The point $P(10, 7)$ lies outside the circle $x^2 + y^2 - 4x - 2y - 20 = 0$. The greatest distance of $P$ from the circle is

The equation of the circle whose centre is $(3, -1)$ and which cuts off a chord of length $6$ on the line $2x - 5y + 18 = 0$ is

If a circle $C$ passing through the point $(4, 0)$ touches the circle $x^2+y^2+4x-6y=12$ externally at the point $(1, -1)$,then the radius of $C$ is

The equation of a circle touching the curve $|x - 1| + |y - 4| = 6$ is

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 $C$.

Does the point $(-2.5, 3.5)$ lie inside,outside,or on the circle $x^{2}+y^{2}=25$?