AP²+BP²=AC²+AP²+CP²=BC²+BP²+CP².Express the common value above in terms of the side lengths a, b, and c, and circumradius R of triangle ABC.
Original LaTeX notation
Given triangle $ABC,$ there exists a unique point $P$ such that
\[AB^2 + AP^2 + BP^2 = AC^2 + AP^2 + CP^2 = BC^2 + BP^2 + CP^2.\]Express the common value above in terms of the side lengths $a,$ $b,$ and $c,$ and circumradius $R$ of triangle $ABC.$

level

Level 5

type

Precalculus

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Source and history

task_id
14b823de-c29c-53dd-8516-2764bb36f9aa
task_key
precalculus--test--14b823de-c29c-53dd-8516-2764bb36f9aa
task_revision_id
1
config / split
precalculus / test

Official source

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