A geometrical enigma

Geometry Level 4

Find the ratio between the area of a square inscribed in a circle,and an equilateral triangle circumscribed about the same circle.

If the ratio is in the form \(\dfrac{\sqrt{{a}}}{{b}}\), where \(a\) and \(b\) are positive integers with \(a\) and \(b\) as small as possible, find \({a}+{b}\).

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