cf13B Letter A（分类+简单计算几何，，）

题意：

给三个线段（每个线段的两个端点的坐标），问这三个线段能否组成字母A。

组成字母A的条件：

1.两个线段有公共端点。

2.这两个线段夹角小于等于90度。

3.第三个线段的两个端点分别在这两个线段上，且各自分割的大小比率不超过4：1

思路：

直接。。。。。

应该开始积累计算几何的代码了，，，，

代码：

struct Point{
    double x,y;
};
struct segment{
    Point a,b;
}
S[5];

bool samePoint(Point a,Point b){
    if(fabs(a.x-b.x)<eps && fabs(a.y-b.y)<eps){
        return true;
    }
    return false;
}
bool PointOnSegment(Point a,segment L){
    if((a.x-L.a.x)*(L.b.y-L.a.y)==(a.y-L.a.y)*(L.b.x-L.a.x)
       && min(L.a.x,L.b.x)<=a.x && a.x<=max(L.a.x,L.b.x)
       && min(L.a.y,L.b.y)<=a.y && a.y<=max(L.a.y,L.b.y)){
            return true;
       }
       return false;
}
double rates(Point a,segment L){
    double l1=(a.x-L.a.x)*(a.x-L.a.x)+(a.y-L.a.y)*(a.y-L.a.y);
    double l2=(a.x-L.b.x)*(a.x-L.b.x)+(a.y-L.b.y)*(a.y-L.b.y);
    if(l1<eps || l2<eps){
        return 999999.0;
    }
    if(l1<l2){
        return l2/l1;
    }
    else{
        return l1/l2;
    }
}
ll Cos(double x1,double y1,double x2,double y2){
    if(x1*x2+y1*y2>=0){
        return true;
    }
    return false;
}
bool solve(){
    //1 and 2
    bool t1=samePoint(S[1].a,S[2].a);
    bool t2=samePoint(S[1].a,S[2].b);
    bool t3=samePoint(S[1].b,S[2].a);
    bool t4=samePoint(S[1].b,S[2].b);
    if(t1||t2||t3||t4){
        bool flag=false;
        if(t1){
            double x1,y1,x2,y2;
            x1=S[1].b.x-S[1].a.x;
            y1=S[1].b.y-S[1].a.y;
            x2=S[2].b.x-S[2].a.x;
            y2=S[2].b.y-S[2].a.y;
            if(Cos(x1,y1,x2,y2)){
                flag=true;
            }
        }
        if(t2){
            double x1,y1,x2,y2;
            x1=S[1].b.x-S[1].a.x;
            y1=S[1].b.y-S[1].a.y;
            x2=S[2].a.x-S[2].b.x;
            y2=S[2].a.y-S[2].b.y;
            if(Cos(x1,y1,x2,y2)){
                flag=true;
            }
        }
        if(t3){
            double x1,y1,x2,y2;
            x1=S[1].a.x-S[1].b.x;
            y1=S[1].a.y-S[1].b.y;
            x2=S[2].b.x-S[2].a.x;
            y2=S[2].b.y-S[2].a.y;
            if(Cos(x1,y1,x2,y2)){
                flag=true;
            }
        }
        if(t4){
            double x1,y1,x2,y2;
            x1=S[1].a.x-S[1].b.x;
            y1=S[1].a.y-S[1].b.y;
            x2=S[2].a.x-S[2].b.x;
            y2=S[2].a.y-S[2].b.y;
            if(Cos(x1,y1,x2,y2)){
                flag=true;
            }
        }
        if(flag){
            if(PointOnSegment(S[3].a,S[1]) && PointOnSegment(S[3].b,S[2])){
                if(rates(S[3].a,S[1])<=16.0 && rates(S[3].b,S[2])<=16.0){
                    return true;
                }
            }
            if(PointOnSegment(S[3].b,S[1]) && PointOnSegment(S[3].a,S[2])){
                if(rates(S[3].b,S[1])<=16.0 && rates(S[3].a,S[2])<=16.0){
                    return true;
                }
            }
        }
    }

    //1 and 3
     t1=samePoint(S[1].a,S[3].a);
     t2=samePoint(S[1].a,S[3].b);
     t3=samePoint(S[1].b,S[3].a);
     t4=samePoint(S[1].b,S[3].b);
    if(t1||t2||t3||t4){
        bool flag=false;
        if(t1){
            double x1,y1,x2,y2;
            x1=S[1].b.x-S[1].a.x;
            y1=S[1].b.y-S[1].a.y;
            x2=S[3].b.x-S[3].a.x;
            y2=S[3].b.y-S[3].a.y;
            if(Cos(x1,y1,x2,y2)){
                flag=true;
            }
        }
        if(t2){
            double x1,y1,x2,y2;
            x1=S[1].b.x-S[1].a.x;
            y1=S[1].b.y-S[1].a.y;
            x2=S[3].a.x-S[3].b.x;
            y2=S[3].a.y-S[3].b.y;
            if(Cos(x1,y1,x2,y2)){
                flag=true;
            }
        }
        if(t3){
            double x1,y1,x2,y2;
            x1=S[1].a.x-S[1].b.x;
            y1=S[1].a.y-S[1].b.y;
            x2=S[3].b.x-S[3].a.x;
            y2=S[3].b.y-S[3].a.y;
            if(Cos(x1,y1,x2,y2)){
                flag=true;
            }
        }
        if(t4){
            double x1,y1,x2,y2;
            x1=S[1].a.x-S[1].b.x;
            y1=S[1].a.y-S[1].b.y;
            x2=S[3].a.x-S[3].b.x;
            y2=S[3].a.y-S[3].b.y;
            if(Cos(x1,y1,x2,y2)){
                flag=true;
            }
        }
        if(flag){
            if(PointOnSegment(S[2].a,S[1]) && PointOnSegment(S[2].b,S[3])){
                if(rates(S[2].a,S[1])<=16.0 && rates(S[2].b,S[3])<=16.0){
                    return true;
                }
            }
            if(PointOnSegment(S[2].b,S[1]) && PointOnSegment(S[2].a,S[3])){
                if(rates(S[2].b,S[1])<=16.0 && rates(S[2].a,S[3])<=16.0){
                    return true;
                }
            }
        }
    }

    //2 and 3
    t1=samePoint(S[2].a,S[3].a);
     t2=samePoint(S[2].a,S[3].b);
     t3=samePoint(S[2].b,S[3].a);
     t4=samePoint(S[2].b,S[3].b);
    if(t1||t2||t3||t4){
        bool flag=false;
        if(t1){
            double x1,y1,x2,y2;
            x1=S[2].b.x-S[2].a.x;
            y1=S[2].b.y-S[2].a.y;
            x2=S[3].b.x-S[3].a.x;
            y2=S[3].b.y-S[3].a.y;
            if(Cos(x1,y1,x2,y2)){
                flag=true;
            }
        }
        if(t2){
            double x1,y1,x2,y2;
            x1=S[2].b.x-S[2].a.x;
            y1=S[2].b.y-S[2].a.y;
            x2=S[3].a.x-S[3].b.x;
            y2=S[3].a.y-S[3].b.y;
            if(Cos(x1,y1,x2,y2)){
                flag=true;
            }
        }
        if(t3){
            double x1,y1,x2,y2;
            x1=S[2].a.x-S[2].b.x;
            y1=S[2].a.y-S[2].b.y;
            x2=S[3].b.x-S[3].a.x;
            y2=S[3].b.y-S[3].a.y;
            if(Cos(x1,y1,x2,y2)){
                flag=true;
            }
        }
        if(t4){
            double x1,y1,x2,y2;
            x1=S[2].a.x-S[2].b.x;
            y1=S[2].a.y-S[2].b.y;
            x2=S[3].a.x-S[3].b.x;
            y2=S[3].a.y-S[3].b.y;
            if(Cos(x1,y1,x2,y2)){
                flag=true;
            }
        }
        if(flag){
            if(PointOnSegment(S[1].a,S[2]) && PointOnSegment(S[1].b,S[3])){
                if(rates(S[1].a,S[2])<=16.0 && rates(S[1].b,S[3])<=16.0){
                    return true;
                }
            }
            if(PointOnSegment(S[1].b,S[2]) && PointOnSegment(S[1].a,S[3])){
                if(rates(S[1].b,S[2])<=16.0 && rates(S[1].a,S[3])<=16.0){
                    return true;
                }
            }
        }
    }

    return false;
}


int T;
int main(){

    cin>>T;
    while(T--){
        scanf("%lf%lf%lf%lf",&S[1].a.x,&S[1].a.y,&S[1].b.x,&S[1].b.y);
        scanf("%lf%lf%lf%lf",&S[2].a.x,&S[2].a.y,&S[2].b.x,&S[2].b.y);
        scanf("%lf%lf%lf%lf",&S[3].a.x,&S[3].a.y,&S[3].b.x,&S[3].b.y);
        if(solve()){
            puts("YES");
        }else{
            puts("NO");
        }
    }

    return 0;
}