# Problem 510: Tangent Circles

![graphic](img510.gif)

Circles A and B are tangent to each other and to line L at three
distinct points. Circle C is inside the space between A, B and L, and
tangent to all three. Let rA, rB and rC be the radii of A, B and C
respectively. Let S(n) = Σ rA + rB + rC, for 0 < rA ≤ rB ≤ n where
rA, rB and rC are integers. The only solution for 0 < rA ≤ rB ≤ 5 is
rA = 4, rB = 4 and rC = 1, so S(5) = 4 + 4 + 1 = 9. You are also given
S(100) = 3072. Find S(109).