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 Python3 (judge verdict: Accepted)

import math
n = int(input())
for i in range(n):
    x1,y1,x2,y2,x3,y3 = map(float,input().split())
    a = 2*(x2 - x1)
    b = 2*(y2 - y1)
    c = x2**2 + y2**2 - x1**2 -y1**2
    d = 2*(x3 - x1)
    e = 2*(y3 - y1)
    f = x3**2 + y3**2 - x1**2 -y1**2
    x = (c*e - f*b)/(a*e - b*d)
    y = (c*d - f*a)/(b*d - e*a)
    r = math.sqrt((x1 - x)**2 + (y1 - y)**2)
    x = round(x,3)
    y = round(y,3)
    r = round(r,3)
    if x == -0.0:
        x = 0.0
    if y == -0.0:
        y = 0.0
    print("{0:.3f}".format(x),end = ' ')
    print("{0:.3f}".format(y),end = ' ')
    print("{0:.3f}".format(r))