Question

Circle A has a center at `(5 ,-4 )` and a radius of `7`. Circle B has a center at `(-6 ,-8 )` and a radius of `5`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

overlap

Explanation:

First step is to calculate the distance between the centres using the `color(blue)" distance formula "`

`d = sqrt((x_2 - x_!)^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)`

`d = sqrt((-6-5)^2 + (-8-(-4))^2) = sqrt((-11)^2 + (-4)^2)`

`= sqrt(121 + 16) = sqrt137 ≈ 11.7`

now, radius of A + radius of B = 7 + 5 = 12

Since , sum of radii > distance between centres , circles
overlap.