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Let complex numbers alpha " and " (1)/...

Let complex numbers ` alpha " and " (1)/(bar alpha)` lies on circles ` (x - x_(0))^(2) + (y- y_(0))^(2) = r^(2) ` and
` (x - x_(0))^(2) + (y - y_(0))^(2) = 4x^(2)` , , respectively. If `z_(0) = x_(0) + iy_(0) ` satisfies the equation ` 2 | z_(0) |^(2) = r^(2) + 2 ` , then ` |alpha|` is equal to:

A

`1/(sqrt(2))`

B

`1/2`

C

`1/(sqrt(7))`

D

`1/3`

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