Go: package main

import (
	"fmt"
	"math"
)

func main() {
	n := scanInt()
	for i := 0; i < n; i++ {
		cal()
	}
}

func scanInt() int {
	var n int
	fmt.Scanf("%d", &n)
	return n
}

func cal() {
	var x1, y1, x2, y2, x3, y3 float64
	fmt.Scanf("%f%f%f%f%f%f", &x1, &y1, &x2, &y2, &x3, &y3)
	a := 2 * (x1 - x2)
	b := 2 * (y1 - y2)
	c := 2 * (x1 - x3)
	d := 2 * (y1 - y3)
	e := x1*x1 - x2*x2 + y1*y1 - y2*y2
	f := x1*x1 - x3*x3 + y1*y1 - y3*y3

	px := (d*e - b*f) / (a*d - b*c)
	py := (a*f - c*e) / (a*d - b*c)

	r := math.Sqrt((x1-px)*(x1-px) + (y1-py)*(y1-py))
	fmt.Printf("%.3f %.3f %.3f\n", px, py, r)
}

Python: import math

def simultaneous_equasion(a, b, c, d, e, f):
    "??£???????¨????"
    det = a * d - b * c
    a11 = d / det
    a12 = - b / det
    a21 = - c / det
    a22 = a / det
    return a11 * e + a12 * f, a21 * e + a22 * f

n = int(input())
for i in range(n):
    x1, y1, x2, y2, x3, y3 = map(float, input().split())
    # (x1, y1), (x2, y2)????????´????????????
    # 2 * (x2 - x1) * x + 2 * (y2 - y1) * y = (y2 - y1) ^ 2 + (x2 - x1) ^ 2
    a = 2 * (x2 - x1)
    b = 2 * (y2 - y1)
    c = 2 * (x3 - x1)
    d = 2 * (y3 - y1)
    e = (y2 - y1) ** 2 + (x2 - x1) ** 2
    f = (y3 - y1) ** 2 + (x3 - x1) ** 2
    px, py = simultaneous_equasion(a, b, c, d, e, f)
    r = math.sqrt((px - x1) ** 2 + (py - y1) ** 2)
    print("%.3f %.3f %.3f" % (round(px, 3), round(py, 3), round(r, 3)))

Python: def circumcenter(vert1, vert2, vert3):
    # H/T: wikipedia.org/wiki/Circumscribed_circle
    # refer from https://gist.github.com/dhermes/9ce057da49df63345c33
    Ax, Ay = vert1
    Bx, By = vert2
    Cx, Cy = vert3

    D = 2 * (Ax * (By - Cy) + Bx * (Cy - Ay) + Cx * (Ay - By))
    norm_A = Ax**2 + Ay**2
    norm_B = Bx**2 + By**2
    norm_C = Cx**2 + Cy**2

    Ux = norm_A * (By - Cy) + norm_B * (Cy - Ay) + norm_C * (Ay - By)
    Uy = -(norm_A * (Bx - Cx) + norm_B * (Cx - Ax) + norm_C * (Ax - Bx))

    r = (Ax - Ux/D)*(Ax - Ux/D) + (Ay - Uy/D)* (Ay - Uy/D)
    r = float(r)**0.5
    return [Ux/D, Uy/D, r]

n  = int(input())
for i in range(n):
  xs = list(map(float, input().split()))
  a = circumcenter(xs[0:2], xs[2:4], xs[4:6])
  print(' '.join(map(lambda x:f'{x:0.03f}', a)))

Python: from decimal import Decimal
import math
for _ in range(int(input())):
    x1,y1,x2,y2,x3,y3=list(map(Decimal,input().split()))
    a=x1-x3
    b=y2-y3
    c=x2-x3
    d=y1-y3
    e=y1-y2
    f=x1+x3
    g=x2+x3
    X=(b*d*e+a*b*f-c*d*g)/2/(a*b-c*d)
    try:
        Y=-(a/d)*(X-f/2)+(y1+y3)/2
    except:
        Y=-(c/b)*(X-g/2)+(y2+y3)/2
    R=math.sqrt((x1-X)**2+(y1-Y)**2)
    print(" ".join(["{:.3f}".format(i) for i in [X,Y,R]]))

Python: import math
n = int(input())
i = 0
while i < n:
   x1, y1, x2, y2, x3, y3 = map(float,input().split())
   a = x2 - x1
   b = y2 - y1
   c = x3 - x1
   d = y3 - y1
   e = a * (x1 + x2) + b * (y1 + y3)
   f = c * (x1 + x2) + d * (y1 + y3)
   g = 2.0 * (a * (y3 - y2) - b * (x3 - x2))
   if g == 0:
       exit()
   px = (d * e - b * f) / g
   py = (a * f - c * e) / g
   radius = ( (py - y1)*(py - y1) + (px - x1)*(px - x1) )
   print("%.3f %.3f %.3f"%(px,py,math.sqrt(radius)))
   i=i+1

Python: from math import *
def g(x):
    y = (((1000 * abs(x)) * 2 + 1) // 2) / 1000
    if x < 0:
        y *= -1
    return y
def f(x):
    a = (x[2] - x[4]) * (x[1] - x[3]) - (x[0] - x[2]) * (x[3] - x[5])
    b = (x[0] - x[2]) * (x[4] - x[0]) - (x[5] - x[1]) * (x[1] - x[3])
    l = 0.5 * b / a
    X = 0.5 * x[2] + 0.5 * x[4] + l * (x[3] - x[5])
    Y = 0.5 * x[3] + 0.5 * x[5] + l * (x[4] - x[2])
    R = sqrt((X - x[0]) ** 2 + (Y - x[1]) ** 2)
    X = g(X)
    Y = g(Y)
    R = g(R)
    print("{0:.3f} {1:.3f} {2:.3f}".format(X, Y, R))
n = int(input())
a = []
for _ in range(n):
    a.append(list((map(float, input().split()))))
for i in a:
    f(i)

Python: for _ in[0]*int(input()):
 a,b,c,d,e,f=map(float,input().split())
 x=((a*a+b*b)*(d-f)+(c*c+d*d)*(f-b)+(e*e+f*f)*(b-d))/2/(a*(d-f)+c*(f-b)+e*(b-d))
 y=((a*a+b*b)*(c-d)+(c*c+d*d)*(e-a)+(e*e+f*f)*(a-c))/2/(b*(c-e)+d*(e-a)+f*(a-c))
 print(f"{x:.4} {y:.4} {(x*x+y*y)**.5:.4}")

Python: for i in range(int(input())):
    x1, y1, x2, y2, x3, y3 = list(map(float,input().split()))

    a = x2 - x1
    b = y2 - y1
    c = (x1**2 - x2**2) + (y1**2 - y2**2)

    d = x3 - x1
    e = y3 - y1
    f = (x1**2 - x3**2) + (y1**2 - y3**2)

    l = (e*c - b*f) / (a*e - b*d)
    m = (c*d - f*a) / (b*d - a*e)
    n = -(x1**2 + y1**2 + l*x1 + m*y1)

    import math
    px = round(-l/2, 3)
    py = round(-m/2, 3)
    r = round(math.sqrt(l**2 + m**2 - 4*n ) / 2, 3)
    print("{:.3f} {:.3f} {:.3f}".format(px, py, r))

Python: import math
for _ in range(int(input())):
    x1, y1, x2, y2, x3, y3 = map(float, input().split())
    p = ((y1-y3)*(y1**2 -y2**2 +x1**2 -x2**2) -(y1-y2)*(y1**2 -y3**2 +x1**2 -x3**2)) / 2/ ((y1-y3)*(x1-x2)-(y1-y2)*(x1-x3))
    q = ((x1-x3)*(x1**2 -x2**2 +y1**2 -y2**2) -(x1-x2)*(x1**2 -x3**2 +y1**2 -y3**2)) / 2/ ((x1-x3)*(y1-y2)-(x1-x2)*(y1-y3))
    r = math.sqrt((x1 - p) ** 2 + (y1 - q) ** 2)
    p = abs(p) if abs(p) < 10e-5 else p
    q = abs(q) if abs(q) < 10e-5 else q
    print("{:.3f} {:.3f} {:.3f}".format(p, q, r))

Python: n = int(input())
for _ in range(n):
    x1, y1, x2, y2, x3, y3 = map(float, input().split())
    a = pow((x3-x2) ** 2 + (y3-y2) ** 2, 0.5)
    b = pow((x3-x1) ** 2 + (y3-y1) ** 2, 0.5)
    c = pow((x1-x2) ** 2 + (y1-y2) ** 2, 0.5)
    cosA = (b**2 + c**2 - a**2) / (2*b*c)
    sinA = pow(1 - cosA**2, 0.5)
    R = a / sinA / 2
    a, b, c = x1-x2, y1-y2, -(x1**2 + y1**2) + (x2**2 + y2**2)
    d, e, f = x2-x3, y2-y3, -(x2**2 + y2**2) + (x3**2 + y3**2)
    l = (c*e - b*f) / (e*a - b*d)
    m = (c*d - a*f) / (b*d - a*e)
    l, m = l*-0.5, m*-0.5
    print("{:.3f} {:.3f} {:.3f}".format(l, m, R))

Python: n = int(input())
for i in range(n):
    x1, y1, x2, y2, x3, y3 = list(map(float, input().split()))
    a = complex(x1, y1)
    b = complex(x2, y2)
    c = complex(x3, y3)
    a -= c
    b -= c
    z0 = abs(a)**2 * b - abs(b)**2 * a
    z0 /= a.conjugate() * b - a * b.conjugate()
    z = z0 + c
    zx = "{0:.3f}".format(z.real)
    zy = "{0:.3f}".format(z.imag)
    r  = "{0:.3f}".format(abs(z0))
    print(zx, zy, r)

Python: #!/usr/bin/env python
#-*- coding:utf-8 -*-
 
import sys
import math
 
n = int(input())
 
for data in sys.stdin:
    x1, y1, x2, y2, x3, y3 = map(float, data.split())
    a1 = x2 - x1
    b1 = y2 - y1
    a2 = x3 - x1
    b2 = y3 - y1
    px = (b2 * (a1 * a1 + b1 * b1) - b1 * (a2 * a2 + b2 * b2)) / (2 * (a1 * b2 - a2 * b1))
    py = (a1 * (a2 * a2 + b2 * b2) - a2 * (a1 * a1 + b1 * b1)) / (2 * (a1 * b2 - a2 * b1))
    r = math.sqrt(px * px + py * py)
    px += x1
    py += y1
    print("{0:.3f} {1:.3f} {2:.3f}".format(px, py, r))