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$\underline{\textbf{Answer: A}}\Rightarrow$

$\underline{\textbf{Explanation:}}\Rightarrow$

When an equilateral triangle is inscribed in a circle then the radius of the circle is given by:

$r = \frac{b}{\sqrt3}$

When a square is inscribed in a circle its diagonal = $\sqrt a$ (Since, side = $a$, hence just use the Pythagoras theorem)

Now, equating both the radius, we get:

$\frac{b}{\sqrt{3}} = \frac{a}{\sqrt 2} = \frac{a}{b} = \sqrt\frac{2}{3}$

Therefore, the correct answer is option $\textbf A$.
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