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)

loop = gets.to_i
loop.times do
    x1, y1, x2, y2, x3, y3 = gets.split.map(&:to_f)
    
    a = ((x2 - x1)**2 + (y2 - y1)**2) ** (1/2.0)
    b = ((x3 - x2)**2 + (y3 - y2)**2) ** (1/2.0)
    c = ((x1 - x3)**2 + (y1 - y3)**2) ** (1/2.0)
    
    s = (a + b + c) / 2
    r = (a * b * c) / (((s * (s - a) * (s - b) * (s - c)) ** ( 1 / 2.0)) * 4)
    
    a1 = 2*(x2 - x1)
    b1 = 2*(y2 - y1)
    c1 = x1**2 - x2**2 + y1**2 - y2**2
    a2 = 2*(x3 - x1)
    b2 = 2*(y3 - y1)
    c2 = x1**2 - x3**2 + y1**2 - y3**2
     
    x = (b1*c2 - b2*c1) / (a1*b2 - a2*b1)
    y = (c1*a2 - c2*a1) / (a1*b2 - a2*b1)
    
    printf "%.3f %.3f %.3f\n", x, y, r
end