The radius of a circle touching all the four circles $(x \pm \lambda)^2+(y \pm \lambda)^2=\lambda^2$ is

If the radical centre of the given three circles $x^2+y^2=1, x^2+y^2-2 x-3=0$ and $x^2+y^2-2 y-3=0$ is $C(\alpha, \beta)$ and $r$ is the sum of the radii of the given circles, then the circle with $C(\alpha, \beta)$ as centre and $r$ as radius is

The equation of the circle inscribed in a square formed by the lines $x+y-2=0, x+y-6=0, x-y+1=0$ and $x-y+5=0$ is

Let the circle $S \equiv x^2+y^2+2 g x+2 f y+c=0$ touch the positive $X$-axis and the positive $Y$-axis. Let $(2,4)$ be a point on the circle $S=0$. If two such circles exist, then the difference of their areas is