#include <bits/stdc++.h>
#define ll long long
using namespace std;
#define fi first
#define se second
#define mkp make_pair
#define pb push_back
typedef pair <int, int> pii;
const long double PI = acos(-1);

inline ll read() {
	ll x = 0, f = 0;
	char c = getchar();
	while (!isdigit(c)) {if (c == '-') f = 1; c = getchar();}
	while (isdigit(c)) x = (x << 1) + (x << 3) + (c & 15), c = getchar();
	return f? -x : x;
}

void getc(ll x1, ll y1, ll x2, ll y2, long double &x, long double &y, long double &r) {
	x = (x1 + x2) / 2.0;
	y = (y1 + y2) / 2.0;
	r = sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)) / 2.0;
}

int main() {
///	freopen ("std.in", "r", stdin);
//	freopen ("std.out", "w", stdout);
	int T;
	T = read();
	while (T--) {
		ll t1, t2, t3, t4;
		long double x1, y1, r1, x2, y2, r2;
		t1 = read(), t2 = read(), t3 = read(), t4 = read();
		getc(t1, t2, t3, t4, x1, y1, r1);
		t1 = read(), t2 = read(), t3 = read(), t4 = read();
		getc(t1, t2, t3, t4, x2, y2, r2);
		long double x = fabs(x2 - x1);
		long double y = fabs(y2 - y1);
		// x = x - r2 * cos(PI / 4.0);
		// y = y - r2 * sin(PI / 4.0);
		printf("%.10Lf", x + y - r2 * sqrt(2.0));
	}
	return 0;
}