# Circle A has a center at (5 ,4 ) and a radius of 3 . Circle B has a center at (6 ,-8 ) and a radius of 1 . Do the circles overlap? If not, what is the smallest distance between them?

Mar 11, 2016

no overlap ,d ≈ 8.042 units

#### Explanation:

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

d =sqrt((x_2-x_1)^2 + (y_2-y_1)^2

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

let $\left({x}_{1} , {y}_{1}\right) = \left(5 , 4\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(6 , - 8\right)$

rArr d = sqrt((6-5)^2 +(-8-4)^2) = sqrt145 ≈ 12.042

now: radius of A + radius of B = 3 + 1 = 4

since 4 < 12.042 the circles do not overlap

and distance between them = 12.042 - 4 = 8.042