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: 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))