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Circle Packing II

Published on Saturday, 14th June 2014, 01:00 pm; Solved by 349;
Difficulty rating: 45%

Problem 476

Let R(a, b, c) be the maximum area covered by three non-overlapping circles inside a triangle with edge lengths a, b and c.

Let S(n) be the average value of R(a, b, c) over all integer triplets (a, b, c) such that 1 ≤ a ≤ b ≤ c < a + b ≤ n

You are given S(2) = R(1, 1, 1) ≈ 0.31998, S(5) ≈ 1.25899.

Find S(1803) rounded to 5 decimal places behind the decimal point.