A semicircle with radius a is inscribed in a rectangle with its diameter along one...........Solve for the value of a/b.

Question

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.
Solve for the value of a/b.

Answer 1

(√2+1)/(√2-1) or 5.83

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See attached

As we can see above
AD=AB+BC+CD
AB= b√2, BC=b, CD=a, AD=a√2
a√2=a+b+b√2
a√2-a=b+b√2
a(√2-1)=b(√2+1)
a/b=(√2+1)/(√2-1)= 5.83