Tangents

Geometry Level 3

Let \(y=x\) and \(y=2x\) be the equations of tangents from a given point \(O\) to a circle of radius 3 units with centre in the first quadrant. If \(A\) is one of the points of contact and \(|OA|=a+b\sqrt{10} \), find \(a+b\).

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