# Circle A has a center at (5 ,1 ) and an area of 4 pi. Circle B has a center at (2 ,8 ) and an area of 9 pi. Do the circles overlap? If not, what is the shortest distance between them?

The circles do not overlap
Shortest distance$= d - {r}_{a} - {r}_{b} = \sqrt{58} - 5 = 2.615$

#### Explanation:

Compute first the distance between the centers

$d = \sqrt{{\left(5 - 2\right)}^{2} + {\left(1 - 8\right)}^{2}}$

d=sqrt((3^2+(-7)^2)

d=sqrt((9+49)
$d = \sqrt{58} = 7.615$

Compute the sum of the radius

${r}_{a} + {r}_{b} = \sqrt{4} + \sqrt{9} = 5$

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