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MATH / The medians AD, BE, and CF of triangle ABC intersect at the centroid G. The line through G that is parallel to BC intersects AB and AC at M and N, respectively. If the area of tria…

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problem

The medians ADAD, BEBE, and CFCF of triangle ABCABC intersect at the centroid GG. The line through GG that is parallel to BCBC intersects ABAB and ACAC at MM and NN, respectively. If the area of triangle ABCABC is 810, then find the area of triangle AMNAMN.
Plain-text mathematical notation (without MathML)
The medians AD, BE, and CF of triangle ABC intersect at the centroid G.  The line through G that is parallel to BC intersects AB and AC at M and N, respectively.  If the area of triangle ABC is 810, then find the area of triangle AMN.
Original LaTeX notation
The medians $AD$, $BE$, and $CF$ of triangle $ABC$ intersect at the centroid $G$.  The line through $G$ that is parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively.  If the area of triangle $ABC$ is 810, then find the area of triangle $AMN$.

level

Level 5

type

Geometry

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Source and history

task_id
8dbbea67-3673-5a29-8768-7d0a5d60ac49
task_key
geometry--test--8dbbea67-3673-5a29-8768-7d0a5d60ac49
task_revision_id
1
config / split
geometry / test

Official source

initial import