#include <stdio.h>#include <math.h>const int maxn = 1005;const double eps = 1e-6;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 ***Area(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) { 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 / ***Area(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; } }}int main() { int n,i; while (scanf("%d", &n) != EOF && n) { for (i = 1; i <= n; i++) scanf("%lf%lf", &a[i].x, &a[i].y); TTriangle ce; MinCircle(n, 0, ce); printf("%.2lf %.2lf %.2lfn", c.centre.x, c.centre.y, c.r); } return 0;}
