Question:
If one of the diameters of the circle $x^{2}+y^{2}-2 x-6 y+6=0$ is a chord of another circle ' $C$ ', whose center is at $(2,1)$, then its radius is
Solution:
$x^{2}+y^{2}+2 x-6 y+6=0$
center $(1,3)$
radius $=2$
distance between $(1,3)$ and $(2,1)$ is $\sqrt{5}$
$\therefore(\sqrt{5})^{2}+(2)^{2}=r^{2}$
$\Rightarrow \mathrm{r}=3$