In a square of side 8 cm, 5 identical circles are placed as shown in the figure. Then the radius (in cms) of each of the circle is

So,length of the diagonal of the square=$$\sqrt{2}r+\sqrt{2}r+\left(4\times r\right)=\left(4r+2\sqrt{2}r\right)$$cm.

But ,diagonal of Square=$$\sqrt{a^2+a^2\ }=\sqrt{2}a$$=$$8\sqrt{2}.$$(square of side 8 cm)

So,

$$8\sqrt{2}=4r+2\sqrt{2}r.$$

or,$$r=\frac{8\sqrt{2}}{4+2\sqrt{2}}.$$

or,$$r=\frac{8\sqrt{2}\left(4-2\sqrt{2}\right)}{16-8}=\sqrt{2}\left(2\left(2-\sqrt{2}\right)\right)=2\left(2\sqrt{2}-2\right)=4\left(\sqrt{2}-1\right).$$

C is correct choice.