Archimedean Twins

Geometry Level 3

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

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