# Circle A has a center at (9 ,-2 ) and a radius of 4 . Circle B has a center at (-2 ,6 ) and a radius of 2 . Do the circles overlap? If not, what is the smallest distance between them?

Mar 9, 2016

no overlap , 7.6

#### Explanation:

The first step is to calculate the distance betwee 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$\left({x}_{1} , {y}_{1}\right) = \left(9 , - 2\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(- 2 , 6\right)$

substitute values into distance formula

d=sqrt((-2-9)^2+(6-(-2))^2) = sqrt(121+64)=sqrt185 ≈ 13.6

now radius of circle A + radius of circle B = 4+2 = 6

Since 6 < 13.6 there is no overlap

and distance between them is 13.6 - 6 = 7.6