A semicircle with radius a is inscribed in a rectangle with its diamet

A semicircle with radius a is inscribed in a rectangle with its diameter along one side of the rectangle. A circle with radius b is then inscribed so it is tangent to the rectangle and the semicircle, as shown above. What is the value of a/b?


A. \(\frac{\sqrt{2}}{\sqrt{2} - 1}\)

B. \(\frac{\sqrt{2} + 1}{\sqrt{2}}\)

C. 2:1

D. \(\frac{\sqrt{2} + 1}{\sqrt{2} - 1}\)

E. 6:1