The points $C$ and $D$ on a semicircle with $AB$ as diameter are such that $AC=1, CD=2$ and $DB=3$. Then,the length of $AB$ lies in the interval.

If the radius of the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ is $r$,then it will touch both the axes if:

When is the angle of intersection of two circles $0^{\circ}$?

The curve $xy = c, (c > 0)$,and the circle $x^2 + y^2 = 1$ touch at two points. Then the distance between the points of contact is

If the power of a point $(4, 2)$ with respect to the circle $x^2 + y^2 - 2\alpha x + 6y + \alpha^2 - 16 = 0$ is $9$,then the sum of the lengths of all possible intercepts made by such circles on the coordinate axes is:

Match the statements in Column $I$ with the properties in Column $II$.

Column $I$	Column $II$
$(A)$ Two intersecting circles	$(p)$ have a common tangent
$(B)$ Two mutually external circles	$(q)$ have a common normal
$(C)$ Two circles,one strictly inside the other	$(r)$ do not have a common tangent
$(D)$ Two branches of a hyperbola	$(s)$ do not have a common normal