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 C# (judge verdict: Accepted)

using System;

namespace Volume0_0010
{
    class Program
    {
        static void Main(string[] args)
        {
            int len = Convert.ToInt32(Console.ReadLine());

            for(int i = 0; i < len;i++)
            {
                String[] inputs = Console.ReadLine().Split(' ');
                double x1 = Convert.ToDouble(inputs[0]);
                double y1 = Convert.ToDouble(inputs[1]);
                double x2 = Convert.ToDouble(inputs[2]);
                double y2 = Convert.ToDouble(inputs[3]);
                double x3 = Convert.ToDouble(inputs[4]);
                double y3 = Convert.ToDouble(inputs[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 = Math.Sqrt(Math.Pow((x1-x),2)+(Math.Pow(y1-y,2)));

                x = (Math.Round(x * 1000)) / 1000;
                y = (Math.Round(y * 1000)) / 1000;
                r = (Math.Round(r * 1000)) / 1000;

                Console.WriteLine(x.ToString("F3") + " " + y.ToString("F3") + " " + r.ToString("F3"));
            }
        }
    }
}