Circle A has a center at #(5 ,4 )# and an area of #4 pi#. Circle B has a center at #(2 ,8 )# and an area of #9 pi#. Do the circles overlap? If not, what is the shortest distance between them?
The circles touch, but they do not overlap. The shortest distance between them is
The distance between the points
If the circles overlap, the sum of their radii will be greater than
Since the sum of the radii matches the distance between the two circles' centers, the circles touch, but they do not overlap. The shortest distance between the two circles is