Circle A has a center at #(3 ,5 )# and a radius of #1 #. Circle B has a center at #(-1 ,1 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?

1 Answer
Feb 2, 2016

The circles do not overlap.
The minimum distance between them is #4sqrt(2)-5 ~~0.66#

Explanation:

The distance between the centers of the two circles is
#color(white)("XXX")sqrt((3-(-1))^2+(5-1)^2) = 4sqrt(2) ~~5.66#

Consider a line segment joining the two centers.
The distance from A's center to A's circumference is #1#.
The distance from B's center to B's circumference is #4#.
The sum of the radial distances is #1+4=5# which is less than the length of the line segment #4sqrt(2)~~5.66#
by #5.66-5=0.66# (units).
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