Question

Circle A has a center at `(7 ,2 )` and a radius of `8`. Circle B has a center at `(3 ,-3 )` and a radius of `6`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

circles overlap

Explanation:

First step is to find 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)=(7,2)" and " (x_2,y_2)= (3,-3)`

so d `= sqrt((3-7)^2 + (-3-2)^2) = sqrt41 ≈ 6.403`

radius of A + radius of B = 8 + 6 = 14

since sum of radii > distance between centres → overlap