cf--1C

 1 //Accepted    0 KB    60 ms
 2 //给出正多变形上的三个点，求正多形的最小面积
 3 //记三个点之间的距离a,b,c;
 4 //由余弦定理得cosA
 5 //从而可求出sinA,和正多边形所在外接圆的半径r
 6 //设三条边所对的圆心角为:theta1,theta2,theta3
 7 //则正多边形所对的圆心角为gcd(theta1,gcd(theta2,theta3))
 8 //其中gcd(theta1,theta2)为求两个浮点数的最大公约数
 9 //至此我们可以根据正多边形所在外接圆的半径r和圆心角求出正多边形的面积
10 #include <cstdio>
11 #include <cstring>
12 #include <iostream>
13 #include <queue>
14 #include <cmath>
15 #include <algorithm>
16 using namespace std;
17 const double Pi=acos(-1.0);
18 /**
19   * This is a documentation comment block
20   * @authr songt
21   */
22   struct Point
23   {
24       double x,y;
25   }p[3];
26 double getDis(Point p1,Point p2)
27 {
28     return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y));
29 }
30 double gcd(double a,double b)
31 {
32     if (fabs(b)<1e-4) return a;
33     if (fabs(a)<1e-4) return b;
34     return gcd(b,fmod(a,b));
35 }
36 void slove()
37 {
38     double a=getDis(p[1],p[2]);
39     double b=getDis(p[1],p[3]);
40     double c=getDis(p[2],p[3]);
41     double cosA=(b*b+c*c-a*a)/(2*b*c);
42     double sinA=sqrt(1-cosA*cosA);
43     double r=a/(2*sinA);
44     //printf("r=%lf\n",r);
45     double thetaA=2*asin(a/(2*r));
46     double thetaB=2*asin(b/2/r);
47     //double thetaC=2*asin(c/2/r);
48     double thetaC=2*Pi-thetaA-thetaB;
49     //printf("%lf\n",thetaA+thetaB+thetaC);
50     double theta=gcd(thetaA,gcd(thetaB,thetaC));
51     //printf("theta=%lf\n",theta);
52     //printf("Pi=%lf\n",Pi);
53     double s=2*Pi/theta*r*r/2*sin(theta);
54     printf("%.6lf\n",s);
55 }
56 int main()
57 {
58     while (scanf("%lf%lf%lf%lf%lf%lf",&p[1].x,&p[1].y,&p[2].x,&p[2].y,&p[3].x,&p[3].y)!=EOF)
59     slove();
60     return 0;
61 }