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

Sep 9, 2016

Yes, the circles do overlap. See explanation.

#### Explanation:

Circle A, center(2,3), r=2.
Circle B, center(4,2), r=3

In the graph above, the red one is Circle A, and the green one Circle B. The white line is the distance between the two center points.

Distance between the centers of the two circles =
$\sqrt{{\left(4 - 2\right)}^{2} + {\left(2 - 5\right)}^{2}} = \sqrt{{2}^{2} + {3}^{2}} = \sqrt{13} = 3.61$

As the distance between the two centers (3.61) is smaller than the sum of the two radii (2+3=5), the two circles overlap.