Locus Problem

Geometry Level 3

The circle \(x^2+y^2-4x-4y+4=0\) is inscribed in a triangle which has two of its sides along the coordinate axes. The locus of the circumcentre of the triangle is \(x+y-xy+k(x^2+y^2)^{1/2}=0\). Find \(k\).

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