If a circle of radius $r$ touches the positive coordinate axes and also the circle $x^2+y^2-12x-10y+52=0$ externally,then the distance between the centres of the two circles is

The number of circles passing through the origin $(0,0)$ and touching the lines $x + y = 1$ and $x - y = 1$ is ...

The equation of a circle passing through the point $(2,8)$,touching the lines $4x-3y-24=0$ and $4x+3y-42=0$,and having the $x$-coordinate of its centre less than or equal to $8$ is

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

Let $C$ be the centre of the circle $x^{2}+y^{2}-x+2 y=\frac{11}{4}$ and $P$ be a point on the circle. $A$ line passes through the point $C$,makes an angle of $\frac{\pi}{4}$ with the line $CP$ and intersects the circle at the points $Q$ and $R$. Then the area of the triangle $PQR$ (in unit$^{2}$) 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: