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 Python (judge verdict: Accepted)

#! -*- coding:utf-8 -*-
import math
n = input()
for x in xrange(n):
    x1,y1,x2,y2,x3,y3 = map(float,raw_input().split())
    a1 = 2.0*(x2-x1)
    b1 = 2.0*(y2-y1)
    x12 = x1**2
    y12 = y1**2
    c1 = x12-x2**2+y12-y2**2
    a2 = 2.0*(x3-x1)
    b2 = 2.0*(y3-y1)
    c2 = x12-x3**2+y12-y3**2
    denom=(a1*b2-a2*b1)
    # print "x1^2 : "+str(x12)
    # print "y1^2 : "+str(y12)
    # print "a1 : "+str(a1)
    # print "b1 : "+str(b1)
    # print "c1 : "+str(c1)
    # print "a2 : "+str(a2)
    # print "b2 : "+str(b2)
    # print "c2 : "+str(c2)
    # print "denom : "+str(denom)
    x = (b1*c2-b2*c1)/denom
    y = (c1*a2-c2*a1)/denom
    r = math.sqrt((x-x1)**2+(y-y1)**2)

    print "%.3f %.3f %.3f"%(x,y,r)