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

The range of values of $'a'$ such that the angle $\theta$ between the pair of tangents drawn from the point $(a, 0)$ to the circle $x^2 + y^2 = 1$ satisfies $\frac{\pi }{2} < \theta < \pi$ is :

The equation of the circle having its centre on the line $x + 2y - 3 = 0$ and passing through the points of intersection of the circles ${x^2} + {y^2} - 2x - 4y + 1 = 0$ and ${x^2} + {y^2} - 4x - 2y + 4 = 0$, is

Circles ${x^2} + {y^2} + 2gx + 2fy = 0$ and ${x^2} + {y^2}$ $ + 2g'x + 2f'y = $ $0$ touch externally, if

If ${x^2} + {y^2} + px + 3y - 5 = 0$ and ${x^2} + {y^2} + 5x$ $ + py + 7 = 0$ cut orthogonally, then $p$ is

The radical centre of the circles ${x^2} + {y^2} + 4x + 6y = 19,{x^2} + {y^2} = 9$ and ${x^2} + {y^2} - 2x - 2y = 5$ will be