5654번 - In-circles Again 다국어

In the figure below you can see triangle ABC and its in-circle (Circle that touches all the sides of a triangle internally). The radius of this in circle is r. Three other circles are drawn. Each of them touches two sides of this triangle and the in circle of ABC. The radiuses of these circles are r₁, r₂ and r₃.

Given the values of r, r₁, r₂ and r₃ you will have to find the area of triangle ABC.

The input file can contain up to 1000 lines of inputs. Each line contains four positive floatingpoint numbers which denotes the values of r, r₁, r₂ and r₃ respectively.

Input is terminated by a line containing four negative integers.

For each line of input produce one line of output. This line contains serial of output followed by a floating-point number which denotes the area of triangle ABC. This floating-point number may have two digits after the decimal point. You can assume that for the given values of r, r₁, r₂ and r₃ it will always be possible to construct a triangle ABC. If required you can assume that pi = 3.141592653589793 and also use double precision floating-point numbers for floating-point calculations. You can assume that there will be no such input for which small precision errors will cause difference in printed output. Look at the output for sample input for details.