Beautiful Geometry

Geometry Level 4

In the above image we have five circles: The white one with radious of 4, a blue one, a green one, a red one and a pink one, all four congruent to each other. If the area enclosed by arcs AB (green), BC (pink), CD (blue) and DA (white) can be written like \(\frac{a\sqrt{3}}{b} - \frac{cπ}{d}\) Find the minimum value of \(a+b+c+d\).

Assume \(a,b,c,d\) are positive integers.

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