Figure shows $\Delta ABC$ with $AB = 3, AC = 4$ & $BC = 5$. Three circles $S_1, S_2$ & $S_3$ have their centres on $A, B $ & $C$ respectively and they externally touches each other. The sum of areas of three circles is
$11\pi$
$12\pi$
$13\pi$
$14\pi$
Let $C$ be a circle passing through the points $A (2,-1)$ and $B (3,4)$. The line segment $AB$ is not a diameter of $C$. If $r$ is the radius of $C$ and its centre lies on the circle $(x-5)^{2}+(y-1)^{2}=\frac{13}{2}$, then $r^{2}$ is equal to
For the two circles $x^2 + y^2 = 16$ and $x^2 + y^2 -2y = 0,$ there is/are
If one of the diameters of the circle $x^{2}+y^{2}-2 x-6 y+6=0$ is a chord of another circle $'C'$, whose center is at $(2,1),$ then its radius is..........
If ${x^2} + {y^2} + px + 3y - 5 = 0$ and ${x^2} + {y^2} + 5x$ $ + py + 7 = 0$ cut orthogonally, then $p$ is
The number of common tangents to the circles ${x^2} + {y^2} = 1$and ${x^2} + {y^2} - 4x + 3 = 0$ is