IMO Shortlist 1996 problem G7

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Dodao/la: arhiva
2. travnja 2012.
Let ABC be an acute triangle with circumcenter O and circumradius R. AO meets the circumcircle of BOC at A', BO meets the circumcircle of COA at B' and CO meets the circumcircle of AOB at C'. Prove that OA'\cdot OB'\cdot OC'\geq 8R^{3}. Sorry if this has been posted before since this is a very classical problem, but I failed to find it with the search-function.
Izvor: Međunarodna matematička olimpijada, shortlist 1996