As shown in the figure, $O$ is the center of a circle, $OA$ is the radius, arc $AB$ is part of the circle with center $O$ and radius $OA$, $C$ is the midpoint of chord $AB$, $D$ is on arc $AB$, and $CD \perp AB$. The formula for calculating the chord value $s$ is: $s = AB + \frac { CD ^ { 2 } } { OA }$. When $OA = 2$ and $\angle AOB = 60 ^ { \circ }$, then $s =$ A. $\frac { 11 - 3 \sqrt { 3 } } { 2 }$ B. $\frac { 11 - 4 \sqrt { 3 } } { 2 }$ C. $\frac { 9 - 3 \sqrt { 3 } } { 2 }$ D. $\frac { 9 - 4 \sqrt { 3 } } { 2 }$
As shown in the figure, $O$ is the center of a circle, $OA$ is the radius, arc $AB$ is part of the circle with center $O$ and radius $OA$, $C$ is the midpoint of chord $AB$, $D$ is on arc $AB$, and $CD \perp AB$. The formula for calculating the chord value $s$ is: $s = AB + \frac { CD ^ { 2 } } { OA }$. When $OA = 2$ and $\angle AOB = 60 ^ { \circ }$, then $s =$\\
A. $\frac { 11 - 3 \sqrt { 3 } } { 2 }$\\
B. $\frac { 11 - 4 \sqrt { 3 } } { 2 }$\\
C. $\frac { 9 - 3 \sqrt { 3 } } { 2 }$\\
D. $\frac { 9 - 4 \sqrt { 3 } } { 2 }$