If $A=(0,-2)$ and $B$ is any point on the circle $x^2+y^2-2 x-2 y+1=0$, then the maximum value of $(\mathbf{A B})^2$ is

If $(\alpha, \beta)$ is the pole of the line $3 x-5 y+6=0$ with respect to the circle $x^2+y^2-10 x+14 y+46=0$, then $\alpha+\beta=$

$O(0,0)$ and $A(1,0)$ are centres of two units circles $C_1$ and $C_2$, respectively. $C_3$ is also a unit circle having its centre above $X$ - axis and passing through $O$ and $A$. The equation of the common tangent to $C_1$ and $C_3$ which does not intersect the circle $C_2$ is

If the circles $x^2+y^2-16 x-20 y+164=r^2(r>0)$ and $x^2+y^2-8 x-14 y+29=0$ intersect in two distinct points, then the maximum possible integral value of $r$ is