# Circle A has a center at (-6 ,2 ) and a radius of 8 . Circle B has a center at (2 ,-5 ) and a radius of 3 . Do the circles overlap? If not, what is the smallest distance between them?

Mar 6, 2016

circles overlap.

#### Explanation:

The 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))

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

rArr d = sqrt((2+6)^2+(-5-2)^2) = sqrt(64+49)=sqrt113 ≈ 10.63

now radius of A + radius of B = 8 + 3 = 11

since 11 > 10.63 circles overlap.