Circle A has a center at (5 ,4 ) and a radius of 3 . Circle B has a center at (6 ,-8 ) and a radius of 2 . Do the circles overlap? If not, what is the smallest distance between them?

1 Answer
Feb 9, 2016

They don't overlap. The smallest distance between them is sqrt(145)-5~=7.042.

Explanation:

The distance between centers is:
d=sqrt((6-5)^2+(-8-4)^2)=sqrt(1+144)=sqrt(145)~=12.042

r_1+r_2=3+2=5

d>r_1+r_2

Since the distance between centers is longer than the sum of the radii, they don't overlap and the smallest distance between these circles is
=d-r_1-r_2=sqrt(145)-5~=7.042