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 JAVA (judge verdict: Wrong Answer)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		new Main().run();
	}
	
	private void run() {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		for (int p = 0; p < n; p++) {
			double x1 = scan.nextDouble();
			double y1 = scan.nextDouble();
			double x2 = scan.nextDouble();
			double y2 = scan.nextDouble();
			double x3 = scan.nextDouble();
			double y3 = scan.nextDouble();
			
			double a = Math.sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1));
			double b = Math.sqrt((x2 - x3) * (x2 - x3) + (y2 - y3) * (y2 - y3));
			double c = Math.sqrt((x3 - x1) * (x3 - x1) + (y3 - y1) * (y3 - y1));
			
			double r = a * b * c / Math.sqrt((a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c));
			
			double a1 = 2 * (x2 - x1);
			double b1 = 2 * (y2 - y1);
			double c1 = x1 * x1 - x2 * x2 + y1 * y1 - y2 * y2;
			double a2 = 2 * (y3 - y1);
			double b2 = 2 * (y3 - y1);
			double c2 = x1 * x1 - x3 * x3 + y1 * y1 - y3 * y3;
			
			double px = (b1 * c2 - b2 * c1) / (a1 * b2 - a2 * b1);
			double py = (c1 * a2 - c2 * a1) / (a1 * b2 - a2 * b1);
			
			System.out.printf("%.3f %.3f %.3f\n", px, py, r);
		}
	}

}