Two circles with equal radii intersecting at the points $(0, 1)$ and $(0, -1).$ The tangent at the point $(0, 1)$ to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is
$1$
$2$
$2\sqrt 2$
$\sqrt 2$
The centre of the circle passing through $(0, 0)$ and $(1, 0)$ and touching the circle ${x^2} + {y^2} = 9$ is
If one of the diameters of the circle $x^{2}+y^{2}-2 x-6 y+6=0$ is a chord of another circle $'C'$, whose center is at $(2,1),$ then its radius is..........
The number of direct common tangents to the circles $x^2 + y^2 = 4$ and $x^2 + y^2 -8x -8y + 7 = 0$ , is
Give the number of common tangents to circle ${x^2} + {y^2} + 2x + 8y - 23 = 0$ and ${x^2} + {y^2} - 4x - 10y + 9 = 0$
The number of circles touching the line $y - x = 0$ and the $y$-axis is