Concentric circles and equilateral triangle

Geometry Level 4

Three concentric circles each have radii \(8\text{ cm}, 15\text{ cm}, 17\text{ cm}.\)

If the largest possible area of the equilateral triangle with one vertex on each circle is of the form \(\left(a+b\dfrac{\sqrt{3}}{4}\right) \text{cm}^2,\) where \(a\) and \(b\) are positive integers, find \(a+b.\)

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