Question

Circle A has a center at `(-6 ,2 )` and a radius of `8`. Circle B has a center at `(2 ,-5 )` and a radius of `3`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

circles overlap.

Explanation:

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

`d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2))`

let`(x_1,y_1) = (-6,2)" and "(x_2,y_2) = (2,-5)`

`rArr d = sqrt((2+6)^2+(-5-2)^2) = sqrt(64+49)=sqrt113 ≈ 10.63`

now radius of A + radius of B = 8 + 3 = 11

since 11 > 10.63 circles overlap.