smc

Note that the length 4 forms a semicircle. We can then use the Law of Cosines. Take the center and form a line segment with the other two points. Let's find the cosine of angle $AOB$. The cosine of that angle is 7/8. We use the double cosine angle to find angle $AOC$: $cos(2x)=2co{s}^2(x)-1$ Therefore, $cos(2x)=17/32$ Applying the Law of Cosines to the triangle $DOC$, we get $C{D}^2=2^2+2^2-2(4)(-17/32)$ (because $cos(x)=-cos(180-x)$) Therefore, $C{D}^2=8+17/4$ and we find that $CD=\boxed{\frac{7}{2}}$!