# Circle A has a center at (8 ,1 ) and an area of 81 pi. Circle B has a center at (4 ,2 ) and an area of 36 pi. Do the circles overlap? If not, what is the shortest distance between them?

Sep 8, 2016

Circle A and Circle do overlap.

#### Explanation:

Circle A, centered at (8,1), area $= \pi {r}^{2} = 81 \pi \implies r = 9$

Circle B, centered at (4,2), area $= \pi {r}^{2} = 36 \pi \implies r = 6$

distance between the two center points
$= \sqrt{{\left(2 - 1\right)}^{2} + {\left(4 - 8\right)}^{2}} = \sqrt{17} = 4.123$

As the distance between the two centers (4.123) is smaller than the sum of the two radii (9+6=15), the two circle overlaps.