IMO Shortlist 2009 problem G6
Kvaliteta:
Avg: 3,0Težina:
Avg: 8,0 Let the sides and of the quadrilateral (such that is not parallel to ) intersect at point . Points and are circumcenters and points and are orthocenters of triangles and , respectively. Denote the midpoints of segments and by and , respectively. Prove that the perpendicular from on , the perpendicular from on and the lines are concurrent.
Proposed by Ukraine
Proposed by Ukraine
Izvor: Međunarodna matematička olimpijada, shortlist 2009