Given an acute and scalene triangle ABC, let H be its orthocenter, O its circumcenter, E and F the feet of the altitudes drawn from B and C, respectively. Line AO intersects the circumcircle of the triangle again at point G and segments FE and BC at points X and Y respectively. Let Z be the point of intersection of line AH and the tangent line to the circumcircle at G. Prove that HX is parallel to YZ. geometrycircumcircleprojective geometrygeometric transformationhomothetygeometry proposed