判断圆与三角形是否有交点

#include <bits/stdc++.h>
using namespace std;

const double eps = 1e-7;
struct Point
{
    double x,y;
    Point (double x = 0,double y = 0):x(x),y(y) {} };
typedef Point Vector;

Vector operator+ (Vector A,Vector B)
{
    return Vector(A.x+B.x,A.y+B.y);
}
Vector operator- (Vector A,Vector B)
{
    return Vector(A.x-B.x,A.y-B.y);
}
Vector operator* (Vector A,double p)
{
    return Vector(A.x*p,A.y*p);
}
Vector operator/ (Vector A,double p)
{
    return Vector(A.x/p,A.y/p);
}

bool operator<(const Point& a,const Point& b)
{
    return a.x<b.x||(a.x==b.x&&a.y<b.y);
}
int dcmp(double x)
{
    if (fabs(x)<eps) return 0;
    return x<0?-1:1;
}
bool operator== (const Point& a,const Point& b)
{
    return dcmp(a.x-b.x)==0 && dcmp(a.y-b.y)==0;
}
//极角 = atan2(y,x); 单位弧度

double Dot(Vector A,Vector B)
{
    return A.x*B.x+A.y*B.y;    //cos符号一致
}
double Length(Vector A)
{
    return sqrt(Dot(A,A));
}
double Angle(Vector A,Vector B)
{
    return acos(Dot(A,B)/Length(A)/Length(B));    //向量ab的夹角,范围为在0，pi
}
double Cross(Vector A,Vector B)
{
    return A.x*B.y-A.y*B.x;    //sin符号一致
}
double Area2(Point A,Point B,Point C)
{
    return Cross(B-A,C-A);
}
Vector Rotate(Vector A,double rad)
{
    return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
}
Vector Normal(Vector A)
{
    double L = Length(A);    //法向量
    return Vector(-A.y/L,A.x/L);
}
//圆相关
struct Line
{
    Point p;
    Vector v;
    double ang; // 极角，即从x正半轴旋转到向量v所需要的角（弧度）
    Line() {}
    Line(Point P, Vector v):p(P),v(v)
    {
        ang = atan2(v.y, v.x);
    }
    Point point (double t)
    {
        return Point(p+v*t);
    }
    Line Move(double d)
    {
        return Line(p + Normal(v)*d, v);    //平移
    }
    bool operator < (const Line& L) const
    {
        return ang < L.ang;
    }
};

struct Circle
{
    Point c;
    double r;
    Circle(Point c,double r) :c(c),r(r) {};
    Point point (double a)
    {
        return Point(c.x+cos(a)*r,c.y+sin(a)*r);
    }
};
//直线和圆的交点
int getLineCircleIntersection(Line L,Circle C,double &t1,double &t2,vector<Point>& sol)//返回交点的个数
{
    double a = L.v.x, b = L.p.x - C.c.x, c = L.v.y, d = L.p.y - C.c.y;
    double e = a*a + c*c,f = 2*(a*b+c*d),g= b*b+d*d-C.r*C.r;
    double delta = f*f - 4*e*g;
    if (dcmp(delta)<0) return 0;
    if (dcmp(delta)==0)
    {
        t1 = t2 = -f/(2*e);
        sol.push_back(L.point(t1));
        return 1;
    }
    t1 = (-f-sqrt(delta))/(2*e);
    sol.push_back(L.point(t1));
    t2 = (-f+sqrt(delta))/(2*e);
    sol.push_back(L.point(t2));
    return 2;
}

int f(Point a,Point b,Circle c)
{
    Vector v = (Vector)
    {
        b.x-a.x,b.y-a.y
    };
    Line l(a,v);
    vector<Point>sol;
    double t1,t2;
    int ans = getLineCircleIntersection(l,c,t1,t2,sol);
    if (!ans) return 0;
    if (ans==1)
    {
        return ( dcmp(t1)>=0 && dcmp(t1-1)<=0 );
    }
    else if (ans==2)
    {
        return ( dcmp(t1)>=0 && dcmp(t1-1)<=0 )||( dcmp(t2)>=0 && dcmp(t2-1)<=0 );
    }
    return 0;
}

int main()
{
    Point o,a,b,c;
    double r;
    int T ;
    cin>>T;
    while (T--)
    {
        cin>>o.x>>o.y>>r;
        Circle C(o,r);
        cin>>a.x>>a.y;
        cin>>b.x>>b.y;
        cin>>c.x>>c.y;

        if ( f(a,b,C) || f(a,c,C)||f(b,c,C))
            puts("Yes");
        else puts("No");

    }
    return 0;
}