Question

Circle A has a center at `(6 ,4 )` and a radius of `3`. Circle B has a center at `(-3 ,3 )` and a radius of `2`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

no overlap , d ≈ 4.055

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)=(6,4)" and (x_2,y_2)=(-3,3)`

`rArr d = sqrt((-3-6)^2 + (3-4)^2) = sqrt(81+1) ≈ 9.055`

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

since sum of radii < distance between centres
The circles do not overlap and distance between them
is d ≈ 9.055 - 5 = 4.055