Question

Circle A has a radius of `3` and a center at `(3 ,3 )`. Circle B has a radius of `5` and a center at `(1 ,7 )`. If circle B is translated by `<2 ,4 >`, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Answer 1

Yes, they do overlap.

Explanation:

The center of B after transformation is `(3,11)`. The new distance between the two centers is `sqrt((3-3)^2+(11-4)^2)=7`. The sum of the radii is `3+5=8`. Since Distance between centers `<` Sum of radii, the two circles overlap.