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: # Circumscribed Circle of a Triangle
import math
def simul_eq(a,b,c,d,e,f):
    # A = [[a,b],[d,e]]
    C = [c,f]
    detA = a*e - b*d
    # if detA == 0: raise # det(A) == 0.
    At = [[e,-b],[-d,a]]
    x = sum(map((lambda x,y: x*y), At[0], C)) / detA
    y = sum(map((lambda x,y: x*y), At[1], C)) / detA
    fx,fy = '{0:.3f}'.format(x), '{0:.3f}'.format(y)
    if fx == '-0.000': fx = fx[1:]
    if fy == '-0.000': fy = fy[1:]
    return (fx,fy)

n = int(input())
for _ in range(n):
    x1,y1,x2,y2,x3,y3 = map(float, input().split())
    a = math.sqrt(pow(x2-x3, 2) + pow(y2-y3, 2))
    b = math.sqrt(pow(x1-x3, 2) + pow(y1-y3, 2))
    c = math.sqrt(pow(x2-x1, 2) + pow(y2-y1, 2))
    cosA = (pow(b,2) + pow(c,2) - pow(a,2)) / (2*b*c)
    sinA = math.sqrt(1 - pow(cosA,2))
    R = a / (2 * sinA)
    cen = simul_eq(x2-x1, y2-y1, (y2**2 - y1**2 + x2**2 - x1**2) / 2, x3-x1, y3-y1, (y3**2 - y1**2 + x3**2 - x1**2) / 2)
    print(' '.join(cen), '{0:.3f}'.format(R))

Python: import math

def da(li):
    x1,y1,x2,y2,x3,y3=[float(i) for i in li]
    xp,yp=(x2-x1)/2,(y2-y1)/2
    xq,yq=(x3-x1)/2,(y3-x1)/2
    t=(xq**2+yq**2-xp*xq-yp*yq)/(xp*yq-xq*yp)
    return xp-t*yp,yp+t*xp
def sis(fl):
    fls=str(fl)
    if len(fls)<6:return fls+"".join(["0" for i in range(5-len(fls))])
    if int(fls[5:6])>4:
        return fls[:4]+str(int(fls[4:5])+1)
    else:
        return fls[:5]

n=int(input())
for i in range(n):
    li=input().split(" ")
    x,y=da(li)
    print(sis(x)+" "+sis(y)+" "+sis(math.sqrt(x**2+y**2)))

Python: import math

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

    s = 0.5*((x1-x3)*(y2-y3) - (x2-x3)*(y1-y3))
    a = (x2-x3)**2 + (y2-y3)**2
    b = (x1-x3)**2 + (y1-y3)**2
    c = (x2-x1)**2 + (y2-y1)**2

    rx = (a*(b+c-a)*x1 + b*(c+a-b)*x2 + c*(a+b-c)*x3)/(16*s**2)
    ry = (a*(b+c-a)*y1 + b*(c+a-b)*y2 + c*(a+b-c)*y3)/(16*s**2)
    r = math.sqrt((rx-x1)**2 + (ry-y1)**2)
    print( "{0:.3f} {1:.3f} {2:.3f}".format(rx+0, ry+0, r+0))

Python: import math

n = int(input())
for i in range(n):
    x1, y1, x2, y2, x3, y3 = map(float, input().split())
    a1 = x1 ** 2 - x2 ** 2 + y1 ** 2 - y2 ** 2
    a2 = y1 ** 2 - y3 ** 2 + x1 ** 2 - x3 ** 2
    px = ((y1 - y3) * a1 - (y1 - y2) * a2) / (2 * (y1 - y3) * (x1 - x2) - 2 * (y1 - y2) * (x1 - x3))
    py = ((x1 - x3) * a1 - (x1 - x2) * a2) / (2 * (x1 - x3) * (y1 - y2) - 2 * (x1 - x2) * (y1 - y3))
    r = math.sqrt(px ** 2 + py ** 2)
    print("{0:.3f} {1:.3f} {2:.3f}".format(px, py, r))

Python: # Aizu Problem 0010: Circumscribed Circle of a Triangle
#
import sys, math, os

# read input:
PYDEV = os.environ.get('PYDEV')
if PYDEV=="True":
    sys.stdin = open("sample-input.txt", "rt")


def circumscribed_circle(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 px, py, r

          
N = int(input())
for k in range(N):
    x1, y1, x2, y2, x3, y3 = [float(_) for _ in input().split()]
    px, py, r = circumscribed_circle(x1, y1, x2, y2, x3, y3)
    print("%.3f %.3f %.3f" % (px, py, r))

Python: import math
n=int(raw_input())
for i in range(n):
    x1,y1,x2,y2,x3,y3=[float(i) for i in raw_input().split()]
    t1=x1*(x2+x3-x1)+y1*(y2+y3-y1)
    t2=x2*(x1+x3-x2)+y2*(y1+y3-y2)
    t3=x3*(x1+x2-x3)+y3*(y1+y2-y3)
    px=(t1*x1+t2*x2+t3*x3)/(t1+t2+t3)
    py=(t1*y1+t2*y2+t3*y3)/(t1+t2+t3)
    r=math.hypot(px-x1,py-y1)
    print("{0} {1} {2}".format(round(px,3),round(py,3),round(r,3)))

Python: from math import hypot
n=int(input())
for i in range(n):
	x1,y1,x2,y2,x3,y3=map(int,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))