Circle A has a center at #(-2 ,-1 )# and a radius of #3 #. Circle B has a center at #(-8 ,3 )# and a radius of #2 #. Do the circles overlap? If not what is the smallest distance between them?

1 Answer
Burglar
Jun 19, 2016

They do not overlap and the distance is #2.21#.

Explanation:

enter image source here

Two circles overlaps if the distance between the two centers is smaller or equal to the sum of the radius. It is quite clear looking at the picture. We can calculate the distance between the centers:

#d=sqrt((-2-(-8))^2+(-1-3)^2)#

#=sqrt(6^2+(-4)^2)=sqrt(36+16)=sqrt(52)\approx7.21#.

The sum of the two radius is #r_A+r_B=3+2=5#, then the two circles will not overlap.
The distance between them is the difference between the distance of the centers and the sum of the two radius:

#7.21-5=2.21#.

Related questions
See all questions in Distance between Points
Impact of this question
2153 views around the world
You can reuse this answer
Creative Commons License