# Circle A has a center at (9 ,4 ) and a radius of 3 . Circle B has a center at (-1 ,6 ) and a radius of 5 . Do the circles overlap? If not, what is the smallest distance between them?

Dec 7, 2017

They do not overlap - min distance is about 2.2

#### Explanation:

If the distance between the two centers is less than the sum of their radii, then they overlap.

We find the distance between the centers with the Pythagorean theorem:

$d = \sqrt{{\left(9 - \left(- 1\right)\right)}^{2} + {\left(4 - 6\right)}^{2}}$

$= \sqrt{100 + 4}$

= 10.2 (rounding)

$10.2 - 8 = 2.2$ (rounding)