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 Python3 (judge verdict: Wrong Answer)

def main():
    import math
    for i in range(int(input())):
        x1,y1,x2,y2,x3,y3=map(float,input().split())

        a=y1-y2
        b=y1-y3

        if a==0:
            x=(x1+x2)/2
            c=(x3-x1)/(y1-y3)
            d=(-x1-x3)/2+(y1+y3)/2
            y=c*x+d

        elif b==0:
            x=(x1+x3)/2
            c=(x2-x1)/(y1-y2)
            d=(-x1-x3)/2+(y1+y3)/2
            y=c*x+d

        else:
            a=(x2-x1)/(y1-y2)
            b=(-x1-x2)/2+(y1+y2)/2
            c=(x3-x1)/(y1-y3)
            d=(-x1-x3)/2+(y1+y3)/2

            x=(d-b)/(a-c)
            y=a*x+b

        r=math.sqrt((x-x1)**2+(y-y1)**2)

        print("{0:.3f} {1:.3f} {2:.3f}".format(x,y,r))