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Omni-MATH / Suppose ABC is a triangle with incircle ω, and ω is tangent to (BC)¯ and (CA)¯ at D and E respectively. The bisectors of ∠A and ∠B intersect line DE at F and G respectively, such t…

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problem

Suppose ABCA B C is a triangle with incircle ω\omega, and ω\omega is tangent to BC¯\overline{B C} and CA¯\overline{C A} at DD and EE respectively. The bisectors of ∠A\angle A and ∠B\angle B intersect line DED E at FF and GG respectively, such that BF=1B F=1 and FG=GA=6F G=G A=6. Compute the radius of ω\omega.
Plain-text mathematical notation (without MathML)
Suppose ABC is a triangle with incircle ω, and ω is tangent to (BC)¯ and (CA)¯ at D and E respectively. The bisectors of ∠A and ∠B intersect line DE at F and G respectively, such that BF=1 and FG=GA=6. Compute the radius of ω.
Original LaTeX notation
Suppose $A B C$ is a triangle with incircle $\omega$, and $\omega$ is tangent to $\overline{B C}$ and $\overline{C A}$ at $D$ and $E$ respectively. The bisectors of $\angle A$ and $\angle B$ intersect line $D E$ at $F$ and $G$ respectively, such that $B F=1$ and $F G=G A=6$. Compute the radius of $\omega$.

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Source and history

task_id
950e3e45-89be-5f8d-be86-f70fcee29081
task_key
test--950e3e45-89be-5f8d-be86-f70fcee29081
task_revision_id
1
config / split
/ test

Official source

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