Question 55
Suppose $ABC$ is a triangle with incircle $\omega$, and $\omega$ is tangent to $\overline{BC}$ and $\overline{CA}$ at $D$ and $E$ respectively. The bisectors of $\angle A$ and $\angle B$ intersect line $DE$ at $F$ and $G$ respectively, such that $BF=1$ and $FG=GA=6$. Compute the radius of $\omega$.