If the circles $x^2 + y^2 - 16x - 20y + 164 = r^2$ and $(x - 4)^2 + (y - 7)^2 = 36$ intersect at two distinct points,then

If the straight line $x \cos \alpha + y \sin \alpha = P$ intersects the circle $x^2 + y^2 = a^2$ at $A$ and $B$,then the equation of the circle with diameter $\overline{AB}$ is

The circles $x^2+y^2-10x+16=0$ and $x^2+y^2=a^2$ intersect at two distinct points if

From any point on the circle $x^2 + y^2 = a^2$,tangents are drawn to the circle $x^2 + y^2 = a^2 \sin^2 \alpha$. The angle between them is:

If $\left(0, \frac{3}{4}\right)$ is the radical centre of the circles $S \equiv x^2+y^2+\alpha x+6y=0$,$S^{\prime} \equiv x^2+y^2+2\alpha x+\alpha y+6=0$ and $S^{\prime\prime} \equiv x^2+y^2+6\alpha x-\alpha y+3=0$,then the distance between the radical centre and the centre of the circle $S^{\prime}=0$ is:

The radical centre of the circles $x^2 + y^2 + 4x + 6y = 19$,$x^2 + y^2 = 9$,and $x^2 + y^2 - 2x - 2y = 5$ is: