Question

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

Answer 1

They do not overlap
Smallest distance `=0`, they are tangent to each other.

Explanation:

Center to center distance `=sqrt((x_a-x_b)^2+(y_a-y_b)^2)`
`=sqrt((0)^2+(-5)^2)=5`

Sum of radii `=r_a+r_b=3+2=5`

God bless....I hope the explanation is useful.