Question 39
Regular hexagon $ABCDEF$ has side length $2$. Circle $\omega$ lies inside the hexagon and is tangent to segments $\overline{AB}$ and $\overline{AF}$. There exist two perpendicular lines tangent to $\omega$ that pass through $C$ and $E$, respectively. Given that these two lines do not intersect on line $AD$, compute the radius of $\omega$.
Proposed by: Karthik Venkata Vedula
Proposed by: Karthik Venkata Vedula