Question

Circle A has a center at `(5 ,4 )` and a radius of `3`. Circle B has a center at `(6 ,-8 )` and a radius of `2`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

They don't overlap. The smallest distance between them is `sqrt(145)-5~=7.042`.

Explanation:

The distance between centers is:
`d=sqrt((6-5)^2+(-8-4)^2)=sqrt(1+144)=sqrt(145)~=12.042`

`r_1+r_2=3+2=5`

`d>r_1+r_2`

Since the distance between centers is longer than the sum of the radii, they don't overlap and the smallest distance between these circles is
`=d-r_1-r_2=sqrt(145)-5~=7.042`