Question 87
Equilateral $\triangle ABC$ has side length $6$. Let $\omega$ be the circle through $A$ and $B$ such that $CA$ and $CB$ are both tangent to $\omega$. A point $D$ on $\omega$ satisfies $CD = 4$. Let $E$ be the intersection of line $CD$ with segment $AB$. What is the length of segment $DE$?