# Circle A has a center at (5 ,3 ) and a radius of 1 . Circle B has a center at (0 ,-5 ) and a radius of 2 . Do the circles overlap? If not, what is the smallest distance between them?

Feb 23, 2016

Circles do not overlap each other. The smallest distance between the circles is $6.434$.

#### Explanation:

Distance between two centers $\left(5 , 3\right)$ and (0,−5) is given by

$\sqrt{{\left(- 5 - 3\right)}^{2} + {\left(0 - 5\right)}^{2}}$ or sqrt(8^2+5^2 or $\sqrt{89} = 9.434$.

As sum of the radii of two circles is $1 + 2 = 3$ and is less than $9.434$ which is distance between their centers, circles do not overlap each other.

The smallest distance between the circles is $9.434 - 3 = 6.434$.