IMO 1976 LL USS42

For a point O inside a triangle ABC, denote by A1, B1, C1

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IMO 1976 LL USS42

Origin: USS

Problem

For a point O inside a triangle ABC, denote by A1, B1, C1 the respective intersection points of AO, BO, CO with the corresponding sides. Let n1 = AO A1O, n2 = BO B1O, n3 = CO C1O . What possible values of n1, n2, n3 can all be positive integers?