Just touching

Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?
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Problem

 

Image
Just touching
Two semi-circles are drawn on one side of a line segment. Another semi-circle touches them externally as shown in the diagram.
 
What is the radius of the circle that touches all three semi-circles in terms of the radii of the first two semi-circles?