Let the latus ractum of the parabola $y ^{2}=4 x$ be the common chord to the circles $C _{1}$ and $C _{2}$ each of them having radius $2 \sqrt{5}$. Then, the distance between the centres of the circles $C _{1}$ and $C _{2}$ is

Choose the incorrect statement about the two circles whose equations are given below

$x^{2}+y^{2}-10 x-10 y+41=0$ and $x^{2}+y^{2}-16 x-10 y+80=0$

If two circles ${(x - 1)^2} + {(y - 3)^2} = {r^2}$ and ${x^2} + {y^2} - 8x + 2y + 8 = 0$ intersect in two distinct points, then

The points of intersection of the circles ${x^2} + {y^2} = 25$and ${x^2} + {y^2} - 8x + 7 = 0$ are

The number of common tangents of the circles given by $x^2 +y^2 - 8x - 2y + 1 = 0$ and $x^2 + y^2 + 6x + 8y = 0$ is

Let $C_i \equiv  x^2 + y^2 = i^2 (i = 1,2,3)$ are three circles. If there are $4i$ points on circumference of circle $C_i$. If no three of all the points on three circles are collinear then number of triangles which can be formed using these points whose circumcentre does not lie on origin, is-