Problem:
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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 C# (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Programminng
{
    class AOJ_Volume0010
    {
        public static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());

            for (int i = 0; i < n; i++)
            {
                string[] s = Console.ReadLine().Split(' ');
                double x1 = double.Parse(s[0]);
                double y1 = double.Parse(s[1]);
                double x2 = double.Parse(s[2]);
                double y2 = double.Parse(s[3]);
                double x3 = double.Parse(s[4]);
                double y3 = double.Parse(s[5]);
                
                double a1 = 2 * (x2 - x1);
                double b1 = 2 * (y2 - y1);
                double c1 = x1 * x1 - x2 * x2 + y1 * y1 - y2 * y2;

                double a2 = 2 * (x3 - x1);
                double b2 = 2 * (y3 - y1);
                double c2 = x1 * x1 - x3 * x3 + y1 * y1 - y3 * y3;

                double x = (b1 * c2 - b2 * c1) / (a1 * b2 - a2 * b1);
                double y = (c1 * a2 - c2 * a1) / (a1 * b2 - a2 * b1);

                double r_2 = (x1 - x) * (x1 - x) + (y1 - y) * (y1 - y);
                double r = Math.Sqrt(r_2);

                Console.WriteLine("{0:F3} {1:F2} {2:F3}",x,y,r);
            }
        }
    }
}