Circle A has a center at (8 ,-1 ) and a radius of 3 . Circle B has a center at (-2 ,-2 ) and a radius of 7 . Do the circles overlap? If not, what is the smallest distance between them?

Mar 5, 2016

No overlap. distance≈ 0.05

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$\left({x}_{1} , {y}_{1}\right) , \left({x}_{2} , {y}_{2}\right) \text{ are the coords of 2 points }$

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

hence d=sqrt((-2-8)^2+(-2+1)^2)=sqrt(101) ≈ 10.05

now: radius of A + radius of B = 3+7 = 10

thus : 10 < 10.05 so no overlap and distance between them is

10.05 -10 = 0.05