# Circle A has a center at (5 ,-2 ) and a radius of 2 . Circle B has a center at (2 ,-1 ) and a radius of 3 . Do the circles overlap? If not what is the smallest distance between them?

Yes, the circles overlap.

#### Explanation:

compute the center to center disance

Let ${P}_{2} \left({x}_{2} , {y}_{2}\right) = \left(5 , - 2\right)$ and ${P}_{1} \left({x}_{1} , {y}_{1}\right) = \left(2 , - 1\right)$

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

$d = \sqrt{{\left(5 - 2\right)}^{2} + {\left(- 2 - - 1\right)}^{2}}$

d=sqrt((3^2+(-1)^2)

$d = \sqrt{10} = 3.16$

Compute the sum of the radii

${r}_{t} = {r}_{1} + {r}_{2} = 3 + 2 = 5$

${r}_{1} + {r}_{2} > d$

the circles overlap

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