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

def get_length(x1, y1, x2, y2, x3, y3)
  a = sqrt((x1 - x2)*(x1 - x2) + (y1 - y2)*(y1 - y2))
  b = sqrt((x2 - x3)*(x2 - x3) + (y2 - y3)*(y2 - y3))
  c = sqrt((x3 - x1)*(x3 - x1) + (y3 - y1)*(y3 - y1))
  return a, b, c
end

def get_radius(x1, y1, x2, y2, x3, y3)
  a, b, c = get_length(x1, y1, x2, y2, x3, y3)
  s = (a + b + c)/2.0
  area = sqrt(s*(s-a)*(s-b)*(s-c))
  (a*b*c)/(4.0*area)
end

def get_center(x1, y1, x2, y2, x3, y3)
  a1 = 2.0*(x2 - x1)
  b1 = 2.0*(y2 - y1)
  c1 = x1**2 - x2**2 + y1**2 - y2**2
  a2 = 2.0*(x3 - x1)
  b2 = 2.0*(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)
  return x, y
end

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

  # 外接円の半径を求める
  #=> http://ja.wikipedia.org/wiki/%E3%83%98%E3%83%AD%E3%83%B3%E3%81%AE%E5%85%AC%E5%BC%8F
  #=> http://blogs.yahoo.co.jp/oka_yadokary/5718559.html
  r = get_radius(x1, y1, x2, y2, x3, y3)

  # 外接円の中心座標を求める
  #=> http://www.h6.dion.ne.jp/~jpe02_tn/ki-5.html
  px, py = get_center(x1, y1, x2, y2, x3, y3)

  puts sprintf("%.3f %.3f %.3f", px, py, r)
end