The number of circles that touch all the straight lines $x+y=4$,$x-y=-2$,and $y=2$ is

The total number of common tangents of $x^{2}+y^{2}-6x-8y+9=0$ and $x^{2}+y^{2}=1$ is

If a circle $C,$ whose radius is $3,$ touches the circle $x^2 + y^2 + 2x - 4y - 4 = 0$ externally at the point $(2, 2),$ then the length of the intercept cut by circle $C$ on the $x-$axis is equal to

Let $C$ be a circle having centre in the first quadrant and touching the $x$-axis at a distance of $3$ units from the origin. If the circle $C$ has an intercept of length $6\sqrt{3}$ on the $y$-axis, then the length of the chord of the circle on the line $x - y = 3$ is:

The number of common tangents to the circles $x^2 + y^2 - 2x - 1 = 0$ and $x^2 + y^2 - 2y - 7 = 0$ is:

In a circle of diameter $40 \, cm$,the length of a chord is $20 \, cm$. Find the length of the minor arc of the chord.