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 $AC$? $\textbf{(A)}\ \sqrt {10} \qquad$ $ \textbf{(B)}\ \frac {7}{2} \qquad$ $ \textbf{(C)}\ \sqrt {14} \qquad$ $ \textbf{(D)}\ \sqrt {15} \qquad$ $ \textbf{(E)}\ 4$
Solution
Let $OC$ intersect $AB$ at $D$. Since $C$ is the midpoint of the arc, $OC\perp AB$ and $D$ is the midpoint of $AB$.
