A circle is circumscribed around a square as shown in the figure. The area of one of the four shaded portions is equal to 4/7 . The radius of the circle is :

Answer: Option A

Let the radius of the circle be r and the side of the square be a
Then,
Diagonal of the square = 2r
⇒ $$\sqrt{2}$$ a = 2r
⇒ a = $$\frac{2}{\sqrt{2}}$$ r
⇒ a = $$\sqrt{2}$$ r
Area of one shaded portion :
$$\begin{array}{rl}& =\frac{1}{4}\left[\pi r^2-{\left(\sqrt{2}r\right)}^2\right]\\ & =\frac{1}{4}\left(\pi -2\right)r^2\\ & \therefore \frac{1}{4}\left(\pi -2\right)r^2=\frac{4}{7}\\ & \Rightarrow \left(\frac{22}{7}-2\right)r^2=\frac{16}{7}\\ & \Rightarrow r^2=\frac{16}{7}\times \frac{7}{8}\times 2\\ & \Rightarrow r=\sqrt{2}\end{array}$$