The large circle is tangent to each of the purple circles, which are tangent to each other.  The radius of the large circle is the sum of the radii of the purple circles.

The Yellow circles are each tangent to one of the purple circles, to the large circle and to the common tangent of the two purple circles.

The yellow circles are called the Archimedes Twins, and have the same radius.

Can you work out what this radius is in terms of the radii of the purple circles?