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 ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());

            for (int i = 0; i < n; i++)
            {
                double[] input = Array.ConvertAll(Console.ReadLine().Split(' '), double.Parse);

                double x1 = input[0], y1 = input[1];
                double x2 = input[2], y2 = input[3];
                double x3 = input[4], y3 = input[5];

                double dx1 = x1 - x2, dx2 = x1 - x3;
                double dy1 = y1 - y2, dy2 = y1 - y3;
                double dxy1 = x1 * x1 - x2 * x2 + y1 * y1 - y2 * y2;
                double dxy2 = x1 * x1 - x3 * x3 + y1 * y1 - y3 * y3;

                double px = (dy2 * dxy1 - dy1 * dxy2) / (2 * dx1 * dy2 - 2 * dx2 * dy1);
                double py = (dx2 * dxy1 - dx1 * dxy2) / (2 * dx2 * dy1 - 2 * dx1 * dy2);

                double r = Math.Sqrt((x1 - px) * (x1 - px) + (y1 - py) * (y1 - py));

                Console.WriteLine("{0:f3} {1:f3} {2:f3}",
                    Math.Round(px, 3, MidpointRounding.AwayFromZero),
                    Math.Round(py, 3, MidpointRounding.AwayFromZero),
                    Math.Round(r, 3, MidpointRounding.AwayFromZero));
            }
        }
    }
}