Question

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?

Answer 1

No overlap. distance≈ 0.05

Explanation:

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)`

where`(x_1,y_1) , (x_2,y_2) " are the coords of 2 points "`

let`(x_1,y_1) = (8,-1) " and " (x_2,y_2_) = (-2,-2)`

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