IMO Shortlist 2011 problem G1

  Avg: 3,3
  Avg: 6,3
Dodao/la: arhiva
23. lipnja 2013.
Let ABC be an acute triangle. Let \omega be a circle whose centre L lies on the side BC. Suppose that \omega is tangent to AB at B' and AC at C'. Suppose also that the circumcentre O of triangle ABC lies on the shorter arc B'C' of \omega. Prove that the circumcircle of ABC and \omega meet at two points.

Proposed by Härmel Nestra, Estonia
Izvor: Međunarodna matematička olimpijada, shortlist 2011