Chords In Concentric Circles

Geometry Level 3

Let \(O_1\) and \(O_2\) be concentric circles with radii \(4\) and \(6\), respectively. A chord \(AB\) is drawn in \(O_1\) with length \(2\). Extend \(AB\) to intersect \(O_2\) in points \(C\) and \(D\). If the length of \(CD\) can be expressed as \(a\sqrt{b}\), where \(a\) and \(b\) are positeve integers, find the value of \(a+b\).

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