AMC 12 2008b Problem 9

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 $AC$?

(Solution)

\textbf{(A)}\ \sqrt {10} \textbf{(B)}\ \frac {7}{2} \textbf{(C)}\ \sqrt {14} \textbf{(D)}\ \sqrt {15} \textbf{(E)}\ 4