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 Python (judge verdict: Wrong Answer)

# coding: utf-8

import math

n = int(raw_input())

for i in range(n):
	data = map(float, raw_input().split())
	x1 = data[0]
	y1 = data[1]
	x2 = data[2]
	y2 = data[3]
	x3 = data[4]
	y3 = data[5]

	k = 0.5 * ( (x3-x2)*(x3-x1) + (y3-y2)*(y3-y1) ) / ( (x2-x1)*(y3-y1) + (y2-y1)*(x3-x1) )

	x = 0.5 * (x1 + x2) - k * (y2 - y1)
	y = 0.5 * (y1 + y2) + k * (x2 - x1)

	r = math.sqrt( (x-x1)**2 + (y-y1)**2 )

	print("{:.3f} {:.3f} {:.3f}".format(x,y,r))