1 /*
2 几何
3 求给定三角形的外接圆圆心
4 方法：求解二元方程组
5 */
6 #include<stdio.h>
7 #include<string.h>
8 #include<math.h>
9 #include<stdlib.h>
10 const double pi = acos(-1.0);
11 const double eps = 1e-8;
12 struct Point{
13 double x,y;
14 };
15 struct Circle{
16 Point center;
17 double r;
18 };
19 Point a,b,c,tp;
20 Circle cc;
21
22 double dis( Point a,Point b ){
23 return sqrt( (a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y) );
24 }
25
26 bool JudgeTriangle( Point a,Point b,Point c ){
27 double len1 = dis( a,b );
28 len1 *= len1;
29 double len2 = dis( a,c );
30 len2 *= len2;
31 double len3 = dis( b,c );
32 len3 *= len3;
33 if( len1+len2-len3<=0||len1+len3-len2<=0||len2+len3-len1<=0 ) return false;
34 else return true;
35 }/*判断是否是钝角三角形*/
36
37 void GetCircle( Point a,Point b,Point c ){
38 bool judge = JudgeTriangle( a,b,c );
39 if( judge==false ){
40 double ans;
41 int op ;
42 double len1 = dis( a,b );
43 ans = len1;
44 op = 1;
45 double len2 = dis( a,c );
46 if( len2>ans ){
47 ans = len2;
48 op = 2;
49 }
50 double len3 = dis( b,c );
51 if( len3>ans ){
52 ans = len3;
53 op = 3;
54 }
55 cc.r = ans / 2.0;
56 if( op==1 ){
57 cc.center.x = ( a.x+b.x )/2.0;
58 cc.center.y = ( a.y+b.y )/2.0;
59 }
60 else if( op==2 ){
61 cc.center.x = ( a.x+c.x )/2.0;
62 cc.center.y = ( a.y+c.y )/2.0;
63 }
64 else {
65 cc.center.x = ( b.x+c.x )/2.0;
66 cc.center.y = ( b.y+c.y )/2.0;
67 }
68 return ;
69 }/*钝角三角形*/
70 double x1 = a.x,x2 = b.x,x3 = c.x;
71 double y1 = a.y,y2 = b.y,y3 = c.y;
72 cc.center.x=((y2-y1)*(y3*y3-y1*y1+x3*x3-x1*x1)-(y3-y1)*(y2*y2-y1*y1+x2*x2-x1*x1))/(2*(x3-x1)*(y2-y1)-2*((x2-x1)*(y3-y1)));
73 cc.center.y=((x2-x1)*(x3*x3-x1*x1+y3*y3-y1*y1)-(x3-x1)*(x2*x2-x1*x1+y2*y2-y1*y1))/(2*(y3-y1)*(x2-x1)-2*((y2-y1)*(x3-x1)));
74 cc.r = dis( cc.center,a );
75 return ;
76 }/*求外接圆圆心*/
77
78 int main(){
79 int T;
80 scanf("%d",&T);
81 int ca = 1;
82 while( T-- ){
83 scanf("%lf%lf%lf%lf%lf%lf%lf%lf",&a.x,&a.y,&b.x,&b.y,&c.x,&c.y,&tp.x,&tp.y);
84 GetCircle( a,b,c );
85 printf("Case #%d: ",ca++);
86 if( dis( tp,cc.center )<=cc.r ) printf("Danger\n");
87 else printf("Safe\n");
88 }
89 return 0;
90 }
