Circle A has a center at #(3 ,7 )# and a radius of #2 #. Circle B has a center at #(4 ,-1 )# and a radius of #6 #. Do the circles overlap? If not, what is the smallest distance between them?

1 Answer
Feb 18, 2016

The circles do not overlap;
there is a minimum distance of (approximately) #0.06# between them

Explanation:

The distance between the centers of A and B is
#color(white)("XXX")sqrt((3-4)^2+(7-(-0))^2) = sqrt(65) ~~8.06#

Considering the line segment which joins the two centers
#color(white)("XXX")#Circle A covers 2 units of this line segment
#color(white)("XXX")#Circle B covers 6 units of this line segment.

Together the two circles cover #(2+6)=8# units of the line segment which is #8.06# long; leaving a distance of #0.06# between the two circles.