Coordinate Coordinate!!!

Geometry Level 5

Let \(A=(0,0), B=(-1,-1), C=(x,y)\) and \(D=(x+1,y)\) where \(x>y\) are positive integers. Suppose the points \(A,B,C,D\) lie on a circle with radius \(r\). Denote by \(r_{1}\) and \(r_{2}\) the smallest and the second smallest possible values of \(r\). Compute \(r_{1}^{2}+r_{2}^{2}\).

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