If the lines $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ are tangent to a circle,then the radius of the circle is

If $P$ is a point on the circle $x^{2}+y^{2}=4$,$Q$ is a point on the straight line $5x+y+2=0$ and $x-y+1=0$ is the perpendicular bisector of $PQ$,then $13$ times the sum of the abscissae of all such points $P$ is ........... .

$A$ circle is drawn in a sector of a larger circle of radius $r$,as shown in the figure. The smaller circle is tangent to the two bounding radii and the arc of the sector. The radius of the small circle 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:

If the radical axis of the circles $x^2 + y^2 - 1 = 0$ and $x^2 + y^2 - 2x - 2y + 1 = 0$ forms a triangle of area $A$ with the coordinate axes,then the value of $\frac{1}{A}$ is

Tangent $L_1 \equiv 3x - 4y - 8 = 0$ and the chord $L_2 \equiv x + y - 1 = 0$ are at a distance of $2$ and $\sqrt{2}$ units respectively from the centre of a circle $S$. $(h, k)$ is the centre of $S$ such that $h^2 + k^2 = 13$. If the midpoint of the chord $L_2 = 0$ is $(\alpha, \beta)$ and the radius of the circle is $r$,then $\alpha + \beta + r =$