C++ :

#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
#include<string>
#include<vector>
#include<queue>
#include<cmath>
#include<set>
using namespace std;
const double eps = 1e-10;
struct Point{
    double x, y;
    Point(){}
    Point(double x, double y):x(x), y(y){}
};
Point operator - (Point a, Point b){
    return Point(a.x-b.x, a.y-b.y);
}
int dcmp(double x){
    if(fabs(x) < eps)return 0;
    return x < 0 ? -1 : 1;
}
double Cross(Point a, Point b){
    return a.x * b.y - a.y * b.x;
}
bool Segem(Point a1, Point a2, Point b1, Point b2){
    double c1 = Cross(a1-b1, b2-b1); double c2 = Cross(a2-b1, b2-b1);
    double c3 = Cross(b2-a1, a2-a1); double c4 = Cross(b1-a1, a2-a1);
    return dcmp(c1) * dcmp(c2) < 0 && dcmp(c3) * dcmp(c4) < 0;
}
double Len(Point a, Point b){
    double d = (a.x-b.x) * (a.x-b.x) + (a.y-b.y) * (a.y-b.y);
    return sqrt(d);
}
int main()
{
    int cas = 1;
    double x1, y1, x2, y2;
    Point a, b, c, d;
    while(~scanf("%lf %lf %lf %lf", &x1, &y1, &x2, &y2)){
        if(x1 + x2 + y1 + y2 == 0)break;
        a = Point(x1, y1); b = Point(x2, y2);
        scanf("%lf %lf %lf %lf", &x1, &y1, &x2, &y2);
        c = Point(x1, y1); d = Point(x2, y2);
        double dis  = 0;
        if(Segem(a, b, c, d) == 0){
            dis = Len(a, b);
        }
        else{
            dis = min(Len(a, c) + Len(c, b), Len(a, d) + Len(d, b));
        }
        printf("Case %d: %.3lf\n",cas++, dis / 2);
    }
    return 0;
}