codeforces1c给出三点求面积

 1 #include <iostream>
 2 #include <stdio.h>
 3 #include <stdlib.h>
 4 #include <math.h>//采用三角函数大部分使用弧度
 5 #include <utility>
 6 #include <algorithm>
 7 using namespace std;
 8 const double eps=1e-5;
 9 const double pi=acos(-1.0);
10 pair<double,double> p1;
11 pair<double,double> p2;
12 pair<double,double> p3;
13 /*
14  三角形外接圆半径:r=abc/4*s;
15  面积:s=(a*b*sinC)/2=abc/4r;sinC=c/2r;
16  最小k边形边数=2*pi/gcd(2A,gcd(2B,2C)),gcd(2A,gcd(2B,2C))表示能够符合正n边形的最大角度
17  园周角=园心角的一半  A,B,C为三角形对应得园周角
18  正n边形面积:n(r^2/2*sin(最大角度))
19 */
20 double area(double a,double b,double c)
21 {
22     double p=(a+b+c)/2;
23     return sqrt(p*(p-a)*(p-b)*(p-c));
24 }
25 double length(pair<double,double> &a,pair<double,double> &b)
26 {
27     return sqrt((a.first-b.first)*(a.first-b.first)+(a.second-b.second)*(a.second-b.second));
28 }
29 double gcd(double a,double b)
30 {
31     while(fabs(a-b)>eps&&a>0&&b>0)
32     {
33         if(a-b>eps)
34         {
35             a-=b;
36         }
37         else if(b-a>eps)
38         {
39             b-=a;
40         }
41     }
42     return a;
43 }
44 int main()
45 {
46     double s,a,r,n,angelp1,angelp2,angelp3,len1,len2,len3;
47     while(scanf("%lf%lf%lf%lf%lf%lf",&p1.first,&p1.second,&p2.first,&p2.second,&p3.first,&p3.second)!=EOF)
48     {
49         len1=length(p1,p2);
50         len2=length(p1,p3);
51         len3=length(p2,p3);
52         a=(len1+len2+len3)/2;
53         s=sqrt(a*(a-len1)*(a-len2)*(a-len3));
54         r=len1*len2*len3/(4*s);
55         angelp1=(len1*len1+len2*len2-len3*len3)/(2*len1*len2);
56         angelp2=(len1*len1+len3*len3-len2*len2)/(2*len1*len3);
57         angelp3=(len2*len2+len3*len3-len1*len1)/(2*len2*len3);
58         n=pi/gcd(acos(angelp1),gcd(acos(angelp2),acos(angelp3)));
59         double ans=n/2*r*r*sin(2*pi/n);
60         printf("%lf\n",ans);
61     }
62     return 0;
63 }