#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; template inline bool chmin(T &a,const T &b) { if(a > b) { a = b; return true; } return false; } template inline bool chmax(T &a,const T &b) { if(a < b) { a = b; return true; } return false; } template void print(const vector &V) { for(int i = 0;i < (int)V.size();i++) { cerr << V[i] << (i + 1 == (int)V.size() ? "\n":" "); } } #include #include #include #include #include #include using namespace std; namespace geometry { using real = long double; const real EPS = 1e-9; bool EQ(real a,real b) { return abs(a - b) < EPS; } struct Point { real x,y; Point(real x_ = 0,real y_ = 0) : x(x_),y(y_) {} Point operator-() const { return Point(-x,-y); } Point operator+(const Point &rhs) const { return Point(x + rhs.x,y + rhs.y); } Point operator-(const Point &rhs) const { return Point(x - rhs.x,y - rhs.y); } Point operator*(const real k) const { return Point(x * k,y * k); } Point operator/(const real k) const { assert(!EQ(0,k)); return Point(x / k,y / k); } bool operator<(const Point &rhs) const { return EQ(x,rhs.x) ? y < rhs.y : x < rhs.x; } bool operator==(const Point &rhs) const { return EQ(x,rhs.x) && EQ(y,rhs.y); } }; istream &operator>>(istream &is,Point &p) { return is >> p.x >> p.y; } ostream &operator<<(ostream &os,const Point &p) { return os << p.x << " " << p.y; } struct Line { Point p1,p2; Line(Point p1_ = Point(),Point p2_ = Point()) : p1(p1_),p2(p2_) {} }; struct Segment : Line { Segment(Point p1_ = Point(),Point p2_ = Point()) : Line(p1_,p2_) {} }; struct Circle { Point O; real r; Circle(Point O_ = Point(),real r_ = 0) : O(O_),r(r_) {} }; using Polygon = vector; Point vec(const Line &l) { return l.p2 - l.p1; } real norm2(const Point &p) { return p.x * p.x + p.y * p.y; } real abs(const Point &p) { return hypot(p.x,p.y); } real dot(const Point &a,const Point &b) { return a.x * b.x + a.y * b.y; } real cross(const Point &a,const Point &b) { return a.x * b.y - a.y * b.x; } Point rotate(const Point &p,const real &theta) { return Point(p.x * cos(theta) - p.y * sin(theta), p.x * sin(theta) + p.y * cos(theta)); } Point rotate(const Point &a,const Point &p,const real &theta) { Point q = rotate(p - a,theta); return a + q; } enum { ONLINE_FRONT = -2, CLOCKWISE= -1, ON_SEGMENT = 0, COUNTER_CLOCKWISE = 1, ONLINE_BACK = 2 }; int ccw(const Point &a,const Point &b) { real C = cross(a,b); return C > EPS ? COUNTER_CLOCKWISE : C < -EPS ? CLOCKWISE : dot(a,b) < -EPS ? ONLINE_BACK : norm2(b) - norm2(a) > EPS ? ONLINE_FRONT : ON_SEGMENT; } int ccw(const Point &a,const Point &b,const Point &c) { return ccw(b - a,c - a); } bool orthogonal(const Point &a,const Point &b) { return EQ(dot(a,b),0); } bool orthogonal(const Line &a,const Line &b) { return orthogonal(vec(a),vec(b)); } bool parallel(const Point &a,const Point &b) { return EQ(cross(a,b),0); } bool parallel(const Line &a,const Line &b) { return parallel(vec(a),vec(b)); } bool intersect(const Line &l,const Point &p) { return parallel(vec(l),p - l.p1); } bool intersect(const Segment &s,const Point &p) { return ccw(s.p1,s.p2,p) == ON_SEGMENT; } bool intersect(const Segment &a,const Segment &b) { return ccw(a.p1,a.p2,b.p1) * ccw(a.p1,a.p2,b.p2) <= 0 && ccw(b.p1,b.p2,a.p1) * ccw(b.p1,b.p2,a.p2) <= 0; } Point cross_point(const Line &a,const Line &b) { real s1 = cross(vec(a),b.p1 - a.p1); real s2 = -cross(vec(a),b.p2 - a.p1); return b.p1 + vec(b) * (s1 / (s1 + s2)); } Point crossPoint(const Line &s, const Line &t) { real d1 = cross(s.p2 - s.p1, t.p2 - t.p1); real d2 = cross(s.p2 - s.p1, s.p2 - t.p1); if(EQ(abs(d1), 0) && EQ(abs(d2), 0)) { return t.p1; } return t.p1 + (t.p2 - t.p1) * (d2 / d1); } enum { OUT, ON, IN }; Polygon convex_hull(Polygon P,bool ONLINE = false,bool SORT = false) { if((int)P.size() <= 2) { return P; } sort(P.begin(),P.end()); Polygon res(2 * P.size()); int sz = 0; real threshold = EPS; if(ONLINE) { threshold = -EPS; } for(int i = 0;i < (int)P.size();i++) { while(sz >= 2 && cross(res[sz - 1] - res[sz - 2],P[i] - res[sz - 1]) < threshold) { sz--; } res[sz++] = P[i]; } for(int i = (int)P.size() - 2,t = sz + 1;i >= 0;i--) { while(sz >= t && cross(res[sz - 1] - res[sz - 2],P[i] - res[sz - 1]) < threshold) { sz--; } res[sz++] = P[i]; } res.resize(sz - 1); if(SORT) { int mi = 0; for(int i = 1;i < (int)res.size();i++) { if((EQ(res[mi].y,res[i].y) && res[mi].x > res[i].x) || res[mi].y > res[i].y) { mi = i; } } rotate(res.begin(),res.begin() + mi,res.end()); } return res; } int convex_contain(const Polygon &P,const Point &p) { if(P[0] == p) { return ON; } int L = 0,R = (int)P.size(); while(R - L > 1) { int M = (L + R) / 2; if(ccw(P[0],P[M],p) == CLOCKWISE) { R = M; } else { L = M; } } if(R == 1) { return OUT; } if(L + 1 == (int)P.size()) { if(intersect(Segment(P[0],P[L]),p)) { return ON; } return OUT; } if(L == 1) { if(intersect(Segment(P[0],P[L]),p)) { return ON; } } real tri = cross(P[L] - p,P[R] - p); return EQ(tri,0) ? ON : tri < -EPS ? OUT : IN; } }; //namespace geometry void Main() { geometry::Polygon P(2),Q(2); for(int i = 0;i < 2;i++) { cin >> P[i]; } for(int i = 0;i < 2;i++) { cin >> Q[i]; } geometry::Line A(P[0],Q[0]),B(P[1],Q[1]); if(P[0] == Q[0] && P[1] == Q[1]) { cout << "Yes\n"; return; } if(P[0] == Q[0] || P[1] == Q[1]) { cout << "No\n"; return; } geometry::Point C = geometry::crossPoint(A,B); if(C == Q[0] || C == Q[1]) { cout << "No\n"; return; } vector R(2); for(int i = 0;i < 2;i++) { if(geometry::norm2(C - P[i]) - geometry::norm2(Q[i] - P[i]) > geometry::EPS) { R[i] = geometry::norm2(Q[i] - P[i]) / geometry::norm2(C - P[i]); } else { cout << "No\n"; return; } } cout << (geometry::EQ(R[0],R[1]) ? "Yes\n":"No\n"); } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int tt = 1; cin >> tt; while(tt--) Main(); }