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Posted 2020-08-12 Cola

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

/*
  先吐槽一下标程π的取值范围
  蒟蒻表示真没想到怎么求相交的情况，一心就想求交点，其实计算香蕉的面积

可以用扇形减去三角形
*/
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<iostream>
#include<algorithm>
const double pi=3.14159265358979323846264;
using namespace std;
void work()
{
    double x1,y1,r1,x2,y2,r2;
    scanf("%lf%lf%lf%lf%lf%lf",&x1,&y1,&r1,&x2,&y2,&r2);
    double d=sqrt(abs(x1-x2)*abs(x1-x2)+abs(y1-y2)*abs(y1-y2));
    if(r1+r2<=d)//相离
    {
        double ans=r1*r1*pi+r2*r2*pi;
        printf("%.3lf\\n",ans);
        return;
    }
    if(r1+r2>d&&abs(r1-r2)>=d)//内含 
    {
        double ans=max(r2,r1)*max(r2,r1)*pi;
        printf("%.3lf\\n",ans);
        return;
    }
    //相交 
    double ans=r1*r1*pi+r2*r2*pi;
    double j1=acos((d*d+r1*r1-r2*r2)/(2*d*r1));
    double j2=acos((d*d+r2*r2-r1*r1)/(2*d*r2));
    ans-=(r1*r1*j1+r2*r2*j2);
    ans+=d*r1*sin(j1);
    printf("%.3lf\\n",ans);
}
int main()
{
    freopen("jh.in","r",stdin);
    //freopen("standing.in","r",stdin);
    //freopen("standing.out","w",stdout);
    int T;scanf("%d",&T);
    while(T--)
    {
        work();
    }
    return 0;
}

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