Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

Circumscribed Circle of A Triangle.

Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.

Input

Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:

$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$

in a line. All the input are real numbers.

Output

For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.

Constraints

$-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$

$ n \leq 20$

Sample Input

1
0.0 0.0 2.0 0.0 2.0 2.0

Output for the Sample Input

1.000 1.000 1.414

Solution in JAVA (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
    public static double x1,x2,y1,y2,x3,y3,a,b,c,a1,b1,c1,xp,yp;
  	static double z(double z1, double z2, double z3, double z4){
        return Math.sqrt(Math.pow(z3-z1, 2) + Math.pow(z4-z2, 2));
  	}
    public static void main(String[] args) {
    	Scanner sc=new Scanner(System.in);
    	while(sc.hasNextInt()){
    		int n=sc.nextInt();
    		for(int i=0;i<n;i++){
    			  x1=sc.nextDouble();
    	          y1=sc.nextDouble();
    	          x2=sc.nextDouble();
    	          y2=sc.nextDouble();
    	          x3=sc.nextDouble();
    	          y3=sc.nextDouble();
    	          a=2*(x2-x1);
    	          a1=2*(x3-x1);
    	          b=2*(y2-y1);
    	          b1=2*(y3-y1);
    	          c=Math.pow(x1,2)-Math.pow(x2,2)+Math.pow(y1,2)-Math.pow(y2,2);
    	          c1=Math.pow(x1,2)-Math.pow(x3,2)+Math.pow(y1,2)-Math.pow(y3,2);
    	          xp=(b*c1-b1*c)/(a*b1-a1*b);
    	          yp=(c*a1-c1*a)/(a*b1-a1*b);
    	          System.out.printf("%.3f %.3f %3f\n",xp,yp,z(x1,y1,xp,yp));
    		}
    	}
    }
  
}