If $\theta$ is the angle between the circles $x^2+y^2-4 x+2 y-4=0$ and $x^2+y^2-2 x+4 y-11=0$ then $\sin \theta=$

If the line $x+y=2$ cuts the circle $x^2+y^2+2 x-4 y+4=0$ at two points $A$ and $B$, then the radius of the circle passing through $A, B$ and orthogonal to $x^2+y^2-2 x-4 y-4=0$ is

If $(3,-2)$ is the centre of the circle $S \equiv x^2+y^2+2 g x+2 f y-23=0$ and $A$ is a point on the circle $S=0$ such that its distance from a point $P(-1,-5)$ is least, then $A=$

Two circles which touch both the coordinate axes intersect at the points $A$ and $B$. If $A=(1,2)$, then $A B=$