# Chords In Concentric Circles

Geometry Level pending

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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