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

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

Consider the given equation of circle

${\mathrm{x}}^2+{\mathrm{y}}^2-10\mathrm{x}-10\mathrm{y}+41=0$

Then, centre ${\mathrm{C}}_1\equiv (5,5)$ and radius r₁ = 3

${\mathrm{x}}^2+{\mathrm{y}}^2-16\mathrm{x}-10\mathrm{y}+80=0$

C₂ = (8, 5) and radius r₂ = 3

$\because$ Distance between centres = 3. Thus both circles pass through the centre of each other, have two intersection point and distance between two centres is average of radii of both the circles