Archimedean Twins

Geometry Level 3

In the figure there are three semicircles of diameters AB AB , AC AC , BC BC and two circles S1 S_{1} and S2 S_{2} which are touching to the line CF CF ( CF CF is perpendicular to AB AB ). Both circles have same radius and are called Archimedean Twins. Now if AB=10 AB = 10 , AC=6 AC = 6 and BC=4 BC = 4 then find the radius of circle S1 S_{1} .

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