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
$11\pi$
$12\pi$
$13\pi$
$14\pi$
If a variable line, $3x + 4y -\lambda = 0$ is such that the two circles $x^2 + y^2 -2x -2y + 1 = 0$ and $x^2 + y^2 -18x -2y + 78 = 0$ are on its opposite sides, then the set of all values of $\lambda $ is the interval
The radical centre of the circles ${x^2} + {y^2} - 16x + 60 = 0,\,{x^2} + {y^2} - 12x + 27 = 0,$ ${x^2} + {y^2} - 12y + 8 = 0$ is
Three circles of radii $a, b, c\, ( a < b < c )$ touch each other externally. If they have $x -$ axis as a common tangent, then
The equation of director circle of the circle ${x^2} + {y^2} = {a^2},$ is
The number of integral values of $\lambda $ for which $x^2 + y^2 + \lambda x + (1 - \lambda )y + 5 = 0$ is the equation of a circle whose radius cannot exceed $5$ , is