crossed ladders

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

typedef long long int           ll;
typedef unsigned long long int  ull;
typedef vector<int>             vi;
typedef vector<vi>              vvi;
typedef pair<int,int>           pii;
typedef vector< pii >           vii;
typedef set<int>                st;

#define pb                      push_back
#define pob                     pop_back
#define mp                      make_pair
#define ff                      first
#define ss                      second
#define loop(i,n)               for(int i=1; i<=int(n); i++)
#define lps(i,y)                for(int i=0; i<int(y); i++)
#define read()                  freopen("input.txt", "r", stdin)
#define write()                 freopen("output.txt", "w", stdout)

/// Constants
#define eps                     1e-9
#define PI                      acos(-1.0)  // 3.1415926535897932

int main()
{
    read();
    int n,i,j;
    cin>>n;
    double x,y,c,h1,h2,hi,lo,mid,tc;
    loop(i,n){
        cin>>x>>y>>c;
        lo=0.0;
        hi=max(x,y);
        j=50;
        while(j--){
            mid=(hi+lo)/2.0;
            h1=sqrt((x*x)-(mid*mid));
            h2=sqrt((y*y)-(mid*mid));
            tc=(h1*h2)/(h1+h2);
            if(tc<c)
                hi=mid;
            else
                lo=mid;
        }
        printf("Case %d: %.10lf\n",i,mid);
    }
    return 0;
}