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

Apr 23, 2016

Center of 1st Circle $\left(8 , 3\right)$
Radius of 1st Circle $\left({r}_{1} = 4\right)$
Center of 2nd Circle $\left(4 , 4\right)$
Radius of 2nd Circle $\left({r}_{2} = 3\right)$
Distance between their centers
$d = \sqrt{{\left(8 - 4\right)}^{2} + {\left(3 - 4\right)}^{2}} = \sqrt{17} \approx 4.12$
again sum of their radius $= {r}_{1} + {r}_{2} = 4 + 3 = 7$

Since ${r}_{1} + {r}_{2} > d$ the circles will not overlap
Their smallest distance ${d}_{s m} = {r}_{1} + {r}_{2} - d = 7 - 4.12 = 2.88$