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

Feb 17, 2016

Circles do not overlap and smallest distance between them is $5.6023$

#### Explanation:

Distance between $\left(2 , - 1\right)$ and $\left(- 3 , 6\right)$ is given by

$\sqrt{{\left(2 - \left(- 3\right)\right)}^{2} + {\left(\left(- 1\right) - 6\right)}^{2}}$ i.e. $\sqrt{{5}^{2} + {7}^{2}}$ i.e. $\sqrt{74} = 8.6023$

As radius of circle A is $2$ and of circle B is $1$ and

sum of radii i.e. $3$ is less than distance ($8.6023$) between them they do not overlap and smallest distance between them is $8.6023 - 3 = 5.6023$

As sum of the radius of the two circles at $8.4495$ is more than distance of $6.3246$ between them, circles do overlap,