Let $$𝑆$$ be a circle of radius $$10$$ with centre $$O$$. Suppose $$S_{1}$$ and $$S_{2}$$ are two circles which touch $$𝑆$$ internally and intersect each other at two distinct points $$𝐴$$ and $$𝐵$$. If $$\angle OAB =90^{\circ}$$ what is the sum of the radii of $$S_{1}$$ and $$S_{2}$$?

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