Question

Circle A has a center at `(-4 ,2 )` and a radius of `3`. Circle B has a center at `(1 ,9 )` and a radius of `2`. Do the circles overlap? If not what is the smallest distance between them?

Answer 1

no overlap , ≈ 3.6

Explanation:

What we have to do here is to 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"`

The 2 points here are (-4 ,2) and (1 ,9)

`d=sqrt((1+4)^2+(9-2)^2))=sqrt74≈8.6`

radius of A + radius of B = 3 + 2 = 5

Since sum of radii < d , then no overlap

distance = d - sum of radii = 8.6 - 5 = 3.6
graph{(y^2-4y+x^2+8x+11)(y^2-18y+x^2-2x+78)=0 [-20, 20, -10, 10]}