1378 The Falling Circle

#include <cstdio>
#include <iostream>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#define LL long long
#define DB double

using namespace std;
const DB PI = acos(-1.0);
struct cycle{
    DB x,y,r;
    void get(){scanf("%lf%lf%lf",&x,&y,&r);}
};
DB dist(cycle a,cycle b)
{
    return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
int main()
{
    #ifndef ONLINE_JUDGE
    freopen("in.txt","r",stdin);
    freopen("out.txt","r",stdout);
    #endif
    cycle a,c,b;
    int cas,T=1;scanf("%d",&cas);
    while(cas--)
    {
        a.get();b.get();c.get();
        if(a.y-a.r>b.y-b.r) swap(a,b);
        DB d = dist(a,b);
        DB alph = atan((b.y-a.y)/fabs(b.x-a.x))-asin((b.r-a.r)/d);
        DB low = a.y - a.r/cos(alph);
        DB d1 = c.y - low-fabs(c.x-a.x)*tan(alph)-c.r/cos(alph);
        DB d2;
        if(fabs(a.y-a.r-b.y+b.r)<0.1)
        {
            d2 = 0;
        }else
        {
            DB l1 = sqrt((a.r+c.r)*(a.r+c.r)-(a.r-c.r)*(a.r-c.r));
            d2 = fabs(a.x-c.x)/cos(alph)+c.r*tan(alph)-a.r*tan(alph) - l1;
            d2 = d2/c.r/2/PI;
        }
        printf("Case %d: %.10lf\n",T++,d1+d2);
    }
    return 0;
}