【模板】三角形四心

#include<iostream>
#include<cmath>
#include<cstdio>
using namespace std;
struct Point{
    double x,y;
    Point operator - (const Point& b)const{
        return (Point){x-b.x,y-b.y};
    }
    double operator ^ (const Point& b)const{
        return x*b.y - b.x*y;
    }
    Point operator * (const double b){
        return (Point){x*b,y*b};
    }
    Point operator + (const Point& b)const{
        return (Point){x+b.x,y+b.y};
     }
};
struct Line{
    Point s,t;
};
//直线交
Point line_inter(Line l1,Line l2){
    double b = ((l1.t-l1.s)^(l2.s-l1.s))/((l2.t-l2.s)^(l1.t-l1.s));
    return l2.s + (l2.t - l2.s)*b;
}
double dis(Point a,Point b){
    return sqrt((a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y));
}
//外心
Point circumcenter(Point a, Point b, Point c){
    Line u, v;
    u.s.x = (a.x + b.x) / 2;
    u.s.y = (a.y + b.y) / 2;
    u.t.x = u.s.x - a.y + b.y;
    u.t.y = u.s.y + a.x - b.x;
    v.s.x = (a.x + c.x) / 2;
    v.s.y = (a.y + c.y) / 2;
    v.t.x = v.s.x - a.y + c.y;
    v.t.y = v.s.y + a.x - c.x;
    return line_inter(u, v);
}
 
//内心
Point incenter(Point a,Point b,Point c){  //三角形内心 
     double A=dis(b,c);
     double B=dis(a,c);
     double C=dis(a,b);
     double S=A+B+C; 
     double u=(A*a.x+B*b.x+C*c.x)/S;
     double v=(A*a.y+B*b.y+C*c.y)/S;
     return (Point){u,v};    
}
 
//垂心
Point perpencenter(Point a, Point b, Point c){
    Line u, v;
    u.s = c;
    u.t.x = u.s.x - a.y + b.y;
    u.t.y = u.s.y + a.x - b.x;
    v.s = b;
    v.t.x = v.s.x - a.y + c.y;
    v.t.y = v.s.y + a.x - c.x;
    return line_inter(u, v);
}
 
//重心
//三条中线交点 
//到三角形三顶点距离的平方和最小的点
//三角形内到三边距离之积最大的点
Point gravity(Point a, Point b, Point c){
    return (Point){(a.x+b.x+c.x)/3,(a.y+b.y+c.y)/3};
}
 
//费马点
//到三角形三顶点距离之和最小的点
Point fermentpoint(Point a, Point b, Point c){
    Point u, v;
    double step = fabs(a.x) + fabs(a.y) + fabs(b.x) + fabs(b.y) + fabs(c.x) + fabs(c.y);
    int i, j, k;
    u.x = (a.x + b.x + c.x) / 3;
    u.y = (a.y + b.y + c.y) / 3;
    while (step > 1e-10)
        for (k = 0; k < 10; step /= 2, k++)
            for (i = -1; i <= 1; i++)
                for (j = -1; j <= 1; j++){
                    v.x = u.x + step*i;
                    v.y = u.y + step*j;
                    if (dis(u, a) + dis(u, b) + dis(u, c) > dis(v, a) + dis(v, b) + dis(v, c))
                        u = v;
                }
                return u;
}
int main(){
    int T; scanf("%d",&T);
    Point a,b,c;
    while(T--){
        cin>>a.x>>a.y;
        cin>>b.x>>b.y;
        cin>>c.x>>c.y;
        Point ans = perpencenter(a,b,c);
        printf("%.4f %.4f\n",ans.x,ans.y);
    }
    return 0;
}