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;
namespace ConsoleApplication1{
    class Program{
        static void Main(string[] args){
            int n = int.Parse(Console.ReadLine());
            double px,py,r;
            for(int i=0;i<n;i++){
                String[] str = Console.ReadLine().Split();
                double x1 = double.Parse(str[0]);
                double y1 = double.Parse(str[1]);
                double x2 = double.Parse(str[2]);
                double y2 = double.Parse(str[3]);
                double x3 = double.Parse(str[4]);
                double y3 = double.Parse(str[5]);
                px=((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)));
                py=((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)));
                r=Math.Sqrt((x1-px)*(x1-px)+(y1-py)*(y1-py));
                Console.WriteLine("{0:f3} {1:f3} {2:f3}",px,py,r);
            }
        }
    }
}