# Circle A has a center at (7 ,2 ) and a radius of 8 . Circle B has a center at (3 ,-3 ) and a radius of 6 . Do the circles overlap? If not, what is the smallest distance between them?

Mar 13, 2016

circles overlap

#### Explanation:

First step is to find 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 $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 coordinate points }$

let $\left({x}_{1} , {y}_{1}\right) = \left(7 , 2\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(3 , - 3\right)$

so d  = sqrt((3-7)^2 + (-3-2)^2) = sqrt41 ≈ 6.403

radius of A + radius of B = 8 + 6 = 14

since sum of radii > distance between centres → overlap