# Circle A has a center at (8 ,-4 ) and a radius of 2 . Circle B has a center at (4 ,3 ) and a radius of 4 . Do the circles overlap? If not what is the smallest distance between them?

Dec 22, 2016

The circles do not overlap.
The smallest distance is $= 2.1$

#### Explanation:

The distance between the centre is ${d}_{c}$

$\sqrt{{\left(8 - 4\right)}^{2} + {\left(- 4 - 3\right)}^{2}}$

$= \sqrt{16 + 49} = \sqrt{65}$

The sum of the radii is ${r}_{A} + {r}_{B}$

$= 4 + 2 = 6$

As ${d}_{c} > \left({r}_{A} + {r}_{B}\right)$, the circles do not overlap.

The smallest distance between the cicles is

$= \sqrt{65} - 6 = 8.1 - 6 = 2.1$

graph{((x-8)^2+(y+4)^2-4)((x-4)^2+(y-3)^2-16)(y-3+7/4(x-4))=0 [-14.24, 14.24, -7.12, 7.12]}