Let ABC be a triangle, H its orthocenter, and Γ its circumcircle. Let J be the point diametrically opposite to A on Γ. The points D, E and F are the feet of the altitudes from A, B and C, respectively. The line AD intersects Γ again at P. The circumcircle of EFP intersects Γ again at Q. Let K be the second point of intersection of JH with Γ. Prove that K, D and Q are collinear. geometrycollinearitycircumcircle