Go: package main

import (
	"fmt"
	"math"
)

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

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

func circleTriangle() {
	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: 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 = input()
for i in range(n):
    p = map(float, raw_input().split())
    x1, y1, x2, y2, x3, y3 = p[0], p[1], p[2], p[3], p[4], p[5]
    
    px = ((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) - 2 * (y1 - y2) * (x1 - x3))
    py = ((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) - 2 * (x1 - x2) * (y1 - y3))
    r = math.sqrt((x1 - px)**2 + (y1 - py)**2)
    print("%.3f %.3f %.3f" % (px, py, r))

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: from math import sin,cos,sqrt
n=int(input())
out=[]
for i in range(n):
	I=list(map(float,input().split(" ")))
	#( (x_0,y_0), (x_1,y_1) , (x_2,y_2) )
	a_1=I[2]-I[0] #x_1-x_0
	a_2=I[4]-I[0] #x_2-x_0
	b_1=I[3]-I[1] #y_1-y_0
	b_2=I[5]-I[1] #y_2-y_0

	K=(a_2**2 -a_2*b_2+a_1**2-a_1*b_1)/(a_2*b_1-a_1*b_2)

	O_x=0.5*(b_1-K*b_2)
	O_y=0.5*(b_2+K*b_1)
	O_R=sqrt( (I[0]-O_x)**2  + (I[1]-O_y)**2 )
	
	print('{:.3f} {:.3f} {:.3f}'.format(O_x,O_y,O_R))
#	out.append( '{:.3f} {:.3f} {:.3f}'.format(O_x,O_y,O_R) )



#	for i in out:
#		print(i)

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("{:.4f} {:.4f} {:.4f}".format(p, q, r))

Python: import math

n = int(input())
for i in range(n):
    x1,y1,x2,y2,x3,y3 = map(float,input().split())
    a1,b1,c1 = 2*(x2-x1),2*(y2-y1), (x1**2 - x2 **2 + y1 ** 2 - y2 ** 2)
    a2,b2,c2 = 2*(x3-x1), 2*(y3-y1), (x1**2 - x3 **2 + y1 ** 2 - y3 ** 2)

    p1 = (b1*c2 - b2*c1)/(a1*b2 - a2*b1)
    p2 = (c1*a2 - c2*a1)/(a1*b2 - a2*b1)
    r = math.hypot(x1-p1, y1-p2)
    temp = [p1,p2,r]
    ans = map(lambda x:round(x,3),temp)
    print("%03.3f %03.3f %03.3f"%(temp[0],temp[1],temp[2]))

Python: import math

class P(object):
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def width(self, p):
        return math.sqrt((self.x - p.x)**2 + (self.y - p.y)**2)

    def __repr__(self):
        return '{0:.3f} {1:.3f}'.format(self.x, self.y)

def calc_cos(a,b,c):
    return (b**2 + c**2 - a**2) / (2*b*c)

def calc_sin(c):
    return math.sqrt(1 - c**2)

def calc_2sin(s,c):
    return 2 * s * c

def run():
    n = int(input())
    for _ in range(n):
        x1, y1, x2, y2, x3, y3 = list(map(float, input().split()))
        p1, p2, p3 = P(x1, y1), P(x2, y2), P(x3, y3)
        a, b, c = p1.width(p2), p2.width(p3), p3.width(p1)
        cosA, cosB, cosC = calc_cos(a,b,c), calc_cos(b,c,a), calc_cos(c,a,b)
        sinA, sinB, sinC = calc_sin(cosA), calc_sin(cosB), calc_sin(cosC)
        sin2A, sin2B, sin2C = calc_2sin(sinA, cosA), calc_2sin(sinB, cosB), calc_2sin(sinC, cosC)

        r = a / sinA / 2

        x = (p1.x * sin2B + p2.x * sin2C + p3.x * sin2A) / (sin2A + sin2B + sin2C)
        y = (p1.y * sin2B + p2.y * sin2C + p3.y * sin2A) / (sin2A + sin2B + sin2C)

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

if __name__ == '__main__':
    run()

Python: import math

class Circle:
    def __init__(self,x,y,r):
        self.x = x
        self.y = y
        self.r = r

def getCircle(x1, y1, x2, y2, x3, y3):
    d = 2 * (x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2))
    px = ((x1**2 + y1**2) * (y2 - y3) + (x2**2 + y2**2) * (y3 - y1) + (x3**2 + y3**2) * (y1 - y2) ) / d
    py = ((x1**2 + y1**2) * (x3 - x2) + (x2**2 + y2**2) * (x1 - x3) + (x3**2 + y3**2) * (x2 - x1) ) / d
    a = math.sqrt((x1 - x2)**2 + (y1 - y2)**2)
    b = math.sqrt((x1 - x3)**2 + (y1 - y3)**2)
    c = math.sqrt((x2 - x3)**2 + (y2 - y3)**2)
    s = (a + b + c) / 2
    A = math.sqrt(s * (s - a) * (s - b) * (s - c))
    r = a * b * c / (4 * A)
    return Circle(px,py,r)

          
n = int(input())
for k in range(n):
    x1, y1, x2, y2, x3, y3 = [float(x) for x in input().split()]
    circle = getCircle(x1, y1, x2, y2, x3, y3)
    print("%.3f %.3f %.3f" % (circle.x, circle.y, circle.r))

Python: # -*- coding:utf-8 -*-

import sys
import math

def solve(x1,y1,x2,y2,x3,y3):
    z1 = -1 * (x1**2 + y1**2)
    z2 = -1 * (x2**2 + y2**2)
    z3 = -1 * (x3**2 + y3**2)

    a11,a12,a13 = x1,y1,1
    a21,a22,a23 = x2,y2,1
    a31,a32,a33 = x3,y3,1
    det = a11*a22*a33 + a21*a32*a13 + a31*a12*a23 - a11*a32*a23 - a31*a22*a13 - a21*a12*a33

    l = ((a22*a33 - a23*a32)*z1 + (a13*a32 - a12*a33)*z2 + (a12*a23 - a13*a22)*z3)/det
    m = ((a23*a31 - a21*a33)*z1 + (a11*a33 - a13*a31)*z2 + (a13*a21 - a11*a23)*z3)/det
    n = ((a21*a32 - a22*a31)*z1 + (a12*a31 - a11*a32)*z2 + (a11*a22 - a12*a21)*z3)/det

    x,y,r = round(-l/2,3),round(-m/2,3),round(math.sqrt((l**2)/4+(m**2)/4-n),3)
    sol = [x, y, r]
    return sol


n,count = int(input()),0
array = []
for i in sys.stdin:
    array.append(i)
    count += 1
    if count == n:
        break

    
for i in range(len(array)):
    x = array[i]
    p = x.split()
    res = solve(float(p[0]),float(p[1]),float(p[2]),float(p[3]),float(p[4]),float(p[5]))
    print('{:.3f} {:.3f} {:.3f}'.format(res[0], res[1], res[2]))

Python: from __future__ import (division, absolute_import, print_function,
                        unicode_literals)
from sys import stdin
from math import sqrt
N = int(stdin.readline())
for i in xrange(N):
    x1, y1, x2, y2, x3, y3 = (float(n) for n in stdin.readline().split())
    det = x1*y2 + x2*y3 + x3*y1 - x1*y3 - x2*y1 - x3*y2
    a = x1**2 + y1**2
    b = x2**2 + y2**2
    c = x3**2 + y3**2
    L = (a*y2 + b*y3 + c*y1 - a*y3 - b*y1 - c*y2) / det
    M = (x1*b + x2*c + x3*a - x1*c - x2*a - x3*b) / det
    N = (x1*y2*c + x2*y3*a + x3*y1*b - x1*y3*b - x2*y1*c - x3*y2*a) / det
    xp = L / 2.0
    yp = M / 2.0
    r = sqrt(abs(N + xp**2.0 + yp**2.0))
    print('{:.3f} {:.3f} {:.3f}'.format(xp, yp, r))

Python: from math import sqrt
n=input()
for i in range(n):
	x1,y1,x2,y2,x3,y3=map(float,raw_input().split())
	A1=2*(x2-x1)
	B1=2*(y2-y1)
	C1=x2**2+y2**2-x1**2-y1**2
	x=((C1*B2)-(C2*B1))/((A1*B2)-(A2*B1))
	y=((A1*C2)-(A2*C1))/((A1*B2)-(A2*B1))