10556.cpp

/**
 *                                   ____
 *       ____ ___  ____ ________  __/ __/
 *      / __ `__ \/ __ `/ ___/ / / / /_
 *     / / / / / / /_/ / /  / /_/ / __/
 *    /_/ /_/ /_/\__,_/_/   \__,_/_/
 *
 *    @link : https://the-redback.com
 */

#include <bits/stdc++.h>
using namespace std;

#define mem(a, b) memset(a, b, sizeof(a))
#define pb        push_back
#define pp        pop_back
#define inf       10e9  // 10^9
#define meminf    100
#define eps       10e-5
#define NN        1000000
struct P {
    double x, y;
    P(double X, double Y) {
        x = X;
        y = Y;
    }
};

vector<P> v;

P MV(P a, P b) { return P(b.x - a.x, b.y - a.y); }

double DP(P a, P b) { return a.x * b.x + a.y * b.y; }

double CP(P a, P b) { return a.x * b.y - a.y * b.x; }

double A(P a) { return sqrt(a.x * a.x + a.y * a.y); }

P ADD(P a, P b) { return P(a.x + b.x, a.y + b.y); }

P LV(P a, double l) { return P(a.x * l / A(a), a.y * l / A(a)); }

P pvt(0, 0);

bool comp(P a, P b)  // False hoile sort korbe
{
    long long c = CP(MV(pvt, a), MV(pvt, b));
    if (c) return c > 0;
    return A(MV(pvt, a)) < A(MV(pvt, b));
}

void checkPvt(void) {
    pvt.x = inf;
    pvt.y = inf;
    for (int i = 0; i < v.size(); i++) {
        if (pvt.x > v[i].x)
            pvt = v[i];
        else if (pvt.x == v[i].x && pvt.y > v[i].y)
            pvt = v[i];
    }
}

int main() {
    ios_base::sync_with_stdio(false);
    int t = 1, tc;
    int i, j, k, l, m, n;
    double x, y, z, u, w, xx, yy, zz, d, h;
    double aa, bb, cc, dd;
    // cin>>tc;
    while (cin >> x >> y >> h) {
        double low = 0, high = min(x, y);
        double mid;
        while (high - low > eps) {
            mid = (low + high) / 2.0;
            double theta1 = acos(mid / y);
            double theta2 = acos(mid / x);
            double m1 = h / (tan(theta1));
            double m2 = h / (tan(theta2));
            if (mid == (m1 + m2)) break;
            if (mid > (m1 + m2))
                low = mid;
            else
                high = mid;
        }
        printf("%.3lf\n", mid);
    }
    return 0;
}