My problems #8

Geometry Level 4

A square \(OABC\) is formed by line pairs \(xy=0\) and \(xy+1=x+y\) where "O" is the origin .A circle With center \(C_1\) inside the squre is drawn to touch the line pair \(xy=0\) and another circle with center \(C_2\) and radius twice that of \(C_1\),is drawn to touch the circle \(C_1\) and the other line pair.Find the radius of the circle With center \(C_1\).

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