Let complex numbers $$\alpha$$ and $$\frac{1}{\alpha}$$ lie on circles $$(x - x_0)^2 + (y - y_0)^2 = r^2$$ and $$(x - x_0)^2 + (y - y_0)^2 = 4r^2$$, respectively. If $$z_0 = x_0 + iy_0$$ Satisfies the equation $$2 |z_0|^2 = r^2 + 2,$$ then $$|\alpha| = $$

A

$$\frac{1}{\sqrt 2}$$

B

$$\frac{1}{2}$$

C

$$\frac{1}{\sqrt 7}$$

D

$$\frac{1}{3}$$