# Circle A has a center at (-4 ,-1 ) and a radius of 3 . Circle B has a center at (1 ,3 ) and a radius of 2 . Do the circles overlap? If not what is the smallest distance between them?

smallest distance = $1.40312$
Circle $A$ center is located at ${c}_{A} = \left(- 4 , - 1\right)$
Circle $B$ center is located at ${c}_{B} = \left(1 , 3\right)$
Their distance is ${d}_{A B} = \left\lVert {c}_{A} - {c}_{B} \right\rVert = 6.40312$. If they were tangents their center distance will be ${r}_{A} + {r}_{B}$. Where ${r}_{A} , {r}_{B}$ are their respective radius. In the present case we have
${d}_{A B} > {r}_{A} + {r}_{B}$ so their smallest distance is given by ${d}_{A B} - \left({r}_{A} + {r}_{B}\right) = 1.40312$