Question

Circle A has a center at `(5 ,4 )` and a radius of `3`. Circle B has a center at `(6 ,-8 )` and a radius of `1`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

no overlap ,d ≈ 8.042 units

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)=(5,4)" and " (x_2,y_2)=(6,-8)`

`rArr d = sqrt((6-5)^2 +(-8-4)^2) = sqrt145 ≈ 12.042`

now: radius of A + radius of B = 3 + 1 = 4

since 4 < 12.042 the circles do not overlap

and distance between them = 12.042 - 4 = 8.042