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: from math import acos
  from math import sin
  
  
  def ang(ax, ay, ox, oy, bx, by):
      oax, oay = ax - ox, ay - oy
      obx, oby = bx - ox, by - oy
      r1, r2 = oax**2 + oay**2, obx**2 + oby**2
      return acos((oax * obx + oay * oby) / (r1 * r2) ** 0.5)
  
  
  def circumcircle(x1, y1, x2, y2, x3, y3):
      s2A = sin(2 * ang(x3, y3, x1, y1, x2, y2))
      s2B = sin(2 * ang(x1, y1, x2, y2, x3, y3))
      s2C = sin(2 * ang(x2, y2, x3, y3, x1, y1))
      px = (s2A * x1 + s2B * x2 + s2C * x3) / (s2A + s2B + s2C) + 0.0
      py = (s2A * y1 + s2B * y2 + s2C * y3) / (s2A + s2B + s2C) + 0.0
      r = (((x2 - x3) ** 2 + (y2 - y3) ** 2) ** 0.5) / (
          2 * sin(ang(x2, y2, x1, y1, x3, y3))
      ) + 0.0
      return px, py, r
  
  
  n = int(input())
  for i in range(n):
      print(
          "{0[0]:.3f} {0[1]:.3f} {0[2]:.3f}".format(
              circumcircle(*tuple(map(float, input().split())))
          )
      )
  
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"}]