Search ProblemsRSS Feed
projecteuler.net

Tangent Circles

Problem 510 Published on Saturday, 4th April 2015, 04:00 pm; Solved by 783;
Difficulty rating: 30%

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.

p510_tangent_circles.png

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).