poj 2242 数学（给三点求外接圆周长）

题意：给定不共线的三点坐标，求其外接圆的周长。

思路：通过坐标可以求出三点围成三角形的面积S。根据正弦定理有a/sinA = 2*R，根据面积公式有S = (bcsinA)/2。消去sinA可得关于R的等式，进而可求周长。

#include <cstdio>#include <cstring>#include <algorithm>#include <cmath>#include <queue>#include <cstdlib>using namespace std;#define clc(s,t) memset(s,t,sizeof(s))#define PI 3.141592653589793double dis(double a,double b,double c,double d){    return sqrt((c-a)*(c-a)+(d-b)*(d-b));}int main(){    double a,b,c,d,e,f;    while(scanf("%lf %lf %lf %lf %lf %lf",&a,&b,&c,&d,&e,&f)!=EOF){        double s = fabs(a*d+b*e+c*f-d*e-a*f-b*c);        printf("%.2f\n",PI*dis(a,b,c,d)*dis(a,b,e,f)*dis(c,d,e,f)/s);    }    return 0;}