zoj 1439 Area Ratio

 

给你空间三角形，求出内切圆与外接圆面积之比。

 

三角形怎么着也是个平面，所以空间神马的不用考虑。先求出边长。

 

由公式

 

内切圆：S = 1/2(a+b+c)*R ;

 

外接圆：1/2*absinC = S ，c/sinC = 2R.

 

S由海伦公式求得，详见海伦公式

 

面积之比即半径平方之比。

 

#include <cstdio>#include <cstdlib>#include <iostream>#include <cmath>#include <string.h>using namespace std;double len(double x1,double y1,double z1,double x2,double y2,double z2){return sqrt( (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2) + (z1-z2)*(z1-z2) );}double ratio(double a,double b,double c){return (a+b-c)*(a+c-b)*(b+c-a)/(2*a*b*c);}int main(){double a,b,c,x1,y1,z1;double x2,y2,z2;double x3,y3,z3;while( cin >> x1 >> y1 >> z1 ){cin >> x2 >> y2 >> z2;cin >> x3 >> y3 >> z3;a = len(x1,y1,z1,x2,y2,z2);b = len(x1,y1,z1,x3,y3,z3);c = len(x2,y2,z2,x3,y3,z3);printf("%.3lf/n",pow(ratio(a,b,c),2));}return 0;}