IMO Shortlist 2012 problem G4

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Dodao/la: arhiva
3. studenoga 2013.
Let ABC be a triangle with AB \neq AC and circumcenter O. The bisector of \angle BAC intersects BC at D. Let E be the reflection of D with respect to the midpoint of BC. The lines through D and E perpendicular to BC intersect the lines AO and AD at X and Y respectively. Prove that the quadrilateral BXCY is cyclic.
Izvor: Međunarodna matematička olimpijada, shortlist 2012