Question

Circle A has a center at `(7 ,1 )` and a radius of `1`. Circle B has a center at `(2 ,-3 )` and a radius of `2`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

No overlap of the circles. smallest distance `=3.403`

Explanation:

Given :
Circle `A (7,1), r_A=1`,
Circle `B(2,-3), r_B=2`.
Distance between center points of the two circles :
`D=sqrt((7-2)^2+(1-(-3)^2))=6.403`
As `D (6.403)` is greater than the sum of the two radii `(r_A+r_B=1+2=3)`, the two circles do not overlap, as shown in the diagram.

Smallest distance `S = D- (r_A+r_B)`
`=> S=6.403-(1+2)=3.403, (3dp)`