# Circle A has a center at (5 ,8 ) and an area of 18 pi. Circle B has a center at (3 ,1 ) and an area of 27 pi. Do the circles overlap?

The circles overlap

#### Explanation:

the distance from center to center
$d = \sqrt{{\left({x}_{a} - {x}_{b}\right)}^{2} + {\left({y}_{a} - {y}_{b}\right)}^{2}}$
$d = \sqrt{{\left(5 - 3\right)}^{2} + {\left(8 - 1\right)}^{2}}$
$d = \sqrt{4 + 49}$
$d = \sqrt{53} = 7.28011$

The sum of the radii of circle A and B
$S u m = \sqrt{18} + \sqrt{27}$
$S u m = 9.43879$

Sum of radii$>$distance between centers
conclusion: the circles overlap

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