Let $S$ be the set of circles in the coordinate plane that are tangent to each of the three circles with equations $(x-1{)}^2+(y-2{)}^2=1$, $(x-1{)}^2+(y-2{)}^2=49$, and $(x-5{)}^2+(y-2{)}^2=9$. What is the sum of the areas of all circles in $S$?