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

Mar 6, 2016

the circles will overlap

#### Explanation:

The radius of circle A is ${r}_{A} = 8$ unit
The radius of circle B is ${r}_{B} = 4$ unit
The distance between their centers ${d}_{A B} = \sqrt{{\left(- 8 + 3\right)}^{2} + {\left(8 - 3\right)}^{2}} = 5 \sqrt{2}$unit
It is obvious that
${r}_{A} + {r}_{B} > {d}_{A B}$
Hence the circles will overlap
Further
If ${r}_{A} + {r}_{B} = {d}_{A B}$ then they would touch
AND
${r}_{A} + {r}_{B} < {d}_{A B}$ then they would not touch or overlap
In that case the would have minimum distance
${d}_{\min} = {d}_{A B} - \left({r}_{A} + {r}_{B}\right)$

Is it OK?