A geometry problem by crazy singh

Geometry Level 2

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?

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