12-1 三角形

题目
　为二维空间中的点设计一个结构体，在此基础上为三角形设计一个结构体。分别设计独立的函数计算三角形的周长、面积、中心和重心。输入三个点，输出这三个点构成的三角形的周长、面积、外心和重心。结果保留小数点后2位数字。

思路
这是数学题

面积用海伦公式：a=AB,b=BC,c=AC,p=(a+b+c)/2,
三角形面积s=sqrt(p*(p-a)(p-b)(p-c));

重心：x=(x1+x2+x3)/3 ; y=(y1+y2+y3)/3

#include<stdio.h>
#include<math.h>

typedef struct{
    double x,y;
}Point;

typedef struct{
    Point a,b,c;
}Triangle;

double abso(double n){
    if(n<0) return -n;
    else return n;
}

//周长 
void cir(Triangle tri){
    double c1=sqrt((tri.a.x-tri.b.x)*(tri.a.x-tri.b.x)+(tri.a.y-tri.b.y)*(tri.a.y-tri.b.y));//ab
    double c2=sqrt((tri.a.x-tri.c.x)*(tri.a.x-tri.c.x)+(tri.a.y-tri.c.y)*(tri.a.y-tri.c.y));//ac
    double c3=sqrt((tri.b.x-tri.c.x)*(tri.b.x-tri.c.x)+(tri.b.y-tri.c.y)*(tri.b.y-tri.c.y));//bc
    printf("%.2lf\n",c1+c2+c3);
}

//面积 
void area(Triangle tri){
    //海伦公式 
    double a=sqrt((tri.a.x-tri.b.x)*(tri.a.x-tri.b.x)+(tri.a.y-tri.b.y)*(tri.a.y-tri.b.y));
    double b=sqrt((tri.b.x-tri.c.x)*(tri.b.x-tri.c.x)+(tri.b.y-tri.c.y)*(tri.b.y-tri.c.y));
    double c=sqrt((tri.a.x-tri.c.x)*(tri.a.x-tri.c.x)+(tri.a.y-tri.c.y)*(tri.a.y-tri.c.y));
    double p=(a+b+c)/2; 
    double s=sqrt(p*(p-a)*(p-b)*(p-c));
    printf("%.2lf\n",s);
}

//外心 
void outside(Triangle tri){
    Point out;
    double a1=2*(tri.b.x-tri.a.x);
    double b1=2*(tri.b.y-tri.a.y);
    double c1=(tri.b.x)*(tri.b.x)+tri.b.y*tri.b.y-tri.a.x*tri.a.x-tri.a.y*tri.a.y;
    double a2=2*(tri.c.x-tri.b.x); 
    double b2=2*(tri.c.y-tri.b.y);
    double c2=tri.c.x*tri.c.x+tri.c.y*tri.c.y-tri.b.x*tri.b.x-tri.b.y*tri.b.y;
    out.x=(c1*b2-c2*b1)/(a1*b2-a2*b1);
    out.y=(a1*c2-a2*c1)/(a1*b2-a2*b1);
    printf("%.2lf %.2lf\n",out.x,out.y);

}

//重心 
void weight(Triangle tri){
    Point wei;
    wei.x=(tri.a.x+tri.b.x+tri.c.x)/3;
    wei.y=(tri.a.y+tri.b.y+tri.c.y)/3;
    printf("%.2lf %.2lf\n",wei.x,wei.y);
}

int main(){
    Triangle tri;
    scanf("%lf%lf",&tri.a.x,&tri.a.y);
    scanf("%lf%lf",&tri.b.x,&tri.b.y);
    scanf("%lf%lf",&tri.c.x,&tri.c.y);
    cir(tri);
    area(tri);
    outside(tri);
    weight(tri); 
    return 0;
}