Question

Circle A has a center at `(3 ,2 )` and a radius of `2`. Circle B has a center at `(1 ,3 )` and a radius of `4`. 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 the coords of 2 points "`

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

`d = sqrt((1-3)^2 + (3-2)^2) = sqrt(4+1) = sqrt5 ≈ 2.236`

radius of A + radius of B = 2 + 4 = 6

since 6 > 2.236 , circles will overlap