The locus of the centre of a variable circle touching two circles of radius $r_1$ and $r_2$ externally which also touch each other externally is a conic. The eccentricity of the conic, if $\frac{r_1}{r_2}=3+2\sqrt{2}$ is

STATEMENT-$1$: If three circles which are such that their centres are non-collinear, then exactly one circle exists which cuts the three circles orthogonally.

STATEMENT-$2$: Radical axis for two intersecting circles is the common chord.

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

$x^2+y^2-10x-10y+41=0$

$x^2+y^2-22x-10y+137=0$