IMO Shortlist 1961 problem 4


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Dodao/la: arhiva
April 2, 2012
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Consider triangle P_1P_2P_3 and a point p within the triangle. Lines P_1P, P_2P, P_3P intersect the opposite sides in points Q_1, Q_2, Q_3 respectively. Prove that, of the numbers \dfrac{P_1P}{PQ_1}, \dfrac{P_2P}{PQ_2}, \dfrac{P_3P}{PQ_3}
at least one is \leq 2 and at least one is \geq 2
Source: Međunarodna matematička olimpijada, shortlist 1961