Biggest Inscribed Ellipse#5611
Definition. If \mathbf{F_1} and \mathbf{F_2} are two points and is a positive number such that 2R > |\mathbf{F_1F_2}|, then an ellipse can be defined as the set of all points such that |\mathbf{F_1M}| + |\mathbf{F_2M}| \leq 2R.
You are required to inscribe an ellipse of the largest possible area into the given triangle.
The input contains three integers , , : the lengths of the triangle's sides (1 \leq a \leq b \leq c \leq 1000, c < a + b).
Output the numbers |\mathbf{F_1F_2}| and that define the required ellipse. Your answer must have an absolute or relative error of at most 10^{-6}. It is guaranteed that the answer is unique.
Example 1