The length of the tangent drawn from any pointon the circle   x2+y2+2gx+2fy+c=0 to the circlex2+y2+2gx+2fy+c1=0 is

Let (α,β) be a point on  x2+y2+2gx+2fy+c=0 Then, the length of the tangent from  (α,β) tox2+y2+2gx+2fy+c1=0 is given by  l=α2+β2+2gα+2fβ+c1Since  (α,β) lies on  x2+y2+2gx+2fy+c=0  ∴ α2+β2+2gα+2fβ=−cHence l=c1−c