Triangle Partitioning

#include <bits/stdc++.h>
#define Niloy
#define int int64_t
#define MAX 1000
#define MOD 1e9
#define pb push_back
#define pairs pair<int, int>
#define vi vector<int>
#define vb vector<bool>
#define vii vector<pairs>
#define lb lower_bound
#define ub upper_bound
#define endl '\n'
#define llu unsigned long long
using namespace std;
/* ----------------------------------------------------------------------------------- */

// Input/Output
#define fastInput ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
#define all(x) x.begin(), x.end()

#define scan(a)           scanf("%lld", &a);
#define scan2(a, b)       scanf("%lld %lld", &a, &b);
#define scan3(a, b, c)    scanf("%lld %lld %lld", &a, &b, &c);
#define scan4(a, b, c, d) scanf("%lld %lld %lld %lld", &a, &b, &c, &d);

#define scanD(a)          scanf("%lf", &a);
#define scanD2(a, b)      scanf("%lf %lf", &a, &b);
#define scanD3(a, b, c)   scanf("%lf %lf %lf", &a, &b, &c);
#define scanD4(a, b, c, d)scanf("%lf %lf %lf %lf", &a, &b, &c, &d);


#define print(a)           printf("%lld\n", a);
#define print2(a, b)       printf("%lld %lld\n", a, b);
#define print3(a, b, c)    printf("%lld %lld %lld\n", a, b, c);
#define print4(a, b, c, d) printf("%lld %lld %lld %lld\n", a, b, c, d);

#define printD(a)          printf("%lf\n", a);
#define printD2(a, b)      printf("%lf %lf\n", a, b);
#define printD3(a, b, c)   printf("%lf %lf %lf\n", a, b, c);
#define printD4(a, b, c, d)printf("%lf %lf %lf %lf\n", a, b, c, d);
#define printTwoD(a)       printf("%.2lf\n", a);

// File I/O
#define read(x)  freopen(x, "r", stdin);
#define write(x) freopen(x, "w", stdout);

// Loops
#define rep(i, a, n) for (int i = a; i < n; i++)
#define REP(i, a, n) for (int i = a; i <= n; i++)
#define rev(i, n, a) for (int i = n - 1; i >= a; i--)
#define REV(i, n, a) for (int i = n; i >= a; i--)
#define inputArray(a,n) rep(i, 0, n) cin >> a[i];
#define copyArray(a,temp,n) rep(i, 0, n) temp[i]=a[i];
#define printArray(a,n) rep(i, 0, n) cout << a[i] << " "; cout << endl;

/* ----------------------------------------------------------------------------------- */

#define Cases  cout << "Case " << ++Case << ": ";
#define __test int tt; int Case=0; cin >> tt; while(tt--)
#define showTime cerr << "time = " << (clock() / CLOCKS_PER_SEC) << " sec" << '\n';

#define dbgA2(A, n, m) {cout<<"--> "<<#A<<" = \n";rep(i, 0, n){rep(j, 0, m){cout<<A[i][j]<<"";}cout<<"\n";}cout<<"\n";}
#define dbgA(A, n) {cout<<" --> "<<#A<<" = (";rep(i, 0, n)cout<<A[i]<<" ";cout<<")\n";}
#define dbg(args...) {string sss(#args);sss+=',';cout<<" --> ";debugger::call(all(sss), args);cout<<"\n";}

/* ----------------------------------------------------------------------------------- */

int gcd(int n, int m) { return m ? gcd(m, n % m) : n; }
int lcm(int n, int m) { return n / gcd(n, m) * m; }

struct debugger {
    typedef string::iterator si;
    static void call(si it, si ed) {}
    template<typename T, typename ... aT>
    static void call(si it, si ed, T a, aT... rest) {
        string b;
        for(; *it!=','; ++it)
            if(*it!=' ')
                b+=*it;
        cout << b << "=" << a << " ";
        call(++it, ed, rest...);
    }
};

/* ----------------------------------------------------------------------------------- */
void input() {
#ifdef Niloy
    read("input.txt");
    write("output.txt");
#endif
}

/* ----------------------------------------------------------------------------------- */


double findAD(double ab, double ac, double bc, double R) {
    double l = 0, r = ab;
    rep(i, 0, 100) {
        double ad = (l + r) / 2.0;
        double x = ad / ab;
        double ae = x * ac;
        double de = x * bc;

        double pABC = (ab + ac + bc) / 2.0;
        double pADE = (ad + ae + de) / 2.0;

        double ABC = sqrt(pABC * (pABC - ab) * (pABC - ac) * (pABC - bc));
        double ADE = sqrt(pADE * (pADE - ad) * (pADE - ae) * (pADE - de));

        double areaTra = ABC - ADE;
        if (R < (ADE / areaTra)) {
            r = ad;
        } else {
            l = ad;
        }
    }
    return l;
}

void solve() {
    double ab, ac, bc, r;
    scanD4(ab, ac, bc, r);
    cout << fixed << setprecision(10) << findAD(ab, ac, bc, r) << endl;
}

int32_t main() {
    // input();
    // fastInput;
    // solve();

    __test {
        Cases;
        solve();
    }

    // showTime;
    return 0;
}