最小圆覆盖

struct TPoint
{
    double x, y;
    TPoint operator-(TPoint &a)
    {
        TPoint p1;
        p1.x = x - a.x;
        p1.y = y - a.y;
        return p1;
    }
};

struct TCircle
{
    double r;
    TPoint centre;
};

struct TTriangle
{
    TPoint t[3];
};

TCircle c;
TPoint a[maxn];

double distance(TPoint p1, TPoint p2)
{
    TPoint p3;
    p3.x = p2.x - p1.x;
    p3.y = p2.y - p1.y;
    return sqrt(p3.x * p3.x + p3.y * p3.y);
}

double triangleArea(TTriangle t)
{
    TPoint p1, p2;
    p1 = t.t[1] - t.t[0];
    p2 = t.t[2] - t.t[0];
    return fabs(p1.x * p2.y - p1.y * p2.x) / 2;
}

TCircle circumcircleOfTriangle(TTriangle t)
{
    //三角形的外接圆
    TCircle tmp;
    double a, b, c, c1, c2;
    double xA, yA, xB, yB, xC, yC;
    a = distance(t.t[0], t.t[1]);
    b = distance(t.t[1], t.t[2]);
    c = distance(t.t[2], t.t[0]);
    //根据S = a * b * c / R / 4;求半径R 
    tmp.r = a * b * c / triangleArea(t) / 4;
    
    xA = t.t[0].x; yA = t.t[0].y;
    xB = t.t[1].x; yB = t.t[1].y;
    xC = t.t[2].x; yC = t.t[2].y;
    c1 = (xA * xA + yA * yA - xB * xB - yB * yB) / 2;
    c2 = (xA * xA + yA * yA - xC * xC - yC * yC) / 2;
    
    tmp.centre.x = (c1 * (yA - yC) - c2 * (yA - yB)) / 
         ((xA - xB) * (yA - yC) - (xA - xC) * (yA - yB)); 
    tmp.centre.y = (c1 * (xA - xC) - c2 * (xA - xB)) / 
         ((yA - yB) * (xA - xC) - (yA - yC) * (xA - xB)); 
         
    return tmp;     
}

TCircle MinCircle2(int tce, TTriangle ce)
{
    TCircle tmp;
    if(tce == 0) tmp.r = -2;
    else if(tce == 1) 
    {
        tmp.centre = ce.t[0];
        tmp.r = 0;
    }
    else if(tce == 2)
    {
        tmp.r = distance(ce.t[0], ce.t[1]) / 2;
        tmp.centre.x = (ce.t[0].x + ce.t[1].x) / 2;
        tmp.centre.y = (ce.t[0].y + ce.t[1].y) / 2;     
    }
    else if(tce == 3) tmp = circumcircleOfTriangle(ce);
    return tmp;
}

void MinCircle(int t, int tce, TTriangle ce)
{
    int i, j;
    TPoint tmp;
    c = MinCircle2(tce, ce);
    if(tce == 3) return;
    for(i = 1;i <= t;i++)
    {
        if(distance(a[i], c.centre) > c.r)
        {
            ce.t[tce] = a[i];
            MinCircle(i - 1, tce + 1, ce);
            tmp = a[i];
            for(j = i;j >= 2;j--)
            {
                a[j] = a[j - 1];
            }
            a[1] = tmp;
        }
    }
}

void run(int n)
{
    TTriangle ce;
    int i;
    MinCircle(n, 0, ce);
    printf("%.2lf %.2lf %.2lf
", c.centre.x, c.centre.y, c.r);
}

int main()
{
    freopen("circle.in", "r", stdin);
    freopen("out.txt", "w", stdout);
    int n;
    while(scanf("%d", &n) != EOF && n)
    {
        for(int i = 1;i <= n;i++)
            scanf("%lf%lf", &a[i].x, &a[i].y);
        run(n);
    }
    return 0;
}