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Omni-MATH / In triangle ABC,∠BAC=60^(∘). Let …AB at point D and segment AC at point E. Suppose …BC at points F and G such that F lies in between B and G. Given that AD=FG=4 and BF=(1)/(2), fin…

Problem

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problem

In triangle ABC,∠BAC=60∘A B C, \angle B A C=60^{\circ}. Let \omega be a circle tangent to segment ABA B at point DD and segment ACA C at point EE. Suppose \omega intersects segment BCB C at points FF and GG such that FF lies in between BB and GG. Given that AD=FG=4A D=F G=4 and BF=12B F=\frac{1}{2}, find the length of CGC G.
Plain-text mathematical notation (without MathML)
In triangle ABC,∠BAC=60^(∘). Let \omega be a circle tangent to segment AB at point D and segment AC at point E. Suppose \omega intersects segment BC at points F and G such that F lies in between B and G. Given that AD=FG=4 and BF=(1)/(2), find the length of CG.
Original LaTeX notation
In triangle $A B C, \angle B A C=60^{\circ}$. Let \omega be a circle tangent to segment $A B$ at point $D$ and segment $A C$ at point $E$. Suppose \omega intersects segment $B C$ at points $F$ and $G$ such that $F$ lies in between $B$ and $G$. Given that $A D=F G=4$ and $B F=\frac{1}{2}$, find the length of $C G$.

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Source and history

task_id
97d6fe19-4f63-569f-bcfc-b02c1133ab7d
task_key
test--97d6fe19-4f63-569f-bcfc-b02c1133ab7d
task_revision_id
1
config / split
/ test

Official source

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