Let ABC be a triangle and m a line which intersects the sides AB and AC at interior points D and F, respectively, and intersects the line BC at a point E such that C lies between B and E. The parallel lines from the points A, B, C to the line m intersect the circumcircle of triangle ABC at the points A1, B1 and C1, respectively (apart from A, B, C). Prove that the lines A1E , B1F and C1D pass through the same point.
Greece geometrycircumcircleprojective geometryalgebrapolynomialpower of a pointradical axis