Question

Circle A has a center at `(5 ,-2 )` and a radius of `2`. Circle B has a center at `(4 ,6 )` and a radius of `4`. Do the circles overlap? If not what is the smallest distance between them?

Answer 1

no overlap , d ≈ 2.062

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)=(5,-2)" and " (x_2,y_2)=(4,6)`

hence `d = sqrt((4-5)^2 + (6-(-2))^2) = sqrt65 ≈ 8.062`

radius of A + radius of B = 2 + 4 = 6

since sum of radii < distance between centres , no overlap

and distance between A and B ≈ 8.062 - 6 ≈ 2.062