题链：
http://poj.org/problem?id=1329
题解：
计算几何，求过不共线的三点的圆
就是用向量暴力算出来的东西。。。
（设出外心M的坐标，由于$|\vec{MA}|=|\vec{MB}|=|\vec{MC}|$，可以解出M点坐标。）
代码：
#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
using namespace std;
const double eps=1e-8;
int sign(double x){
if(fabs(x)<=eps) return 0;
return x<0?-1:1;
}
void Pout(double x){//Print_Out
if(sign(x)<0) printf(" - ");
else printf(" + ");
printf("%.3lf",fabs(x));
}
struct Point{
double x,y;
Point(double _x=0,double _y=0):x(_x),y(_y){}
int Read(){return scanf("%lf%lf",&x,&y);}
};
typedef Point Vector;
Vector operator + (Vector A,Vector B){return Vector(A.x+B.x,A.y+B.y);}
Vector operator - (Point A,Point B){return Vector(A.x-B.x,A.y-B.y);}
double operator ^ (Vector A,Vector B){return A.x*B.y-A.y*B.x;}
double operator * (Vector A,Vector B){return A.x*B.x+A.y*B.y;}
struct Circle{
Point o; double r;
Circle(Point _o=Point(),double _r=0):o(_o),r(_r){}
void PrintSE(){//Print_Standard_Equation
printf("(x");Pout(-o.x);printf(")^2"); printf(" + ");
printf("(y");Pout(-o.y);printf(")^2"); printf(" = ");
printf("%.3lf^2\n",r);
}
void PrintNE(){//Print_Normal_Equation
printf("x^2 + y^2");
Pout(-2*o.x);printf("x");
Pout(-2*o.y);printf("y");
Pout(o.x*o.x+o.y*o.y-r*r);
printf(" = 0\n\n");
}
};
double GL(Vector A){//Get_Length
return sqrt(A*A);
}
Circle GC(Point P1,Point P2,Point P3){//Get_Circle
Vector B=P2-P1,C=P3-P1; Point P0;
P0.x=((B*B)*C.y-(C*C)*B.y)/(2*(B^C))+P1.x;
P0.y=((B*B)*C.x-(C*C)*B.x)/(2*(C^B))+P1.y;
return Circle(P0,GL(P0-P1));
}
int main(){
Point A,B,C;
while(~A.Read()&&~B.Read()&&~C.Read()){
GC(A,B,C).PrintSE();
GC(A,B,C).PrintNE();
}
return 0;
}