The radius of the circle passing through the points $(-1, 1)$,$(2, -1)$,and $(1, 0)$ is

In the figure shown,the radius of circle $C_1$ is $r$ and that of $C_2$ is $\frac{r}{2}$,where $r = \frac{1}{3} PQ$. Then the length of $AB$ is (where $P$ and $Q$ are the centers of $C_1$ and $C_2$ respectively).

Consider $L_1: 2x + 3y + p - 3 = 0$; $L_2: 2x + 3y + p + 3 = 0$,where $p$ is a real number,and $C: x^2 + y^2 + 6x - 10y + 30 = 0$.
$STATEMENT-1$: If line $L_1$ is a chord of circle $C$,then line $L_2$ is not always a diameter of circle $C$.
$STATEMENT-2$: If line $L_1$ is a diameter of circle $C$,then line $L_2$ is not a chord of circle $C$.

Let $x_0, y_0$ be fixed real numbers such that $x_0^2+y_0^2 > 1$. If $x, y$ are arbitrary real numbers such that $x^2+y^2 \leq 1$,then the minimum value of $(x-x_0)^2+(y-y_0)^2$ is

Three circles,each of radius $1$,touch one another externally and lie between two parallel lines. The minimum possible distance between the lines is:

Suppose two perpendicular tangents can be drawn from the origin to the circle $x^2+y^2-6x-2py+17=0$,for some real $p$. Then,$|p|$ is equal to