Circle A has a center at #(1 ,5 )# and a radius of #3 #. Circle B has a center at #(2 ,-3 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?
They do not overlap.
To overlap the distance between centres has to be less than the sum of their radii.
Let the sum of radii be
Let the distance between radii be
Sum of radii
As we are comparing sizes the