# Circle A has a radius of 3  and a center at (3 ,3 ). Circle B has a radius of 5  and a center at (1 ,7 ). If circle B is translated by <2 ,4 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?

The center of B after transformation is $\left(3 , 11\right)$. The new distance between the two centers is $\sqrt{{\left(3 - 3\right)}^{2} + {\left(11 - 4\right)}^{2}} = 7$. The sum of the radii is $3 + 5 = 8$. Since Distance between centers $<$ Sum of radii, the two circles overlap.