A geometry problem by aziz alasha

Geometry Level 4

The figure above two similar semicircles of radius \(R\) inscribed inside a rectangle.

Let the area of the green region and blue region be denoted by \(A_1\) and \(A_2\), respectively.

If the vaue of (A1-A2)/A1 equals \( \dfrac{a\pi -b}{c\pi -d \sqrt d} \), where \(a,b,c,d\) are all integers with \(d\) square-free, find \(a+b+c+d\).

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