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The radical centre of the three circles ...

The radical centre of the three circles is at the origin. The equations of the two of the circles are `x^(2)+y^(2)=1 and x^(2)+y^(2)+4x+4y-1=0`. If the third circle passes through the points (1, 1) and (-2, 1), and its radius can be expressed in the form of `(p)/(q)`, where p and q are relatively prime positive integers. Find the value of `(p+q)`.

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