# Circle A has a center at (-6 ,4 ) and a radius of 8 . Circle B has a center at (2 ,-5 ) and a radius of 5 . Do the circles overlap? If not, what is the smallest distance between them?

Nov 26, 2016

$\text{overlap}$

#### Explanation:

$\text{distance between "O_1 " and } {O}_{2} :$

${O}_{1} {O}_{2} = d = \sqrt{{\left(2 + 6\right)}^{2} + \left(- 5 - 4\right)}$

$d = \sqrt{{8}^{2} + {\left(- 9\right)}^{2}}$

$d = \sqrt{64 + 81}$

$d = \sqrt{145}$

$d = 12.04$

$k = {r}_{1} + {r}_{2}$

$k = 8 + 5$

$k = 13$

$\text{so "d < k" 'overlap'}$