# 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 16 pi. Do the circles overlap? If not, what is the shortest distance between them?

Nov 11, 2016

They do not overlap. The closest distance is $d = \sqrt{58} - 6 \approx 1.6$

#### Explanation:

The radius of circle A is: 2
The radius of circle B is: 4

The distance, d, between the centers is:

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

$d = \sqrt{{\left(3\right)}^{2} + {\left(- 7\right)}^{2}}$

$d = \sqrt{58}$

This is greater than the sum of the radii, thefore, the circles do not overlap.

Here is a graph of the two circles:

The closest distance is $d = \sqrt{58} - 6 \approx 1.6$