A circle with radius $2$ has a center at point $C$. $\triangle ABC$ is constructed such that $\overline{AB}$ is tangent to circle $C$ at point $D$ and $D$ is the midpoint of $\overline{AB}$. Let $W$ be the area of the region inside $\triangle ABC$ but outside circle $C$ and $Q$ be the area of the region inside both $\triangle ABC$ and circle $C$. Find $\frac{W}{Q}$.