Question

Circle A has a radius of `2` and a center of `(8 ,6 )`. Circle B has a radius of `3` and a center of `(2 ,3 )`. If circle B is translated by `<-1 ,2 >`, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Answer 1

no overlap , d ≈ 2.07

Explanation:

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

Under a translation of `((-1),(2))`

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

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)=(8,6)" and " (x_2,y_2)=(1,5)`

d `= sqrt((1-8)^2 + (5-6)^2) = sqrt(49 + 1) = sqrt50 ≈ 7.07`

now, radius of A + radius of B = 2 + 3 = 5

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

and distance (d) between circles = 7.07 - 5 = 2.07