2022.01.19翻译Ancient Berland Circus

Ancient Berland Circus
题目（https://acs.jxnu.edu.cn/problem/CF1C）描述：

Nowadays all circuses in Berland have a round arena with diameter 13 meters, but in the past things were different.

In Ancient Berland arenas in circuses were shaped as a regular (equiangular) polygon, the size and the number of angles could vary from one circus to another. In each corner of the arena there was a special pillar, and the rope strung between the pillars marked the arena edges.

Recently the scientists from Berland have discovered the remains of the ancient circus arena. They found only three pillars, the others were destroyed by the time.

You are given the coordinates of these three pillars. Find out what is the smallest area that the arena could have.

输入：
The input file consists of three lines, each of them contains a pair of numbers –– coordinates of the pillar. Any coordinate doesn't exceed 1000 by absolute value, and is given with at most six digits after decimal point.

输出：
Output the smallest possible area of the ancient arena. This number should be accurate to at least 6 digits after the decimal point. It's guaranteed that the number of angles in the optimal polygon is not larger than 100.

样例输入：

0.000000 0.000000
1.000000 1.000000
0.000000 1.000000
样例输出：

1.00000000

翻译：

现在，波兰的所有的马戏场里的竞技场都是一个直径13米的圆形区域，但是在古代不是这样。

在古代波兰，马戏场里的竞技场都是一个规则多边形区域，不同马戏场里的竞技场区域的大小和角的数量不同。在竞技场的每个角有一根特别的柱子，柱子用绳索相连用来标记竞技场区域的边界。

最近，波兰的科学家发现了一个尚存的古代马戏团竞技场。他们只发现了三根柱子，其余的柱子都不见了。

给你这三根柱子的坐标，找出竞技场可能的最小面积。

输入：

输入有三行，每行表示一根柱子的坐标。所有坐标的大小不会超过1000，且坐标精度为小数点后6位；

输出：

输出竞技场可能的最小面积。结果保留6位小数。最佳答案的多边形的角的个数不会超过100；

样例输入：

0.000000 0.000000
1.000000 1.000000
0.000000 1.000000
样例输出：

1.00000000