A geometry problem by crazy singh

In the following figure, arc $AB$ is a quadrant of the circle with center at point $O$ and radius $4$ units. further $OC=OD$ , $OC:OA =3:4$ . The ratio of length of $AG$ to $GD$ is given by $\frac { a }{ b }$ where $a$ and $b$ co-prime positive integers. then $a+b$ is equal to?