# Circle A has a center at (-1 ,-4 ) and a radius of 3 . Circle B has a center at (-1 ,1 ) and a radius of 2 . Do the circles overlap? If not, what is the smallest distance between them?

They do not overlap
Smallest distance $= 0$, they are tangent to each other.

#### Explanation:

Center to center distance $= \sqrt{{\left({x}_{a} - {x}_{b}\right)}^{2} + {\left({y}_{a} - {y}_{b}\right)}^{2}}$
$= \sqrt{{\left(0\right)}^{2} + {\left(- 5\right)}^{2}} = 5$

Sum of radii $= {r}_{a} + {r}_{b} = 3 + 2 = 5$

God bless....I hope the explanation is useful.