# Circle A has a center at (3 ,1 ) and a radius of 6 . Circle B has a center at (-2 ,1 ) and a radius of 3 . Do the circles overlap? If not, what is the smallest distance between them?

Feb 8, 2016

The circles overlap.

#### Explanation:

To answer your question, let's compute the distance between the two centers $\left(3 , 1\right)$ and $\left(- 2 , 1\right)$.

The distance can be computed due to Pythagorean theorem as follows:

$d = \sqrt{{\left(3 - \left(- 2\right)\right)}^{2} + {\left(1 - 1\right)}^{2}} = \sqrt{25 + 0} = 5$

As the first circle has a radius of $6$ which is bigger than the distance between the two centers, you know that the two circles overlap.

graph{((x-3)^2 + (y - 1)^2 - 36) * ((x+2)^2 + (y-1)^2 - 9) = 0 [-13.17, 15.31, -6.21, 8.03]}