# Circle A has a center at (1 ,5 ) and a radius of 3 . Circle B has a center at (4 ,-2 ) and a radius of 5 . Do the circles overlap? If not, what is the smallest distance between them?

Feb 4, 2016

The 2 circles overlap.

#### Explanation:

The key to the problem is this: If the distance between the centers of the 2 circles is greater than the sum of the 2 radii, then the 2 circles do not overlap.

The distance between the centers of the 2 circles can be found using the Pythagoras Theorem.

$\sqrt{{\left(4 - 1\right)}^{2} + {\left(- 2 - 5\right)}^{2}} = \sqrt{58} < 8 = 3 + 5$

The 2 circles overlap.