#include <cstdio>
#include <algorithm>
#include <ctime>
#include <cmath>
using namespace std;
#define db double
const int M = 100005;
int read()
{
	int x=0,f=1;char c;
	while((c=getchar())<'0' || c>'9') {if(c=='-') f=-1;}
	while(c>='0' && c<='9') {x=(x<<3)+(x<<1)+(c^48);c=getchar();}
	return x*f;
}
int n;
struct point
{
	db x,y;
	point(db X=0,db Y=0) : x(X) , y(Y) {}
	point operator + (db t) {return point(x+t,y+t);}
	point operator - (db t) {return point(x-t,y-t);}
	point operator * (db t) {return point(x*t,y*t);}
	point operator / (db t) {return point(x/t,y/t);}
	point operator + (point r) {return point(x+r.x,y+r.y);}
	point operator - (point r) {return point(x-r.x,y-r.y);}
	point rotate() {return point(y,-x);}
	db len() {return x*x+y*y;}
}p[M];
db cdt(point a,point b) {return a.x*b.x+a.y*b.y;}
db crs(point a,point b) {return a.x*b.y-a.y*b.x;}
point get(point a,point l0,point b,point l1)
{
	db k=crs(b-a,l1)/crs(l0,l1);
	return a+l0*k;
}
point cir(point a,point b,point c)
{
	return get((a+b)/2,(b-a).rotate(),(b+c)/2,(c-b).rotate());
}
signed main()
{
	n=read();srand(time(0));
	for(int i=1;i<=n;i++)
		scanf("%lf %lf",&p[i].x,&p[i].y);
	random_shuffle(p+1,p+1+n);
	point o;db r=0;
	for(int i=1;i<=n;i++)
	{
		if((p[i]-o).len()>r)
		{
			o=p[i];r=0;
			for(int j=1;j<i;j++)
				if((o-p[j]).len()>r)
				{
					o=(p[i]+p[j])/2;r=(o-p[j]).len();
					for(int k=1;k<j;k++)
						if((o-p[k]).len()>r)
						{
							o=cir(p[i],p[j],p[k]);
							r=(o-p[k]).len();
						}
				}
		}
	}
	printf("%.10f\n%.10f %.10f\n",sqrt(r),o.x,o.y);
}

G56 最小圆覆盖 随机增量法【计算几何】

#include <iostream>
#include <cstring>
#include <algorithm>
#include <cmath>
#define x first
#define y second
using namespace std;

const int N=100010;
const double PI=acos(-1);
int n;
struct Point{double x,y;} p[N];
struct Circle{Point p; double r;} C;

Point operator+(Point a, Point b){
  return {a.x+b.x, a.y+b.y};
}
Point operator-(Point a, Point b){
  return {a.x-b.x, a.y-b.y};
}
Point operator*(Point a, double t){
  return {a.x*t, a.y*t};
}
Point operator/(Point a, double t){
  return {a.x/t, a.y/t};
}
double operator*(Point a, Point b){
  return a.x*b.y-a.y*b.x;
}
Point rotate(Point a, double b){
  return {a.x*cos(b)-a.y*sin(b),a.x*sin(b)+a.y*cos(b)};
}
double dis(Point a, Point b){
  return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
Point cross(Point a,Point u,Point b,Point v){ 
  double t=(a-b)*v/(v*u);
  return a+u*t; //直线交点
}
pair<Point, Point> midperp(Point a, Point b){
  return {(a+b)/2, rotate(b-a,PI/2)}; //中垂线
}
Circle cover(Point a, Point b){
  return {(a+b)/2, dis(a,b)/2}; //覆盖两点的圆
}
Circle cover(Point a, Point b, Point c){
  auto u=midperp(a, b), v=midperp(a, c);
  auto p=cross(u.x, u.y, v.x, v.y);
  return {p, dis(p, a)}; //覆盖三点的圆
}
void increment(){ //增量法
  C={p[1], 0};
  for(int i=2; i<=n; i++){
    if(C.r<dis(C.p, p[i])){
      C={p[i], 0}; //一点圆
      for(int j=1; j<i; j++){
        if(C.r<dis(C.p, p[j])){
          C=cover(p[i], p[j]); //两点圆
          for(int k=1; k<j; k++)
            if(C.r<dis(C.p, p[k]))
              C=cover(p[i],p[j],p[k]); //三点圆
        }
      }
    }
  }  
}
int main(){
  scanf("%d", &n);
  for(int i=1;i<=n;i++) scanf("%lf%lf",&p[i].x,&p[i].y);
  random_shuffle(p+1, p+n+1); //随机化
  increment(); //增量法
  printf("%.10lf\n%.10lf %.10lf\n", C.r, C.p.x, C.p.y);
  return 0;
}