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.*;

public class Main {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		for(int i=0; i<n; i++) {
			double x1 = in.nextDouble();
			double y1 = in.nextDouble();
			double x2 = in.nextDouble();
			double y2 = in.nextDouble();
			double x3 = in.nextDouble();
			double y3 = in.nextDouble();
			double a = (Math.pow(x2,2) - Math.pow(x1,2) + Math.pow(y2,2) - Math.pow(y1,2)) * (y3 - y1);
			double b = (Math.pow(x3,2) - Math.pow(x1,2) + Math.pow(y3,2) - Math.pow(y1,2)) * (y2 - y1);
			double p = (a-b) / ((x2-x1) * (y3-y1) - (x3-x1) * (y2-y1)) / 2;
			double aa = (Math.pow(x3,2) - Math.pow(x1,2) + Math.pow(y3,2) - Math.pow(y1,2)) * (x2 - x1);			
			double bb = (Math.pow(x2,2) - Math.pow(x1,2) + Math.pow(y2,2) - Math.pow(y1,2)) * (x3 - x1);
			double q = (aa-bb) / ((y3-y1) * (x2-x1) - (y2-y1) * (x3-x1)) / 2;
			double r = Math.sqrt(Math.pow(Math.abs(p-x1), 2) + Math.pow(Math.abs(q-x2), 2));
			System.out.printf("%.3f %.3f %.3f\n", p, q, r);
		}
	}
}