已知三点坐标，求外接圆圆心坐标与半径。

已知三点坐标，求外接圆圆心坐标与半径。

a=((y2-y1)*(y3*y3-y1*y1+x3*x3-x1*x1)-(y3-y1)*(y2*y2-y1*y1+x2*x2-x1*x1))/(2.0*((x3-x1)*(y2-y1)-(x2-x1)*(y3-y1)));

b=((x2-x1)*(x3*x3-x1*x1+y3*y3-y1*y1)-(x3-x1)*(x2*x2-x1*x1+y2*y2-y1*y1))/(2.0*((y3-y1)*(x2-x1)-(y2-y1)*(x3-x1)));

r2=(x1-a)*(x1-a)+(y1-b)*(y1-b);

HDU4720：已知三点求最小覆盖圆的圆心坐标与半径。

#include
#include
#include
#include
#include
#include
#include
using namespace std;
int main()
{
int t;
scanf("%d",&t);
int Case=1;
while(t--)
{
  double x,y,x3,x1,x2,y3,y1,y2,a,b,r2;
  scanf("%lf%lf",&x1,&y1);
  scanf("%lf%lf",&x2,&y2);
  scanf("%lf%lf",&x3,&y3);
  scanf("%lf%lf",&x,&y);
  if((x2-x1)*(x3-x1)+(y2-y1)*(y3-y1)<0)            //（x1，y1）是钝角
        {
            a=(x3+x2)/2.0,b=(y3+y2)/2.0;
            r2=(a-x2)*(a-x2)+(b-y2)*(b-y2);
        }
        else if((x1-x2)*(x3-x2)+(y1-y2)*(y3-y2)<0)        //（x2，y2）是钝角
        {
            a=(x3+x1)/2.0,b=(y3+y1)/2.0;
            r2=(a-x1)*(a-x1)+(b-y1)*(b-y1);
        }
        else if((x1-x3)*(x2-x3)+(y1-y3)*(y2-y3)<0)        //（x3，y3）是钝角
        {
            a=(x2+x1)/2.0,b=(y2+y1)/2.0;
            r2=(a-x1)*(a-x1)+(b-y1)*(b-y1);
        }
        else         //三角形是锐角三角形
        {
            a=((y2-y1)*(y3*y3-y1*y1+x3*x3-x1*x1)-(y3-y1)*(y2*y2-y1*y1+x2*x2-x1*x1))/(2.0*((x3-x1)*(y2-y1)-(x2-x1)*(y3-y1)));
            b=((x2-x1)*(x3*x3-x1*x1+y3*y3-y1*y1)-(x3-x1)*(x2*x2-x1*x1+y2*y2-y1*y1))/(2.0*((y3-y1)*(x2-x1)-(y2-y1)*(x3-x1)));
            r2=(x1-a)*(x1-a)+(y1-b)*(y1-b);
        }
if((x-a)*(x-a)+(y-b)*(y-b)<=r2)
            printf("Case #%d: Danger\n",Case++);
        else
            printf("Case #%d: Safe\n",Case++);
}
  return 0;
}