Circle A has a center at #(-2 ,-4 )# and a radius of #2 #. Circle B has a center at #(-3 ,2 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?
The circles overlap
Circle A's center:
Circle B's center:
Distance between centers:
Along the line segment joining the two centers:
circle A covers 2 units and
circle B covers 5 units
for a total of 7 units covered by the circles.
But the line segment joining the two circles only has a length of
So the circles must overlap (by about