#include using namespace std; using ll = long long; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int q; cin >> q; int x1, y1, x2, y2, x3, y3; cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3; for (int i = 0; i < 3; i++) { auto f = [xc = x1 + x2, yc = y1 + y2](int x, int y) { int dx = 2 * x - xc, dy = 2 * y - yc; return dx * dx + dy * dy; }; int r = f(x1, y1); if (f(x3, y3) <= r) { while (q--) { int x, y; cin >> x >> y; cout << (f(x, y) <= r ? "Yes" : "No") << '\n'; } return 0; } tie(x1, x2, x3) = tuple(x2, x3, x1); tie(y1, y2, y3) = tuple(y2, y3, y1); } // The equation of the circle is: // det [ // [1, x1, y1, x1^2+y1^2, ], // [1, x2, y2, x2^2+y2^2, ], // [1, x3, y3, x3^2+y3^2, ], // [1, x, y, x^2+y^2, ], // ] = 0 // , where the left hand side corresponds to (|OP|^2 - R^2) * det A[0,3)[0,3). long long A[][4]{ {1, x1, y1, x1 * x1 + y1 * y1}, {1, x2, y2, x2 * x2 + y2 * y2}, {1, x3, y3, x3 * x3 + y3 * y3}, }; auto det3 = [](auto A) { long long res = 0; res += A[0][0] * (A[1][1] * A[2][2] - A[1][2] * A[2][1]); res += A[0][1] * (A[1][2] * A[2][0] - A[1][0] * A[2][2]); res += A[0][2] * (A[1][0] * A[2][1] - A[1][1] * A[2][0]); return res; }; if (det3(A) < 0) swap(A[0], A[1]); while (q--) { int x, y; cin >> x >> y; array B[3]; for (int i = 0; i < 3; i++) { B[i] = {A[i][1] - x, A[i][2] - y, A[i][3] - (x * x + y * y)}; } long long d = -det3(B); cout << (d <= 0 ? "Yes" : "No") << '\n'; } }