# Circle A has a center at (5 ,4 ) and a radius of 9 . Circle B has a center at (1 ,-2 ) and a radius of 6 . Do the circles overlap? If not, what is the smallest distance between them?

Distance between center of Circle A at $\left(5 , 4\right)$ and center of Circle Bat $\left(1 , - 2\right)$ is given by
$\sqrt{{\left(5 - 1\right)}^{2} + {\left(4 - \left(- 2\right)\right)}^{2}}$ i.e. $\sqrt{{4}^{2} + {6}^{2}}$ i.e. $\sqrt{52} = 7.2111$
As sum of the radii of the two circles at $15$ is more than distance between their centers which is $7.2111$, circles do overlap,