# Circle A has a center at (1 ,3 ) and an area of 18 pi. Circle B has a center at (11 ,7 ) and an area of 54 pi. Do the circles overlap?

##### 1 Answer
Sep 9, 2016

Yes, the circles do overlap.

#### Explanation:

Circle A, center (1,3), $r = \sqrt{18}$, $\left(\pi {r}^{2} = 18 \pi \implies r = \sqrt{18}\right)$
Circle B, center (11,7), $r = \sqrt{54}$

distance between the two center points
$= \sqrt{{\left(7 - 3\right)}^{2} + {\left(11 - 1\right)}^{2}} = \sqrt{116} = 10.77$

As the distance between the two center points is smaller than the sum of the two radii $\left(\sqrt{18} + \sqrt{54} = 11.59\right)$, the two circles do overlap.

Here's an image of the two circles