# Circle A has a center at (6 ,4 ) and a radius of 3 . Circle B has a center at (-3 ,3 ) and a radius of 2 . Do the circles overlap? If not, what is the smallest distance between them?

Mar 24, 2016

no overlap , d ≈ 4.055

#### 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 (x_1,y_1)=(6,4)" and (x_2,y_2)=(-3,3)

rArr d = sqrt((-3-6)^2 + (3-4)^2) = sqrt(81+1) ≈ 9.055

now: radius A + radius B = 3 + 2 = 5

since sum of radii < distance between centres
The circles do not overlap and distance between them
is d ≈ 9.055 - 5 = 4.055