Question

Circle A has a center at `(9 ,8 )` and a radius of `2`. Circle B has a center at `(-8 ,3 )` and a radius of `1`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

no overlap , 14.72

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)" and " (x_2,y_2)" are 2 coord points "`

let`(x_1,y_1)=(9,8)" and (x_2,y_2)=(-8,3)`

`d = sqrt((-8-9)^2 +(3-8)^2)=sqrt((-17)^2+(-5)^2)`

`d = sqrt314 ≈ 17.72`

now radius of A = radius of B = 2+1=3

since 3 < 17.72 there is no overlap

distance between them is 17.72 - 3 = 14.72