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;

class AOJ{
  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, y1, x2, y2, x3, y3, px, py, r;

      x1 = double.Parse(s[0]);
      y1 = double.Parse(s[1]);
      x2 = double.Parse(s[2]);
      y2 = double.Parse(s[3]);
      x3 = double.Parse(s[4]);
      y3 = double.Parse(s[5]);

      px = ((y2 - y3) * (x1 * x1 + y1 * y1) + (y3 - y1) * (x2 * x2 + y2 * y2) + (y1 - y2) * (x3 * x3 + y3 * y3)) / (2 * (x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)));
      py = ((x2 - x3) * (x1 * x1 + y1 * y1) + (x3 - x1) * (x2 * x2 + y2 * y2) + (x1 - x2) * (x3 * x3 + y3 * y3)) / (2 * (y1 * (x2 - x3) + y2 * (x3 - x1) + y3 * (x1 - x2)));

      r = Math.Sqrt(Math.Pow((x1 - px), 2) + Math.Pow((y1 - py), 2));

      Console.WriteLine("{0:f3} {1:f3} {2:f3}", px, py, r);
    }
  }
}