The radical axis of the pair of circle ${x^2} + {y^2} = 144$ and ${x^2} + {y^2} - 15x + 12y = 0$ is

If one of the diameters of the circle $x^{2}+y^{2}-2 \sqrt{2} x$ $-6 \sqrt{2} y+14=0$ is a chord of the circle $(x-2 \sqrt{2})^{2}$ $+(y-2 \sqrt{2})^{2}=r^{2}$, then the value of $r^{2}$ is equal to

Let $C_1, C_2$ be two circles touching each other externally at the point $A$ and let $A B$ be the diameter of circle $C_1$. Draw a secant $B A_3$ to circle $C_2$, intersecting circle $C_1$ at a point $A_1(\neq A)$, and circle $C_2$ at points $A_2$ and $A_3$. If $B A_1=2, B A_2=3$ and $B A_3=4$, then the radii of circles $C_1$ and $C_2$ are respectively

The equation of the circle which passes through the intersection of ${x^2} + {y^2} + 13x - 3y = 0$and $2{x^2} + 2{y^2} + 4x - 7y - 25 = 0$ and whose centre lies on $13x + 30y = 0$ is

The circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$ bisects the circumference of the circle ${x^2} + {y^2} + 2g'x + 2f'y + c' = 0$, if

The centre$(s)$ of the circle$(s)$ passing through the points $(0, 0) , (1, 0)$ and touching the circle $x^2 + y^2 = 9$ is/are :