//Let's join Kaede Takagaki Fan Club !!
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <ctime>
#include <cassert>
#include <string>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <functional>
#include <iostream>
#include <map>
#include <set>
//#include <unordered_map>
//#include <unordered_set>
#include <cassert>
#include <iomanip>
#include <chrono>
#include <random>
#include <bitset>
#include <complex>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
//#include <atcoder/convolution>
//#include <atcoder/lazysegtree>
//#include <atcoder/maxflow>
//#include <atcoder/mincostflow>
//#include <atcoder/segtree>
//#include <atcoder/string>
using namespace std;
//using namespace atcoder;
#define int long long
//#define L __int128
typedef long long ll;
typedef pair<int,int> P;
typedef pair<int,P> P1;
typedef pair<P,P> P2;
#define pu push
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define eps 1e-7
#define INF 1000000000
#define a first
#define b second
#define fi first
#define sc second
#define rng(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define rep(i,x) for(int i=0;i<x;i++)
#define gnr(i,a,b) for(int i=(int)(b)-1;i>=(int)(a);i--)
#define per(i,b) gnr(i,0,b)
#define repn(i,x) for(int i=1;i<=x;i++)
#define SORT(x) sort(x.begin(),x.end())
#define ERASE(x) x.erase(unique(x.begin(),x.end()),x.end())
#define POSL(x,v) (lower_bound(x.begin(),x.end(),v)-x.begin())
#define POSU(x,v) (upper_bound(x.begin(),x.end(),v)-x.begin())
#define all(x) x.begin(),x.end()
#define si(x) (int)(x.size())
#define pcnt(x) __builtin_popcountll(x)
#define all(x) x.begin(),x.end()

#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif
 
template<class t,class u> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}
 
template<class t> using vc=vector<t>;
 
template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.fi<<","<<p.sc<<"}";
}
 
template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}
 
 //https://codeforces.com/blog/entry/62393
struct custom_hash {
	static uint64_t splitmix64(uint64_t x) {
		// http://xorshift.di.unimi.it/splitmix64.c
		x += 0x9e3779b97f4a7c15;
		x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
		x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
		return x ^ (x >> 31);
	}
 
	size_t operator()(uint64_t x) const {
		static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
		return splitmix64(x + FIXED_RANDOM);
	}
	//don't make x negative!
	size_t operator()(pair<int,int> x)const{
		return operator()(uint64_t(x.first)<<32|x.second);
	}
};
//unordered_set -> dtype, null_type
//unordered_map -> dtype(key), dtype(value)
using namespace __gnu_pbds;
template<class t,class u>
using hash_table=gp_hash_table<t,u,custom_hash>;

template<class T>
void o(const T &a,bool space=false){
	cout << a << (space?' ':'\n');
}
//ios::sync_with_stdio(false);
const ll mod = 998244353;
//const ll mod = 1000000007;
mt19937_64 mt(chrono::steady_clock::now().time_since_epoch().count());

struct mint{
	ll v;
	mint(ll vv=0){s(vv%mod+mod);}
	mint& s(ll vv){
		v=vv<mod?vv:vv-mod;
		return *this;
	}
	mint operator-()const{return mint()-*this;}
	mint &operator+=(const mint&rhs){return s(v+rhs.v);}
	mint &operator-=(const mint&rhs){return s(v+mod-rhs.v);}
	mint &operator*=(const mint&rhs){v=ll(v)*rhs.v%mod;return *this;}
	mint &operator/=(const mint&rhs){return *this*=rhs.inv();}
	mint operator+(const mint&rhs)const{return mint(*this)+=rhs;}
	mint operator-(const mint&rhs)const{return mint(*this)-=rhs;}
	mint operator*(const mint&rhs)const{return mint(*this)*=rhs;}
	mint operator/(const mint&rhs)const{return mint(*this)/=rhs;}
	mint pow(ll n)const{
		if(n<0)return inv().pow(-n);
		mint res(1),x(*this);
		while(n){
			if(n&1)res*=x;
			x*=x;
			n>>=1;
		}
		return res;
	}
	mint inv()const{return pow(mod-2);}
	friend mint operator+(ll x,const mint&y){
		return mint(x)+y;
	}
	friend mint operator-(ll x,const mint&y){
		return mint(x)-y;
	}
	friend mint operator*(ll x,const mint&y){
		return mint(x)*y;
	}
	friend mint operator/(ll x,const mint&y){
		return mint(x)/y;
	}
	friend ostream& operator<<(ostream&os,const mint&m){
		return os<<m.v;
	}
	friend istream& operator>>(istream&is,mint&m){
		ll x;is>>x;
		m=mint(x);
		return is;
	}
	bool operator<(const mint&r)const{return v<r.v;}
	bool operator==(const mint&r)const{return v==r.v;}
	bool operator!=(const mint&r)const{return v!=r.v;}
	explicit operator bool()const{
		return v;
	}
};
ll modpow(ll x,ll n,ll _md=mod){
	ll res=1;
	while(n>0){
		if(n&1) res=res*x%_md;
		x=x*x%_md;
		n>>=1;
	}
	return res;
}
#define _sz 1
mint F[_sz],R[_sz];
void make(){
	F[0] = 1;
	for(int i=1;i<_sz;i++) F[i] = F[i-1] * i;
	R[_sz-1] = F[_sz-1].pow(mod-2);
	for(int i=_sz-2;i>=0;i--) R[i] = R[i+1] * (i+1);
}
mint C(int a,int b){
	if(b < 0 || a < b) return mint();
	return F[a]*R[b]*R[a-b];
}
using ld=long double;
using vi=vc<int>;
using ull=unsigned long long;
/*int dst(P p, P q){
	return (p.a-q.a)*(p.a-q.a)+(p.b-q.b)*(p.b-q.b);
}*/
/*template<class t>
void add_inplace(t &a, t b){
	if(a.size() < b.size()) swap(a, b);
	for(int i=0;i<si(b);i++){
		a[i] += b[i];
		if(a[i] < 0) a[i] += mod;
		if(a[i] >= mod) a[i] -= mod;
	}
	return ;
}*/
template<class t>
void ov(const vc<t>&a){
	if(a.empty()) return;
	rep(i, si(a)) cout << a[i] << (i+1==si(a)?'\n':' ');
}
//o(ans?"Yes":"No");
#define ld long double
#define x real()
#define y imag()
using pt=complex<ld>;
using d=array<ld,6>;
d add(d a,d b){
	rep(i,6) a[i]+=b[i];
	return a;
}
bool ok(ld a,ld b,ld c,ld lb=0,ld ub=1){
	if(a*lb*lb+b*lb+c >= 0) return 1;
	if(a*ub*ub+b*ub+c >= 0) return 1;
	ld xx = -b/a/2;
	if(lb<=xx and xx<=ub and a*xx*xx+b*xx+c >= 0) return 1;
	return 0;
}
void solve(){
	pt pp[4],p[4];
	ld xmn=1e18,ymn=1e18,xmx=-1e18,ymx=-1e18;
	rep(i,4){
		ld ap,q;
		cin>>ap>>q;
		pp[i]=pt(ap,q);
		chmin(xmn,ap); chmax(xmx,ap);
		chmin(ymn,q); chmax(ymx,q);
	}
	if(pp[0].x == pp[1].x or pp[0].y == pp[1].y){
		o(1);
		return;
	}
	rep(i,4){
		if(pp[i].x==xmn)p[0] = pp[i];
		if(pp[i].y==ymn)p[1] = pp[i];
		if(pp[i].x==xmx)p[2] = pp[i];
		if(pp[i].y==ymx)p[3] = pp[i];
	}
	d up=d{};
	up[5] = abs(p[0]-p[1])*abs(p[1]-p[2]);
	ld coef1 = 0;
	coef1 += (p[0].y-p[1].y)/(p[1].x-p[0].x);
	coef1 += (p[3].y-p[0].y)/(p[3].x-p[0].x);
	ld coef2 = 0;
	coef2 += (p[1].x-p[0].x)/(p[0].y-p[1].y);
	coef2 += (p[2].x-p[1].x)/(p[2].y-p[1].y);
	ld r = xmx-xmn;
	ld c = ymx-ymn;
	up = add(up,d{-r*r/4*coef1,-c*c/4*coef2,0,0,0,0});
	d dw=d{r*r/4*coef1,c*c/4*coef2,r*c,-r*c,-r*c,r*c};
	/*for(ld ax=0;ax<=1;ax+=0.0001){
		for(ld ay=0;ay<=1;ay+=0.0001){
			ld U = up[0]*ax*ax+up[1]*ay*ay+up[2]*ax*ay+up[3]*ax+up[4]*ay+up[5];
			ld D = dw[0]*ax*ax+dw[1]*ay*ay+dw[2]*ax*ay+dw[3]*ax+dw[4]*ay+dw[5];
			chmax(ans, U/D);
		}
	}*/
	ld lb = 0,ub = 1;
	rep(i,64){
		ld mid=(lb+ub)/2;
		d cur = up;
		rep(i,6) cur[i]-=dw[i]*mid;
		bool f = 0;
		if(ok(cur[1],cur[4],cur[5]))f=1;
		if(ok(cur[1],cur[2]+cur[4],cur[0]+cur[3]+cur[5]))f=1;
		if(ok(cur[0],cur[3],cur[5]))f=1;
		if(ok(cur[0],cur[2]+cur[3],cur[1]+cur[4]+cur[5]))f=1;
		ld a=-cur[2]/cur[1]/2;
		ld b=-cur[4]/cur[1]/2;
		{
			ld lb=-b/a, ub=(1.0L-b)/a;
			if(lb>ub)swap(lb,ub);
			chmax(lb,0.0L); chmin(ub,1.0L);
			if(lb <= ub){
				ld tw = cur[0]+cur[1]*a*a+cur[2]*a;
				ld on = cur[3]+cur[4]*a+cur[2]*b+cur[1]*a*b*2;
				ld ze = cur[1]*b*b+cur[4]*b+cur[5];
				if(ok(tw,on,ze,lb,ub))f=1;
			}
		}
		if(f)lb=mid;
		else ub=mid;
	}
	ld ans = lb;
//	cerr<<ans<<endl;
	if(p[1].x > p[3].x){
		rep(i,4) p[i] = pt(p[i].x, -p[i].y);
		swap(p[1],p[3]);
	}
	ld dx = p[3].x-p[0].x;
	ld dy = p[3].y-p[0].y;
	ld s = dx*dy/sqrt(dx*dx+dy*dy);
	ld t = abs(p[0]-p[1]);
	if(s <= t/2){
		chmax(ans, dx*dy/abs(p[0]-p[1])/abs(p[1]-p[2]));
	}
	else{
		chmax(ans, t*t*dx*dy/abs(p[0]-p[1])/abs(p[1]-p[2])/s/s/4);
		lb = 0,ub = 1;
		rep(i,64){
			ld mid=(lb+ub)/2;
			//t/s/2<=k<=1
		//	ld co = (k-t/s/2);
			//co*co*dx*dy+abs(p[0]-p[1])*abs(p[1]-p[2]);
			//k*k*dx*dy-co*co*dx*dy;
			//t/s*dx*dy k - t*t/s/s/4*dx*dy
			//dx*dy k^2 -t/s*dx*dy k t*t/s/s/4*dx*dy
			array<ld,3>up={0, t/s*dx*dy, -t*t/s/s/4*dx*dy};
			array<ld,3>dw={dx*dy ,-t/s*dx*dy, t*t/s/s/4*dx*dy+abs(p[0]-p[1])*abs(p[1]-p[2])};
			bool f= 0;
			if(ok(up[0]-dw[0]*mid, up[1]-dw[1]*mid, up[2]-dw[2]*mid, t/s/2, 1))f=1;
			if(f)lb=mid;
			else ub=mid;
		}
		//cerr<<lb<<endl;
		chmax(ans, lb);
	}
	o(ans);
}
signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	int t; cin >> t;
	while(t--) solve();
}