If the circle $x^2+y^2+2 \alpha x+c=0$ lies completely inside the circle $x^2+y^2+2 \beta x+c=0$,then which of the following holds?

The point at which the circles $x^2+y^2-4x-4y+7=0$ and $x^2+y^2-12x-10y+45=0$ touch each other is:

$C_1$ and $C_2$ are the external and internal centres of similitude of the circles $x^2+y^2-2x+4y+1=0$ and $x^2+y^2+4x-6y+12=0$. If the radius of the circle having $C_1C_2$ as its diameter is $r$,then $\frac{9}{2}r=$

Where do the circles $x^2 + y^2 + 2x - 2y + 1 = 0$ and $x^2 + y^2 - 2x - 2y + 1 = 0$ touch each other?

The equation of the circle passing through the point of intersection of the circles ${x^2} + {y^2} - 8x - 2y + 7 = 0$ and ${x^2} + {y^2} - 4x + 10y + 8 = 0$ and the point $(3, -3)$ is:

The equation of a circle which passes through the points of intersection of the circles $2x^2+2y^2-2x+6y-3=0$ and $x^2+y^2+4x+2y+1=0$,and whose centre lies on the common chord of these circles is