Question

Circle A has a center at `(8 ,4 )` and a radius of `3`. Circle B has a center at `(-2 ,-2 )` and a radius of `7`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

The circles do not overlap; they are separated by a distance of
`sqrt(136)-10~~1.66`

Explanation:

Distance between `(8,4)` and `(-2,-2)` is
`color(white)("XXX")sqrt((8-(-2))^2+(4-(-2))^2) = sqrt(10^2+6^2)=sqrt(136)`

If Circle A has a radius `3` and Circle B has a radius `7`

then along the line segment joining the centers of the two circles
the circles are separated by a distance of
`color(white)("XXX")sqrt(136)-(3+7) =sqrt(136)-10 ~~1.66`