Go: package main

import (
	"bufio"
	"fmt"
	"io"
	"math"
	"os"
	"strconv"
	"strings"

)


func main() {
	solve(os.Stdin, os.Stdout)
}

type ReaderEx struct {
	baseScanner *bufio.Scanner
	words       []string
	nextWordIdx func() int
	initWordIdx func(int)
}

func NewScannerEx(stdin io.Reader) *ReaderEx {
	var this ReaderEx
	var idx int
	var wordsCnt int
	this.baseScanner = bufio.NewScanner(stdin)
	this.baseScanner.Buffer(make([]byte, 0), 1E+11)
	this.nextWordIdx = func() int {
		cur := idx
		idx = (idx + 1) % wordsCnt
		return cur
	}
	this.initWordIdx = func(wc int) {
		idx = 0
		wordsCnt = wc
	}
	return &this
}

func (me *ReaderEx) Scan(doSplit bool) (isScanned bool) {
	isScanned = me.baseScanner.Scan()
	if doSplit {
		me.words = strings.Fields(me.baseScanner.Text())
	} else {
		me.words = []string{me.baseScanner.Text()}
	}
	me.initWordIdx(len(me.words))
	return
}

func (me *ReaderEx) nextBytes() []byte {
	return []byte(me.words[me.nextWordIdx()])
}
func (me *ReaderEx) nextString() string {
	return me.words[me.nextWordIdx()]
}

type StringArray []string

func (me *ReaderEx) nextStringArray() StringArray {
	return me.words[me.nextWordIdx():]
}

func (me StringArray) toStrings() []string {
	return me
}

func (me StringArray) toInts() []int {
	strValues := me.toStrings()
	values := make([]int, len(strValues))
	for i, v := range strValues {
		n, err := strconv.Atoi(v)
		if err != nil {
			panic(err)
		}
		values[i] = n
	}
	return values
}
func (me *ReaderEx) nextInt() int {
	n, err := strconv.Atoi(me.words[me.nextWordIdx()])

	defer func() {
		if err != nil {
			panic(fmt.Sprintf("getInt(%d)", n))
		}
	}()
	return n
}

func pow(x, y, mod int) (ans int) {

	ans = 1
	for bit := 1 << uint(math.Floor(math.Log2(float64(y)))); ; bit >>= 1 {
		if y&bit != 0 {
			ans *= x
			if mod > 0 {
				ans %= mod
			}
		}
		if bit <= 1 {
			return
		}
		ans *= ans
		if mod > 0 {
			ans %= mod
		}
	}
}

type factType struct {
	prime int
	count int
}

func fact(n int) (facts []*factType) {

	for i := 2; i*i <= n; i++ {
		if n%i == 0 {
			fa := factType{prime: i}
			for n%fa.prime == 0 {
				n /= fa.prime
				fa.count++
			}
			facts = append(facts, &fa)
		}
	}
	if n > 1 {
		facts = append(facts, &factType{prime: n, count: 1})
	}
	return facts
}
func dec2bin(n int) (ret []bool) {
	for bit := 1 << uint(math.Floor(math.Log2(float64(n)))); ; bit >>= 1 {
		ret = append(ret, n&bit != 0)

		if bit <= 1 {
			return
		}
	}

}

func abs(v int) int {
	if v < 0 {
		v = -v
	}
	return v
}

func b2i(b bool) (i int) {
	if b {
		i = 1
	} else {
		i = 0
	}
	return
}

func solve(stdin io.Reader, stdout io.Writer) {

	r := NewScannerEx(stdin)
	r.Scan(true)
	n := r.nextInt()

	type Vec struct {
		x, y float64
	}
	vec := func(a, b Vec) Vec { return Vec{b.x - a.x, b.y - a.y} }
	unv := func(a Vec) Vec { return Vec{-a.y, a.x} }
	cdot := func(a, b Vec) float64 { return a.x*b.x + a.y*b.y }
	times := func(t float64, a Vec) Vec { return Vec{t * a.x, t * a.y} }
	add := func(a, b Vec) Vec { return Vec{a.x + b.x, a.y + b.y} }
	for i := 0; i < n; i++ {

		r.Scan(true)
		nextFloat64 := func() (ret float64) { fmt.Sscanf(r.nextString(), "%f", &ret); return }
		a1, a2, a3 := Vec{nextFloat64(), nextFloat64()}, Vec{nextFloat64(), nextFloat64()}, Vec{nextFloat64(), nextFloat64()}
		unv23 := unv(vec(a2, a3))
		v12 := vec(a1, a2)
		v31 := vec(a3, a1)
		s := cdot(v12, v31) / 2 / cdot(v12, unv23)
		c := add(times(.5, add(a2, a3)), times(s, unv23))
		v1c := vec(a1, c)
		fmt.Fprintf(stdout, "%.3f %.3f %.3f\n", c.x, c.y, math.Sqrt(v1c.x*v1c.x+v1c.y*v1c.y))
	}
}

Python: # -*- coding: utf-8 -*-
from math import sqrt
import numpy as np


# n = int(input())
# tmp = input().split(' ')
tmp = '0.0 0.0 2.0 0.0 2.0 2.0'.split(' ')
# tmp = '0.0 3.0 -1.0 0.0 -3.0 4.0'.split(' ')
a, b, c = [(float(tmp[i]), float(tmp[i+1])) for i in range(0, len(tmp), 2)]

A = np.array(((a[0], a[1], 1),
              (b[0], b[1], 1),
              (c[0], c[1], 1)))

B = np.array((((-(a[0]**2 + a[1]**2))),
              ((-(b[0]**2 + b[1]**2))),
              ((-(c[0]**2 + c[1]**2)))))

tmp = np.dot(np.linalg.inv(A), B)

#tmp = [-6, 10, 18]

x = -tmp[0]/2
y = -tmp[1]/2
r = sqrt((tmp[0]**2 + tmp[1]**2 - 4*tmp[2])/4)

print('{:.3} {:.3} {:.3}'.format(x, y, r))

Python: from math import hypot
n=int(input())
for i in range(n):
	x1,y1,x2,y2,x3,y3=map(float,input().split())
	x4=((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))
	y4=((x1-x3)*(x1**2-x2**2+y1**2-x1**2)-(x1-x2)*(x1**2-x3**2+y1**2-y3**2))/(2*(x1-x3)*(y1-y2)-2*(x1-x2)*(y1-y3))
	r=hypot(x1-x4,y1-y4)
	print("{:.3f} {:.3f} {:.3f}".format(x4,y4,r))

Python: # -*- coding: utf-8 -*-
from math import sqrt
# import numpy as np


n = int(input())

for i in range(n):
    tmp = input().split(' ')
    
    a, b, c = [(float(tmp[i]), float(tmp[i+1])) for i in range(0, len(tmp), 2)]
    
    #A = np.array(((a[0], a[1], 1),
    #              (b[0], b[1], 1),
    #              (c[0], c[1], 1)))
    A_tmp1 = 1/(a[0]*b[1] + a[1]*c[0] + b[0]*c[1] - b[1]*c[0] - a[1]*b[0] - a[0]*c[1])
    A_tmp2 = [[b[1]-c[1], -(a[1]-c[1]), a[1]-b[1]],
              [-(b[0]-c[0]),  (a[0]-c[0]), -(a[0]-b[0])],
              [b[0]*c[1] - b[1]*c[0], -(a[0]*c[1] - a[1]*c[0]), a[0]*b[1] - a[1]*b[0]]]
    A = [list(map(lambda x: A_tmp1*x, A_tmp2[i])) for i in range(3)]
    
    #B = np.array((((-(a[0]**2 + a[1]**2))),
    #              ((-(b[0]**2 + b[1]**2))),
    #              ((-(c[0]**2 + c[1]**2)))))
    B = [[-(a[0]**2 + a[1]**2)],
         [-(b[0]**2 + b[1]**2)],
         [-(c[0]**2 + c[1]**2)]]
    
    
    tmp = [sum([A[i][j]*B[j][0] for j in range(3)]) for i in range(3)]
    # tmp = np.dot(np.linalg.inv(A), B)
    
    x = -tmp[0]/2
    y = -tmp[1]/2
    r = sqrt((tmp[0]**2 + tmp[1]**2 - 4*tmp[2])/4)
    
    print('{:.3f} {:.3f} {:.3f}'.format(x, y, r))

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-e)+(c*c+d*d)*(e-a)+(e*e+f*f)*(a-c))/2/(b*(c-e)+d*(e-a)+f*(a-c))
 print('.3f %.3f %.3f'%(x,y,((x-a)**2+(y-b)**2)**.5))

Python: import math

def run():
    n = int(input())
    for _ in range(n):
        x1, y1, x2, y2, x3, y3 = list(map(float, input().split()))
        u1 = (x1-x3)*(x2-x1)*(x3-x2)
        u2 = (x2-x1)*(y3-y2)*(y3+y2)
        u3 = (x3-x2)*(y2-y1)*(y2+y1)
        v = x1*x2 + x2*y3 + x3*y1 - x1*y3 - x2*y1 + x3*y2
        Py = (-u1 + u2 - u3) / v / 2
        Px = (x2**2 - x1**2 + y2**2 - y1**2 - (y2 - y1)*Py) / (x2-x1) / 2
        r = math.sqrt((Px-x1)**2 + (Py-y1)**2)
        print('{0:.3f} {1:.3f} {2:.3f}'.format(round(Px,3), round(Py,3), round(r,3)))

if __name__ == '__main__':
    run()

Python: #!/usr/bin/env python
from math import *
def g(x):
	y = (int((1000 * abs(x)) * 2 + 1) // 2) / 1000
	return y / abs(y) * y
def func(x):
	x1, y1, x2, y2, x3, y3 = x

	vx1 = x2 - x1
	vy1 = y2 - y1
	vx2 = x3 - x1
	vy2 = y3 - y1
	k = (vx2 ** 2 + vy2 ** 2 - vx1 * vx2 - vy1 * vy2) / (vy1 * vx2 - vx1 * vy2) / 2
	x = vx1 / 2 + k * vy1 + x1
	y = vy1 / 2 - k * vx1 + y1
	r = sqrt((x1 - x) ** 2 + (y1 - y) ** 2)
	print("{0:.3f} {1:.3f} {2:.3f}".format(g(x), g(y), g(r)))
n = int(input())
for _ in range(n):
	func(list(map(float, input().split())))

Python: import math
n=int(input())
for i in range(n):
  x1,y1,x2,y2,x3,y3=map(float,input().split())
  a=(x3-x1)*(x1**2+y1**2-x2**2-y2**2)-(x2-x1)*(x1**2+y1**2-x3**2-y3**2)
  b=2*(x3-x1)*(y1-y2)-2*(x2-x1)*(y1-y3)
  py=a/b
  if x2-x1!=0:
    px=(2*(y1-y2)*py-x1**2-y1**2+x2**2+y2**2)/(2*(x2-x1))
  else:
    px=(2*(y1-y3)*py-x1**2-y1**2+x3**2+y3**2)/(2*(x3-x1))
  r=math.sqrt((px-x1)**2+(py-y1)**2)
  print(f"{px:.3f}",f"{py:.3f}",f"{r:.3f}")