Problem Locus

Geometry Level pending

The circle \(x^{2} + y^{2} - 4x - 4y + 4\) is inscribed in a triangle whose two sides lie on the co-ordinate axes.The locus of the circumcenter of this triangle can be represented as \(ax + by - cxy +k(\sqrt(x^{2} + y^{2})\) =0.Where a,b,c,d are real constants.

Find the value of a+b+c+k.

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