A circle with radius 2 is placed against a right angle. Another smaller circle is also placed as shown in the adjoining figure. What is the radius of the smaller circle?

A

$$3 - 2 \sqrt{2}$$

B

$$4 - 2 \sqrt{2}$$

C

$$7- 4 \sqrt{2}$$

D

$$6- 4 \sqrt{2}$$