Question

Circle A has a radius of `2` and a center of `(8 ,2 )`. Circle B has a radius of `4` and a center of `(2 ,3 )`. If circle B is translated by `<-1 ,5 >`, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Answer 1

no overlap , d ≈ 3.22

Explanation:

A translation does not change the shape of a figure , only it's position.

Under a translation of `((-1),(5))`

centre of B (2,3) → (2-1 , 3+5) → (1,8)

We now require to calculate the distance between the centres of A and B 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)=(8,2)" and " (x_2,y_2)=(1,8)`

`d = sqrt((1-8)^2 + (8-2)^2) = sqrt(49+36) = sqrt85 ≈ 9.22`

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

since sum of radii < distance between centres , no overlap

and distance between them = 9.22 - 6 = 3.22