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MATH / Let G and H denote the centroid and orthocenter of triangle ABC, respectively. Let F be the midpoint of (GH)¯. Express AF²+BF²+CF² in terms of the side lengths a, b, c and circumra…

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problem

Let GG and HH denote the centroid and orthocenter of triangle ABC,ABC, respectively. Let FF be the midpoint of GH¯.\overline{GH}. Express AF2+BF2+CF2AF^2 + BF^2 + CF^2 in terms of the side lengths a,a, b,b, cc and circumradius RR of triangle ABC.ABC.
Plain-text mathematical notation (without MathML)
Let G and H denote the centroid and orthocenter of triangle ABC, respectively.   Let F be the midpoint of (GH)¯.  Express AF²+BF²+CF² in terms of the side lengths a, b, c and circumradius R of triangle ABC.
Original LaTeX notation
Let $G$ and $H$ denote the centroid and orthocenter of triangle $ABC,$ respectively.   Let $F$ be the midpoint of $\overline{GH}.$  Express $AF^2 + BF^2 + CF^2$ in terms of the side lengths $a,$ $b,$ $c$ and circumradius $R$ of triangle $ABC.$

level

Level 5

type

Precalculus

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Source and history

task_id
1e112620-9774-5a97-80be-cf28a4b3168f
task_key
precalculus--test--1e112620-9774-5a97-80be-cf28a4b3168f
task_revision_id
1
config / split
precalculus / test

Official source

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