output_description: 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.
input_description: 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.
attempt: import sys
  
  f = sys.stdin
  
  
  def take2(iterable):
      while True:
          yield next(iterable), next(iterable)
  
  
  # 外積
  def cross(v1, v2):
      return v1.real * v2.imag - v1.imag * v2.real
  
  
  # 線分13と線分24の交点を求める
  def get_intersection(p1, p2, p3, p4):
      a1 = p4 - p2
      b1 = p2 - p3
      b2 = p1 - p2
      s1 = cross(a1, b2) / 2
      s2 = cross(a1, b1) / 2
      print(s1, s2)
      return p1 + (p3 - p1) * s1 / (s1 + s2)
  
  
  n = int(f.readline())
  for i in range(n):
      p1, p2, p3 = [x + y * 1j for x, y in take2(map(float, f.readline().split()))]
      p12 = (p1 + p2) / 2
      p13 = (p1 + p3) / 2
      pxy = get_intersection(p12, p13, p12 + (p2 - p1) * 1j, p13 + (p1 - p3) * 1j)
      r = abs(pxy - p1)
      print("{:.3f} {:.3f} {:.3f}".format(pxy.real, pxy.imag, r))
  
problem_description: 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.
samples: [{"input": "0.0 0.0 2.0 0.0 2.0 2.0", "output": ".000 1.000 1.414"}]