2013 Petrozavodsk, February 2
Biggest Inscribed Ellipse
Definition. If F1, F2 are two points and R is a positive number such that 2R > |F1F2|, then an ellipse can be defined as a set of all points M such that |F1M| + |F2M| ≤ 2R.
Your task is to inscribe an ellipse of the biggest possible area into the given triangle.
The input contains three integers a, b, c: lengths of the triangle’s sides (1 ≤ a ≤ b ≤ c ≤ 1000; c < a + b).
Output numbers |F1F2| and R, which describe the requested ellipse. The answer must be given with absolute or relative error not exceeding 10−6. It is guaranteed that the answer is unique.
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