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: import math

def run():
    n = int(input())
    epsilon = 1e-16
    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 + epsilon) / 2
        Px = (x2**2 - x1**2 + y2**2 - y1**2 - (y2 - y1)*Py) / ((x2-x1) + epsilon) / 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: n = int(input())
for _ in range(n):
    x1,y1,x2,y2,x3,y3 = map(float, input().split())
    gx = (x1+x2+x3)/3
    gy = (y1+y2+y3)/3
    G=( y2*x1-y1*x2 +y3*x2-y2*x3 +y1*x3-y3*x1 )
    Xc= ((x1*x1+y1*y1)*(y2-y3)+(x2*x2+y2*y2)*(y3-y1)+(x3*x3+y3*y3)*(y1-y2))/(2*G)
    Yc=-((x1*x1+y1*y1)*(x2-x3)+(x2*x2+y2*y2)*(x3-x1)+(x3*x3+y3*y3)*(x1-x2))/(2*G)
    r = ( (x1 - Xc) * (x1 - Xc) + (y1 - Yc) * (y1 - Yc) )**0.5
    print("%.3f %.3f %.3f"%(Xc,Yc,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]))