The number of circles that touch all the three lines $x+y-1=0$,$x-y-1=0$,and $y+1=0$ is

If the circles $(x+a)^2+(y+b)^2=a^2$ and $(x+c)^2+(y+d)^2=d^2$ cut orthogonally,then $b(b-2d) =$

The number of circles that touch the coordinate axes and the line with slope $-1$ and $y$-intercept $1$ is:

If the circles $x^2+y^2-2x-2y+k=0$ and $x^2+y^2+4x+6y+4=0$ touch each other externally,then the point of contact of the two circles is

Suppose $d_1$ and $d_2$ are respectively the lengths of intercepts of the circles $x^2+y^2=4$ and $x^2+y^2-10x-14y+65=0$ on the line $2x-2y-3=0$. Then,which of the following is true?

If a straight line through $C(-\sqrt{8}, \sqrt{8})$ making an angle of $135^\circ$ with the $x$-axis cuts the circle $x = 5\cos\theta, y = 5\sin\theta$ at points $A$ and $B$,then the length of $AB$ is