AMC 10 2008b Problem 10

Points $A$ and $B$ are on a circle of radius $5$ and $AB=6$. Point $C$ is the midpoint of the minor arc $AB$. What is the length of the line segment $AC$? $\mathrm{(A)}\ \sqrt{10} \mathrm{(B)}\ \frac{7}{2} \mathrm{(C)}\ \sqrt{14} \mathrm{(D)}\ \sqrt{15} \mathrm{(E)}\ 4$