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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.

Time limit 1 second
Memory limit 64 MiB
Input example #1
1 1 1
Output example #1
0.0000000000 0.2886751346
Author M.Rubinchik, P.Ageev
Source 2013 Petrozavodsk, Winter, Ural FU contest, Kontur Cup, Problem C