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 PHP (judge verdict: Wrong Answer)

<?php
  ini_set('memory_limit', '1G');
  trim(fgets(STDIN));
  while($line=trim(fgets(STDIN))){
    $x1x2x3=explode(" ",$line);
    $x1=$x1x2x3[0];$x2=$x1x2x3[2];$x3=$x1x2x3[4];$y1=$x1x2x3[1];$y2=$x1x2x3[3];$y3=$x1x2x3[5];
    $a=sqrt(pow(abs($x1-$x2),2)+pow(abs($y1-$y2),2));
    $b=sqrt(pow(abs($x3-$x2),2)+pow(abs($y3-$y2),2));
    $c=sqrt(pow(abs($x1-$x3),2)+pow(abs($y1-$y3),2));
    $cosa=(pow($b,2)+pow($c,2)-pow($a,2))/(2*$b*$c);
    /* echo  */rad2deg(acos($cosa)/2)."\n";
    /* echo  */$r=($a/2)/sin(acos($cosa))."\n";
    /* echo "orgx=".abs($x1-$x2)."\n";
       echo "orgy=".abs($y1-$y2)."\n"; */
    if(abs($x1-$x2)==0)
      $rad=90;
    else{
      $slope=abs($y1-$y2)/abs($x1-$x2);
      $rad=rad2deg(atan($slope));
    }
    /* echo "rad=".$rad."\n"; */
    /* $xpos=$x1+cos(deg2rad($rad))*($a/2);
       $ypos=$y1+sin(deg2rad($rad))*($a/2); */
    $angle=$rad+(90-rad2deg(acos($cosa)));
    $xpos=$x1+cos(deg2rad($angle))*$r;
    $ypos=$y1+sin(deg2rad($angle))*$r;
    echo sprintf("%.3f %.3f %.3f",round($xpos,3),round($ypos,3),round($r,3));;
  }