Question

Circle A has a center at `(-1 ,2 )` and a radius of `2`. Circle B has a center at `(5 ,-4 )` and a radius of `3`. Do the circles overlap? If not what is the smallest distance between them?

Answer 1

pl ,click the link

Explanation:

http://socratic.org/questions/circle-a-has-a-center-at-8-8-and-a-radius-of-8-circle-b-has-a-center-at-3-3-and-#235722

Answer 2

No overlap , distance ≈ 3.485

Explanation:

The first step is to calculate the distance between the centres using the `color(blue)" distance formula "`

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

let`(x_1,y_1)=(-1,2) " and " (x_2,y_2) = (5,-4)`

`rArrd = sqrt((5+1)^2 +(-4-2)^2) =sqrt(36+36)`

`= sqrt72 = 6sqrt2≈ 8.485`

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

since 5 < 8.485 there is no overlap.

and distance between them is 8.485 - 5 = 3.485