IMO Shortlist 2009 problem G2
Kvaliteta:
Avg: 3,5Težina:
Avg: 6,0 Let be a triangle with circumcentre . The points and are interior points of the sides and respectively. Let and be the midpoints of the segments and . respectively, and let be the circle passing through and . Suppose that the line is tangent to the circle . Prove that
Proposed by Sergei Berlov, Russia
Proposed by Sergei Berlov, Russia
Izvor: Međunarodna matematička olimpijada, shortlist 2009