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: Accepted)

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

namespace OJcsharp
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            double[] ansx = new double[n];
            double[] ansy = new double[n];
            double[] ansr = new double[n];
            for (int m = 0; m < n; m++)
            {
                string[] str = Console.ReadLine().Split(' ');
                double x1 = double.Parse(str[0]), y1 = double.Parse(str[1]), x2 = double.Parse(str[2]),      y2 = double.Parse(str[3]), x3 = double.Parse(str[4]), y3 = double.Parse(str[5]);
                ansx[m] = (2 * (y2 - y1) * (x1 * x1 - x3 * x3 + y1 * y1 - y3 * y3) - 2 * (y3 - y1) * (x1 * x1 - x2 * x2 + y1 * y1 - y2 * y2)) / (2 * (x2 - x1) * 2 * (y3 - y1) - 2 * (x3 - x1) * 2 * (y2 - y1));
                ansy[m] = ((x1 * x1 - x2 * x2 + y1 * y1 - y2 * y2) * 2 * (x3 - x1) - (x1 * x1 - x3 * x3 + y1 * y1 - y3 * y3) * 2 * (x2 - x1)) / (2 * (x2 - x1) * 2 * (y3 - y1) - 2 * (x3 - x1) * 2 * (y2 - y1));
                ansr[m] = Math.Sqrt((ansx[m] - x1) * (ansx[m] - x1) + (ansy[m] - y1) * (ansy[m] - y1));
            }
            for (int m = 0; m < n; m++)
                Console.WriteLine(string.Format("{0:0.000}",ansx[m])+" "+string.Format("{0:0.000}",ansy[m])+" "+string.Format("{0:0.000}",ansr[m]));
        }
    }
}