Question

Circle A has a radius of `1` and a center at `(3 ,3 )`. Circle B has a radius of `3` and a center at `(6 ,4 )`. If circle B is translated by `<-3 ,4 >`, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Answer 1

Yes they do, because the distance between the two circle centres `CC'=3` is lower than the sum of both radii `R+R'=4`

Explanation:

The circle A has equation `(x-3)^2+(y-3)^2=1` with centre `C(3;3)` and radius `R=1`, whereas the circle B has equation `(x-6)^2+(y-4)^2=9` with radius `R'=3`.
If we translate the second circle by the vector `(-3,4)` the new equation of B circle is `(x-3)^2+y^2=9` and centre `C'(3;0)` and `R'=3`
The distance between the two centres is `CC'=root2((3-3)^2+(3-0)^2)=3`. As the `CC'` is less than the sum of the two radius we can deduce that the two circles overlap