The equation of the pair of straight lines parallel to the $x$-axis and touching the circle $x^2+y^2-6x-4y-12=0$ is

The sum of the squares of the lengths of the chords intercepted on the circle,$x^2 + y^2 = 16$,by the lines,$x + y = n$,$n \in N$,where $N$ is the set of all natural numbers,is

$A$ circle $C_1$ of radius $2$ touches both $x$-axis and $y$-axis. Another circle $C_2$ whose radius is greater than $2$ touches circle $C_1$ and both the axes. Then the radius of circle $C_2$ is

The angle subtended at the centre of a circle of radius $3 \text{ metres}$ by an arc of length $1 \text{ metre}$ is equal to

For the circle $x^2 + y^2 - 2x + 4y - 4 = 0$,what is the line $2x - y - 1 = 0$?

$AB$ is a line segment of length $24 \ cm$ and $C$ is its midpoint. On $AB$,two semicircles with diameters $AC$ and $CB$ are described on the same side. $A$ large semicircle with diameter $AB$ is also described on the same side. Find the radius of the circle that touches all three semicircles. (in $cm$)