Three circles with radii 0<c<b<a are tangent to each other and to a line as shown in the diagram below.
(a) Let radii a=16 and b=4. Find the distance d between the points of tangency of these two circles to the line.
(b) Let radii a=16 and b=4. Find the radius c.
(c) The configuration is called nice if \mathrm{a}, \mathrm{b}, and \mathrm{c} are all integers. Among all nice configurations, find the smallest possible value of c.