A geometry problem by Archit Tripathi

Geometry Level pending

Find the equation of the director circle to the circle circumscribing the quadrilateral formed by the lines in order, \(2x+3y-2=0\), \(x+y=0, 2x+5y-1=0\) and \(5x+27y-1=0\). If the coefficient of \(x\) and \(y\) in the equation is \(a\) and \(b\), respectively then find the absolute value of \(a+b\).

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