Choose the incorrect statement about the two circles whose equations are given below:
\[x^2+y^2-10x-10y+41=0\quad\text{and}\quad x^2+y^2-16x-10y+80=0\]
Solutions · 1
Official solution
Circle 1: centre (5,5), r1=3. Circle 2: centre (8,5), r22=64+25−80=9⇒r2=3.
Distance between centres =3. Since each centre lies exactly on the other circle (radius 3 from the other's centre), each circle passes through the other's centre, and they intersect in two points --- but neither centre lies *inside* the other circle (it lies exactly on it). Hence B is incorrect.