# Circle A has a center at (2 ,3 ) and a radius of 5 . Circle B has a center at (3 ,8 ) and a radius of 1 . Do the circles overlap? If not what is the smallest distance between them?

Feb 4, 2016

If the two circles touched at a single point , then the distance between the centers would be $5 + 1 = 6$ and the distance between the circles would be zero.

#### Explanation:

Using the distance formula, the actual distance between the two centers is:

$\sqrt{{\left(8 - 3\right)}^{2} + {\left(3 - 2\right)}^{2}} = \sqrt{26} \approx 5.1$

Since the distance $5.1 < 6$, the two circles must overlap !

Hope that helped