Question

Circle A has a center at `(2 ,3 )` and a radius of `1`. Circle B has a center at `(0 ,-2 )` and a radius of `4`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

no overlap , d ≈ 0.385

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 coordinate points "`

let `(x_1,y_1)=(2,3)" and " (x_2,y_2)= (0,-2)`

`rArr d = sqrt((0-2)^2+(-2-3)^2) = sqrt(4+25) ≈ 5.385`

radius of A + radius of B = 1 + 4 = 5

since : radius of A + radius of B < distance between centres
there is no overlap.

distance between circles ≈ 5.385 - 5 ≈ 0.385