# Circle A has a center at (9 ,8 ) and a radius of 2 . Circle B has a center at (-8 ,3 ) and a radius of 1 . Do the circles overlap? If not, what is the smallest distance between them?

Mar 9, 2016

no overlap , 14.72

#### Explanation:

First step is to calculate the distance between the centres using the $\textcolor{b l u e}{\text{ distance formula }}$

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

where$\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 coord points }$

let(x_1,y_1)=(9,8)" and (x_2,y_2)=(-8,3)

$d = \sqrt{{\left(- 8 - 9\right)}^{2} + {\left(3 - 8\right)}^{2}} = \sqrt{{\left(- 17\right)}^{2} + {\left(- 5\right)}^{2}}$

d = sqrt314 ≈ 17.72