jmc

To make the problem much simpler while staying in the constraints of the problem, position point $C$ halfway between $A$ and $B$. Then, call $\overline{AC}=\overline{BC}=r$ . The area of the shaded region is then$$\frac{\pi r^2-\pi (r/2{)}^2-\pi (r/2{)}^2}{2}=\frac{\pi r^2}{4}$$Because $\overline{CD}=r$ the area of the circle with $\overline{CD}$ as radius is $\pi r^2$. Our ratio is then$$\frac{\pi r^2}{4}:\pi r^2=\boxed{1:4}$$