#include <set>
#include <map>
#include <queue>
#include <stack>
#include <math.h>
#include <vector>
#include <string>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <iostream>
#include <algorithm>
#define zero(a) fabs(a)<eps
#define max( x, y )  ( ((x) > (y)) ? (x) : (y) )
#define min( x, y )  ( ((x) < (y)) ? (x) : (y) )
#define lowbit(x) (x&(-x))
#define debug(a) cerr<<#a<<"=="<<a<<endl
typedef long long LL;
const long double pi=acos(-1.0);
const long double eps=1e-8;
const int inf=0x3f3f3f3f;
const LL linf=0x3f3f3f3f3f3f3f3f;
using namespace std;#define zero(x) (((x)>0?(x):-(x))<eps)
int sgn(long double x)
{if(fabs(x) < eps)return 0;if(x < 0)return -1;else return 1;
}
struct point
{long double x,y;point (){}point (long double _x,long double _y){x=_x,y=_y;}
};
struct Line
{point a,b;Line(){}Line(point _a,point _b){a=_a;b=_b;}
};
struct circle {point o;long double r;void print() {printf(" center:(%.4Lf, %.4Lf) rad: %.4Lf\n", o.x, o.y, r);}
};
long double xmult(point p1,point p2,point p0)
{return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);
}
point intersection(point u1,point u2,point v1,point v2)
{point ret=u1;long double t=((u1.x-v1.x)*(v1.y-v2.y)-(u1.y-v1.y)*(v1.x-v2.x))/((u1.x-u2.x)*(v1.y-v2.y)-(u1.y-u2.y)*(v1.x-v2.x));ret.x+=(u2.x-u1.x)*t;ret.y+=(u2.y-u1.y)*t;return ret;
}
point intersection(Line u,Line v)
{point ret=u.a;long double t=((u.a.x-v.a.x)*(v.a.y-v.b.y)-(u.a.y-v.a.y)*(v.a.x-v.b.x))/((u.a.x-u.b.x)*(v.a.y-v.b.y)-(u.a.y-u.b.y)*(v.a.x-v.b.x));ret.x+=(u.b.x-u.a.x)*t;ret.y+=(u.b.y-u.a.y)*t;return ret;
}
long double dist(point a,point b)
{return (long double)sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
point circumcenter(point a,point b,point c)
{Line u,v;u.a.x=(a.x+b.x)/2;u.a.y=(a.y+b.y)/2;u.b.x=u.a.x-a.y+b.y;u.b.y=u.a.y+a.x-b.x;v.a.x=(a.x+c.x)/2;v.a.y=(a.y+c.y)/2;v.b.x=v.a.x-a.y+c.y;v.b.y=v.a.y+a.x-c.x;return intersection(u,v);
}
point incenter(point a,point b,point c)
{Line u,v;long double m,n;u.a=a;m=atan2(b.y-a.y,b.x-a.x);n=atan2(c.y-a.y,c.x-a.x);u.b.x=u.a.x+cos((m+n)/2);u.b.y=u.a.y+sin((m+n)/2);v.a=b;m=atan2(a.y-b.y,a.x-b.x);n=atan2(c.y-b.y,c.x-b.x);v.b.x=v.a.x+cos((m+n)/2);v.b.y=v.a.y+sin((m+n)/2);return intersection(u,v);
}
circle getNqc(point a, point b, point c) {long double C = dist(a, b);long double B = dist(a, c);long double A = dist(b, c);circle cir;cir.o.x = (A*a.x + B*b.x + C*c.x) / (A + B + C);cir.o.y = (A*a.y + B*b.y + C*c.y) / (A + B + C);cir.r = sqrt((A + B - C)*(A - B + C)*(-A + B + C) / (A + B + C)) / 2;return cir;
}
void intersection_line_circle(point c,long double r,point l1,point l2,point& p1,point& p2)
{point p=c;long double t;p.x+=l1.y-l2.y;p.y+=l2.x-l1.x;p=intersection(p,c,l1,l2);t=sqrt(r*r-dist(p,c)*dist(p,c))/dist(l1,l2);p1.x=p.x+(l2.x-l1.x)*t;p1.y=p.y+(l2.y-l1.y)*t;p2.x=p.x-(l2.x-l1.x)*t;p2.y=p.y-(l2.y-l1.y)*t;
}
Line line[10];int main()
{int T;scanf("%d",&T);while(T--){int p;long double t1,t2,t3;point A,B,C,I,P,N,M;cin>>p>>t1>>t2>>t3;A=point(0.0,0.0),B=point(t1,0),C=point(t2,t3);circle qwe=getNqc(A,B,C);I=qwe.o;point wo=circumcenter(A,B,C);long double wr=dist(A,wo);point a1,a2;intersection_line_circle(wo,wr,I,A,a1,a2);if(fabs(a1.x-A.x)<eps&&fabs(a1.y-A.y)<eps){M=a2;}else{M=a1;}intersection_line_circle(wo,wr,I,B,a1,a2);if(fabs(a1.x-B.x)<eps&&fabs(a1.y-B.y)<eps){N=a2;}else{N=a1;}intersection_line_circle(wo,wr,I,C,a1,a2);if(fabs(a1.x-C.x)<eps&&fabs(a1.y-C.y)<eps){P=a2;}else{P=a1;}point E,F,K,J,H,G;G=intersection(Line(A,C),Line(M,N));H=intersection(Line(M,N),Line(C,B));J=intersection(Line(C,B),Line(M,P));K=intersection(Line(M,P),Line(A,B));E=intersection(Line(A,B),Line(N,P));F=intersection(Line(N,P),Line(A,C));printf("%d %.4Lf %.4Lf %.4Lf %.4Lf %.4Lf %.4Lf\n",p,dist(E,F),dist(F,G),dist(G,H),dist(H,J),dist(J,K),dist(K,E));}return 0;
}
/*3
1 3 2.5 31
1 2 1 1.732
*/