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 Ruby (judge verdict: Accepted)

include Math

gets.to_i.times do
	x1, y1, x2, y2, x3, y3 = gets.split.map(&:to_f)

	a1 = 2 * (x2 - x1)
	b1 = 2 * (y2 - y1)
	c1 = x1*x1 - x2*x2 + y1*y1 - y2*y2
	a2 = 2 * (x3 - x1)
	b2 = 2 * (y3 - y1)
	c2 = x1*x1 - x3*x3 + y1*y1 - y3*y3

	a = sqrt((x2-x3)**2 + (y2-y3)**2)
	b = sqrt((x3-x1)**2 + (y3-y1)**2)
	c = sqrt((x1-x2)**2 + (y1-y2)**2)

	px = (b1*c2 - b2*c1)/(a1*b2 - a2*b1)
	py = (c1*a2 - c2*a1)/(a1*b2 - a2*b1)
	r = (a*b*c) / sqrt((a+b+c)*(-a+b+c)*(a-b+c)*(a+b-c))

	printf("%.3f %.3f %.3f\n", px, py, r);
end