standing

 

2bc*cosA=b^2+c^2-a^2

 

#include<cstdio>
#include<cstring>
#include<iostream>
#include<cmath>
#include<algorithm>
using namespace std;
const double pi=3.1415926535898;//我不明白他为什么会卡精度
int t;
double x1,y,r1,x2,y2,r2,s,a,b,c,k,m,w,p;
int main()
{
    scanf("%d",&t);
    while(t--)
    {
        scanf("%lf%lf%lf%lf%lf%lf",&x1,&y,&r1,&x2,&y2,&r2);
        double d=sqrt((x2-x1)*(x2-x1)+(y2-y)*(y2-y);
        if(d>=(r1+r2))//两圆相离 
            s=pi*r1*r1+pi*r2*r2;
        else 
          if(d<abs(r1-r2))//两圆内含 
            s=max(pi*r1*r1,pi*r2*r2);
        else//两圆相交 
          {
            s=r1*r1*pi+pi*r2*r2;
            k=sqrt((x1-x2)*(x1-x2)+(y-y2)*(y-y2));
            
            w=(r1*r1+k*k-r2*r2)/(2*r1*k);
            p=2*acos(w);
            s-=((p*r1*r1)/2-sin(p)*r1*r1/2);
            
            w=(r2*r2+k*k-r1*r1)/(2*r2*k);
            p=2*acos(w);
            s-=((p*r2*r2)/2-sin(p)*r2*r2/2);
         }
        printf("%.3lf\n",s);
    }
    return 0;
}