Question

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

Answer 1

no overlap , d ≈ 3.32

Explanation:

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

Under a translation of `((-2),(5))`

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

Require to calculate the distance between the centres of A and B , using the `color(blue)" distance formula "`

`color(red)(|bar(ul(color(white)(a/a)color(black)( d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2))color(white)(a/a)|)))`
where `(x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points "`

let `(x_1,y_1)=(1,2)" and " (x_2,y_2)=(3,8)`

`d = sqrt((3-1)^2 + (8-2)^2)=sqrt(4+36)=sqrt40 ≈ 6.32`

now radius of A + radius of B = 1+2 =3

Since sum of radii < distance between centres , no overlap.

and distance between circles = 6.32 - 3 = 3.32