# Circling complex!

Algebra Level 4

Let complex numbers $$\alpha$$ and $$\frac { 1 }{ \bar { \alpha } }$$ lies on circles $${ \left( x-{ x }_{ 0 } \right) }^{ 2 }+{ \left( y-{ y }_{ 0 } \right) }^{ 2 }={ r }^{ 2 }$$ and $${ \left( x-{ x }_{ 0 } \right) }^{ 2 }+{ \left( y-{ y }_{ 0 } \right) }^{ 2 }=4{ r }^{ 2 }$$ respectively.

If $${ z }_{ 0 }={ x }_{ 0 }+i{ y }_{ 0 }$$ satisfies the equation$2{ \left| { z }_{ 0 } \right| }^{ 2 }={ r }^{ 2 }+2$then find the value of $$\left| \alpha \right|$$

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