If the line $x\, cos \theta + y\, sin \theta = 2$ is the equation of a transverse common tangent to the circles $x^2 + y^2 = 4$ and $x^2 + y^2 - 6 \sqrt{3} \,x - 6y + 20 = 0$, then the value of $\theta$ is :
$5\pi /6$
$2\pi /3$
$\pi /3$
$\pi /6$
The centre of the circle passing through $(0, 0)$ and $(1, 0)$ and touching the circle ${x^2} + {y^2} = 9$ is
Suppose we have two circles of radius 2 each in the plane such that the distance between their centers is $2 \sqrt{3}$. The area of the region common to both circles lies between
The equation of the image of the circle ${x^2} + {y^2} + 16x - 24y + 183 = 0$ by the line mirror $4x + 7y + 13 = 0$ is
The equation of the circle which passes through the origin, has its centre on the line $x + y = 4$ and cuts the circle ${x^2} + {y^2} - 4x + 2y + 4 = 0$ orthogonally, is