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: Wrong Answer)

require "matrix"

def line_length(x1, y1, x2, y2)
  if x1 == x2
    (y1 - y2).abs
  elsif y1 == y2
    (x1 - x2).abs
  else
    Math.sqrt((x2-x1)**2 + (y2-y1)**2)
  end
end

gets
ARGF.each do |line|
  x1,y1,x2,y2,x3,y3 = line.split.map(&:to_f)
  l1 = line_length(x1, y1, x2, y2)
  l2 = line_length(x1, y1, x3, y3)
  l3 = line_length(x2, y2, x3, y3)
  r = (l2 / Math.sin( Vector[x1-x2, y1-y2].angle_with(Vector[x2-x3,y2-x3]) )) / 2
  puts r
end