IMO Shortlist 1998 problem G4


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2. travnja 2012.
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Let M and N be two points inside triangle ABC such that
\angle MAB = \angle NAC\quad \mbox{and}\quad \angle MBA = \angle NBC.
Prove that
\frac {AM \cdot AN}{AB \cdot AC} + \frac {BM \cdot BN}{BA \cdot BC} + \frac {CM \cdot CN}{CA \cdot CB} = 1.
Izvor: Međunarodna matematička olimpijada, shortlist 1998