# Circle A has a center at (7 ,1 ) and a radius of 1 . Circle B has a center at (2 ,-3 ) and a radius of 2 . Do the circles overlap? If not, what is the smallest distance between them?

Dec 27, 2016

No overlap of the circles. smallest distance $= 3.403$

#### Explanation:

Given :
Circle $A \left(7 , 1\right) , {r}_{A} = 1$,
Circle $B \left(2 , - 3\right) , {r}_{B} = 2$.
Distance between center points of the two circles :
$D = \sqrt{{\left(7 - 2\right)}^{2} + \left(1 - {\left(- 3\right)}^{2}\right)} = 6.403$
As $D \left(6.403\right)$ is greater than the sum of the two radii $\left({r}_{A} + {r}_{B} = 1 + 2 = 3\right)$, the two circles do not overlap, as shown in the diagram.

Smallest distance $S = D - \left({r}_{A} + {r}_{B}\right)$
$\implies S = 6.403 - \left(1 + 2\right) = 3.403 , \left(3 \mathrm{dp}\right)$