The circle is inscribed in a triangle which has two of its sides along the coordinate axes

MATHEMATICS · Subjective · ISC · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

The circle x2+y2−4x−4y+4=0x^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(x2+y2)1/2=0x + y - xy + k(x^2 + y^2)^{1/2} = 0. Find kk.

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