IMO Shortlist 1994 problem G4

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2. travnja 2012.
Let ABC be an isosceles triangle with AB = AC. M is the midpoint of BC and O is the point on the line AM such that OB is perpendicular to AB. Q is an arbitrary point on BC different from B and C. E lies on the line AB and F lies on the line AC such that E, Q, F are distinct and collinear. Prove that OQ is perpendicular to EF if and only if QE = QF.
Izvor: Međunarodna matematička olimpijada, shortlist 1994