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

Circles do not overlap. Smallest distance ${d}_{b} = 5 \sqrt{2} - 7 = 0.071067 \text{ }$unit

#### Explanation:

Compute the distance $d$ between centers using distance formula

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

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

$d = 5 \sqrt{2}$

${r}_{t} = {r}_{1} + {r}_{2} = 4 + 3 = 7$
Distance ${d}_{b}$ between circles
${d}_{b} = d - {r}_{t} = 5 \sqrt{2} - 7 = 0.071067 \text{ }$