The angle at which the circles $(x - 1)^2 + y^2 = 10$ and $x^2 + (y - 2)^2 = 5$ intersect is
$\frac{\pi }{6}$
$\frac{\pi }{4}$
$\frac{\pi }{3}$
$\frac{\pi }{2}$
The condition that the line $x\cos \alpha + y\sin \alpha = p$ may touch the circle ${x^2} + {y^2} = {a^2}$ is
The line $2x - y + 1 = 0$ is tangent to the circle at the point $(2, 5)$ and the centre of the circles lies on $x-2y=4$. The radius of the circle is
The tangents are drawn from the point $(4, 5)$ to the circle ${x^2} + {y^2} - 4x - 2y - 11 = 0$. The area of quadrilateral formed by these tangents and radii, is .............. $\mathrm{sq.\, units}$
The angle between the tangents from $(\alpha ,\beta )$to the circle ${x^2} + {y^2} = {a^2}$, is
Tangents drawn from origin to the circle ${x^2} + {y^2} - 2ax - 2by + {b^2} = 0$ are perpendicular to each other, if