# Circle A has a center at (5 ,-2 ) and a radius of 2 . Circle B has a center at (4 ,6 ) and a radius of 4 . Do the circles overlap? If not what is the smallest distance between them?

Mar 14, 2016

no overlap , d ≈ 2.062

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

let $\left({x}_{1} , {y}_{1}\right) = \left(5 , - 2\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(4 , 6\right)$

hence  d = sqrt((4-5)^2 + (6-(-2))^2) = sqrt65 ≈ 8.062

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

since sum of radii < distance between centres , no overlap

and distance between A and B ≈ 8.062 - 6 ≈ 2.062