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.

Find the radius of a circle that touches the $y-$axis at point $P(0,2)$ and touches the circle $x^2 + y^2 = 16$ internally.

Let $R$ be the region of the disc $x^2+y^2 \leq 1$ in the first quadrant. Then,the area of the largest possible circle contained in $R$ is

The radius of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ and having its centre at $(0,3)$ is

For any real number $\lambda \neq 1$,the centre of the circle that passes through $A(1, \lambda)$,$B(\lambda, 1)$,and $C(\lambda, \lambda)$ is

The power of a point $(2,0)$ with respect to a circle $S$ is $-4$ and the length of the tangent drawn from the point $(1,1)$ to $S$ is $2$. If the circle $S$ passes through the point $(-1,-1)$,then the radius of the circle $S$ is