# include <bits/stdc++.h>
using namespace std;
# define IOS ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
# define int long long
# define lowbit(x) (x & (-x))
# define fi first
# define se second
// # define endl '\n'

inline int Read();

typedef pair<int, int> PII;
const int INF = 0x3f3f3f3f;
const int MOD = 998244353;
const int N = 1e6 + 10;

map <int, int> mp;
vector <int> v;

const double eps = 1e-8;
const double pi = acos(-1.0);
int sgn(double x){
    if (fabs(x) < eps) return 0;
    return x > 0 ? 1 : -1;
}
struct Point{
    double x, y;
    Point(double x = 0, double y = 0) : x(x), y(y) {}
    Point operator+(Point b) { return Point(x + b.x, y + b.y); }
    Point operator-(Point b) { return Point(x - b.x, y - b.y); }
    Point operator*(double k) { return Point(x * k, y * k); }
    Point operator/(double k) { return Point(x / k, y / k); }
    Point operator==(Point b) { return sgn(x - b.x) == 0 && sgn(y - b.y) == 0; }
};
double cross(Point a, Point b) { return a.x * b.y - a.y * b.x; }
double dot(Point a, Point b) { return a.x * b.x + a.y * b.y; }
struct Line{
    Point p1, p2;
    Line(Point p1, Point p2) : p1(p1), p2(p2) {}
};
double len2(Point a) { return dot(a, a); }
double distance(Point a, Point b) { return hypot(a.x - b.x, a.y - b.y); }
double dis_point_line(Point p, Line v){
    return fabs(cross(p - v.p1, v.p2 - v.p1)) / distance(v.p1, v.p2);
}
Point point_line_proj(Point p, Line v){
    double k = dot(v.p2 - v.p1, p - v.p1) / len2(v.p2 - v.p1);
    return v.p1 + (v.p2 - v.p1) * k;
}
// 1、圆的定义
struct Circle{
    Point c;
    double r;
    Circle(Point c, double r = 0) : c(c), r(r) {}
    Circle(double x = 0, double y = 0, double _r = 0){
        c = Point(x, y);
        r = _r;
    }
};
// 2、点和圆心的距离
int point_circle_relation(Point p, Circle c){
    double dis = distance(p, c.c);
    if (sgn(dis - c.r) < 0) return 0; // 内
    if (sgn(dis - c.r) == 0) return 1; // 上
    return 2;     // 外
}
// 3、直线和圆关系
int line_circle_relation(Line v, Circle c){
    double dis = dis_point_line(c.c, v);
    if (sgn(dis - c.r) < 0) return 0; // 交
    if (sgn(dis - c.r) == 0) return 1; // 切
    return 2;     // 外
}
// 4、线段和圆关系
int seg_circle_relation(Line v, Circle c){
    double dis = dis_point_line(c.c, v);
    if (sgn(dis - c.r) < 0) return 0; // 内
    if (sgn(dis - c.r) == 0) return 1; // 切
    return 2;     // 外
}
Point a[4];
void Solve(){
    for(int i = 0; i < 4; i ++){
        double x, y;
        cin >> x >> y;
        a[i] = {x, y};
    }
    Point cc1 = (a[1] + a[0]) / 2.0;
    Point cc2 = (a[2] + a[3]) / 2.0;
    double r1 = distance(a[0], a[1]) / 2;
    double r2 = distance(a[2], a[3]) / 2;
    printf("%.10f\n", (fabs(cc1.x - cc2.x) + fabs(cc1.y - cc2.y)- sqrt(2.0) * r2));
    


}
signed main(){
    // IOS;
    int T = 1;
    cin >> T; 
    while (T--) 
        Solve();
    return 0;
}
inline int Read(){
    int x = 0, f = 1; char c = getchar();
    while (c < '0' || c > '9'){ if (c == '-') f = -1; c = getchar();}
    while (c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
    return x * f;
}