Question

Circle A has a center at `(2 ,-7 )` and a radius of `2`. Circle B has a center at `(-3 ,6 )` and a radius of `1`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

no overlap , ≈ 10.928

Explanation:

What we have to do here is compare the distance (d) between the centres with the sum of the radii.

• If sum of radii > d , then circles overlap

• If sum of radii < d , then no overlap

To calculate d , use the `color(blue)"distance formula"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2))color(white)(a/a)|)))`
where `(x_1,y_1)" and " (x_2,y_2)" are 2 points"`

let `(x_1,y_1)=(2,-7)" and " (x_2,y_2)=(-3,6)`

`d=sqrt((-3-2)^2+(6+7)^2)=sqrt(25+169)≈13.928`

radius of A + radius of B = 2 + 1 = 3

Since sum of radii < d , there is no overlap.

smallest distance between them = 13.928 - 3 =10.928
graph{(y^2+14y+x^2-4x+49)(y^2-12y+x^2+6x+44)=0 [-20, 20, -10, 10]}