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

If the equation $2 x-3 y+3=0,2 x+y+1=0$ and $6 x+4 y+1=0$ represent the sides of a triangle, then the equation of the circle passing through the vertices of this triangle is

If $T_1 T^{\prime}{ }_1$ and $T_2 T_2^{\prime}$ are the common tangents of the circles $S \equiv x^2+y^2-2 x-4 y-4=0$ and $S \equiv x^2+y^2+4 x+4=0$, where $T_1, T^{\prime}{ }_1, T_2, T^{\prime}{ }_2$ are the points of contact, then the distance between $T_1$ and $T_1^{\prime}$ is