#include #include #include #include using namespace std; struct Point { double x,y; }; Point a[1005],d; double r; double dist(Point A,Point B) { return sqrt((A.x-B.x)*(A.x-B.x)+(A.y-B.y)*(A.y-B.y)); } double cross(Point A,Point B,Point C) { return (B.x-A.x)*(C.y-A.y)-(C.x-A.x)*(B.y-A.y); } void MiniDiscWith2Point(Point p,Point q,int n) { d.x=(p.x+q.x)/2.0; d.y=(p.y+q.y)/2.0; r=dist(p,q)/2; int k; double c1,c2,t1,t2,t3; for(k=1;k<=n;k++) { if(dist(d,a[k])<=r) continue; if(cross(p,q,a[k])!=0.0) { c1=(p.x*p.x+p.y*p.y-q.x*q.x-q.y*q.y)/2.0; c2=(p.x*p.x+p.y*p.y-a[k].x*a[k].x-a[k].y*a[k].y)/2.0; d.x=(c1*(p.y-a[k].y)-c2*(p.y-q.y))/((p.x-q.x)*(p.y-a[k].y)-(p.x-a[k].x)*(p.y-q.y)); d.y=(c1*(p.x-a[k].x)-c2*(p.x-q.x))/((p.y-q.y)*(p.x-a[k].x)-(p.y-a[k].y)*(p.x-q.x)); r=dist(d,a[k]); } else { t1=dist(p,q); t2=dist(q,a[k]); t3=dist(p,a[k]); if(t1>=t2&&t1>=t3) { d.x=(p.x+q.x)/2.0; d.y=(p.y+q.y)/2.0; r=dist(p,q)/2.0; } else if(t2>=t1&&t2>=t3) { d.x=(a[k].x+q.x)/2.0; d.y=(a[k].y+q.y)/2.0; r=dist(a[k],q)/2.0; } else { d.x=(a[k].x+p.x)/2.0; d.y=(a[k].y+p.y)/2.0; r=dist(a[k],p)/2.0; } } } } void MiniDiscWithPoint(Point pi,int n) { d.x=(pi.x+a[1].x)/2.0; d.y=(pi.y+a[1].y)/2.0; r=dist(pi,a[1])/2.0; int j; for(j=2;j<=n;j++) { if(dist(d,a[j])<=r) continue; else { MiniDiscWith2Point(pi,a[j],j-1); } } } int main() { int i,n; while(scanf("%d",&n)&&n) { for(i=1;i<=n;i++) scanf("%lf %lf",&a[i].x,&a[i].y); if(n==1) { printf("%.2lf %.2lf 0.00\n",a[1].x,a[1].y); continue; } r=dist(a[1],a[2])/2.0; d.x=(a[1].x+a[2].x)/2.0; d.y=(a[1].y+a[2].y)/2.0; for(i=3;i<=n;i++) { if(dist(d,a[i])<=r)continue; else MiniDiscWithPoint(a[i],i-1); } printf("%.2lf %.2lf %.2lf\n",d.x,d.y,r); } return 0; }