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Omni-MATH / Triangle ABC has an area 1. Points E,F,G lie, respectively, on sides BC, CA, AB such that AE bisects BF at point R, BF bisects CG at point S, and CG bisects AE at point T. Find the…

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problem

Triangle ABCABC has an area 1. Points E,F,GE,F,G lie, respectively, on sides BCBC, CACA, ABAB such that AEAE bisects BFBF at point RR, BFBF bisects CGCG at point SS, and CGCG bisects AEAE at point TT. Find the area of the triangle RSTRST.
Plain-text mathematical notation (without MathML)
Triangle ABC has an area 1.  Points E,F,G lie, respectively, on sides BC, CA, AB such that AE bisects BF at point R, BF bisects CG at point S, and CG bisects AE at point T. Find the area of the triangle RST.
Original LaTeX notation
Triangle $ABC$ has an area 1.  Points $E,F,G$ lie, respectively, on sides $BC$, $CA$, $AB$ such that $AE$ bisects $BF$ at point $R$, $BF$ bisects $CG$ at point $S$, and $CG$ bisects $AE$ at point $T$. Find the area of the triangle $RST$.

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Source and history

task_id
c0ed50b5-750f-5b34-8ce9-1e7785d58632
task_key
test--c0ed50b5-750f-5b34-8ce9-1e7785d58632
task_revision_id
1
config / split
/ test

Official source

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