C

 1 #include <cstdio>
 2 #include <cstdlib>
 3 #include <cmath>
 4 
 5 const double pi = acos(-1);
 6 struct point{
 7     double x,y;
 8 }L,R,O;
 9 double r;
10 
11 double dis(const struct point &a,const struct point &b){
12     return sqrt( (a.x - b.x)*(a.x - b.x) + (a.y-b.y)*(a.y-b.y) );
13 }
14 double D_dis(const struct point &a,const struct point &b){
15     return (a.x - b.x)*(a.x - b.x) + (a.y-b.y)*(a.y-b.y) ;
16 }
17 double getArea(const point &x, const point &y, const point & z){
18     double a = dis(x,y);
19     double b = dis(y,z);
20     double c = dis(z,x);
21     double p = (a+b+c)/2;
22     return sqrt(p*(p-a)*(p-b)*(p-c)) * 2;
23 }
24 int main(){
25  //   freopen("1.in","r",stdin);
26  //   freopen("1.out","w",stdout);
27  //freopen("1.txt","w",stdout);
28     int CASE;
29     scanf("%d",&CASE);
30     while(CASE--){
31         scanf("%lf %lf %lf",&O.x,&O.y,&r);
32         scanf("%lf %lf",&L.x,&L.y);
33         scanf("%lf %lf",&R.x,&R.y);
34         if( dis(O,L) < r && dis(O,R) < r ){
35             printf("%.3lf\n",dis(L,R));
36         }else if( dis(O,L) < r || dis(O,R) < r ){
37             printf("Impossible!\n");
38         }else{
39             if ( getArea(L,R,O) / dis(L,R) < r ){
40                 if (D_dis(L,O)+D_dis(L,R)<D_dis(R,O)||D_dis(R,O)+D_dis(L,R)<D_dis(L,O))  {
41                     printf("%.3lf\n",dis(L,R));
42 
43                 }
44                 else {
45                 double ans = sqrt(D_dis(L,O) - r*r) + sqrt(D_dis(R,O) - r*r);
46                 double rads = acos( (D_dis(L,O) + D_dis(R,O) - D_dis(L,R) ) / (2*dis(L,O)*dis(R,O) ) );
47                 //printf("rads = %lf\n",rads);
48                 double left_rads = rads - acos(r / dis(L,O)) - acos(r / dis(R,O) );
49                 ans += left_rads * r;
50                 printf("%.3lf\n",ans);
51                 }
52             }else{
53                 printf("%.3lf\n",dis(L,R));
54             }
55         }
56     }
57     return 0;
58 }