KöMaL 2015 K460

A circle of radius 10 units is centred at point $O$ . $A$ , $B$ and $C$ are points on the circle such that $O$ lies in the interior of triangle $ABC$ . Given that the length of line segment $AB$ is 12 units and the measure of angle $ABC$ is $60^\circ$, find $a)$ the distance of point $O$ from line segment $AB$ , $b)$ the length of line segment $AC$ .