1 struct TPoint
2 {
3 double x, y;
4 TPoint operator-(TPoint &a)
5 {
6 TPoint p1;
7 p1.x = x - a.x;
8 p1.y = y - a.y;
9 return p1;
10 }
11 };
12
13 struct TCircle
14 {
15 double r;
16 TPoint centre;
17 };
18
19 struct TTriangle
20 {
21 TPoint t[3];
22 };
23
24 TCircle c;
25 TPoint a[maxn];
26
27 double distance(TPoint p1, TPoint p2)
28 {
29 TPoint p3;
30 p3.x = p2.x - p1.x;
31 p3.y = p2.y - p1.y;
32 return sqrt(p3.x * p3.x + p3.y * p3.y);
33 }
34
35 double triangleArea(TTriangle t)
36 {
37 TPoint p1, p2;
38 p1 = t.t[1] - t.t[0];
39 p2 = t.t[2] - t.t[0];
40 return fabs(p1.x * p2.y - p1.y * p2.x) / 2;
41 }
42
43 TCircle circumcircleOfTriangle(TTriangle t)
44 {
45 //三角形的外接圆
46 TCircle tmp;
47 double a, b, c, c1, c2;
48 double xA, yA, xB, yB, xC, yC;
49 a = distance(t.t[0], t.t[1]);
50 b = distance(t.t[1], t.t[2]);
51 c = distance(t.t[2], t.t[0]);
52 //根据S = a * b * c / R / 4;求半径R
53 tmp.r = a * b * c / triangleArea(t) / 4;
54
55 xA = t.t[0].x; yA = t.t[0].y;
56 xB = t.t[1].x; yB = t.t[1].y;
57 xC = t.t[2].x; yC = t.t[2].y;
58 c1 = (xA * xA + yA * yA - xB * xB - yB * yB) / 2;
59 c2 = (xA * xA + yA * yA - xC * xC - yC * yC) / 2;
60
61 tmp.centre.x = (c1 * (yA - yC) - c2 * (yA - yB)) /
62 ((xA - xB) * (yA - yC) - (xA - xC) * (yA - yB));
63 tmp.centre.y = (c1 * (xA - xC) - c2 * (xA - xB)) /
64 ((yA - yB) * (xA - xC) - (yA - yC) * (xA - xB));
65
66 return tmp;
67 }
68
69 TCircle MinCircle2(int tce, TTriangle ce)
70 {
71 TCircle tmp;
72 if(tce == 0) tmp.r = -2;
73 else if(tce == 1)
74 {
75 tmp.centre = ce.t[0];
76 tmp.r = 0;
77 }
78 else if(tce == 2)
79 {
80 tmp.r = distance(ce.t[0], ce.t[1]) / 2;
81 tmp.centre.x = (ce.t[0].x + ce.t[1].x) / 2;
82 tmp.centre.y = (ce.t[0].y + ce.t[1].y) / 2;
83 }
84 else if(tce == 3) tmp = circumcircleOfTriangle(ce);
85 return tmp;
86 }
87
88 void MinCircle(int t, int tce, TTriangle ce)
89 {
90 int i, j;
91 TPoint tmp;
92 c = MinCircle2(tce, ce);
93 if(tce == 3) return;
94 for(i = 1;i <= t;i++)
95 {
96 if(distance(a[i], c.centre) > c.r)
97 {
98 ce.t[tce] = a[i];
99 MinCircle(i - 1, tce + 1, ce);
100 tmp = a[i];
101 for(j = i;j >= 2;j--)
102 {
103 a[j] = a[j - 1];
104 }
105 a[1] = tmp;
106 }
107 }
108 }
109
110 void run(int n)
111 {
112 TTriangle ce;
113 int i;
114 MinCircle(n, 0, ce);
115 printf("%.2lf %.2lf %.2lf\n", c.centre.x, c.centre.y, c.r);
116 }
117
118 int main()
119 {
120 freopen("circle.in", "r", stdin);
121 freopen("out.txt", "w", stdout);
122 int n;
123 while(scanf("%d", &n) != EOF && n)
124 {
125 for(int i = 1;i <= n;i++)
126 scanf("%lf%lf", &a[i].x, &a[i].y);
127 run(n);
128 }
129 return 0;
130 }
