Circle A has a center at (5 ,4 )(5,4) and a radius of 3 3. Circle B has a center at (6 ,-8 )(6,8) and a radius of 2 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~=7.04214557.042.

Explanation:

The distance between centers is:
d=sqrt((6-5)^2+(-8-4)^2)=sqrt(1+144)=sqrt(145)~=12.042d=(65)2+(84)2=1+144=14512.042

r_1+r_2=3+2=5r1+r2=3+2=5

d>r_1+r_2d>r1+r2

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=dr1r2=14557.042