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1961 IMO Problems/Problem 4

Revision as of 18:36, 6 April 2007 by Teki-Teki (talk | contribs) (posted problem from IMO Compendium)
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In the interior of triangle $ABC$ a point P is given. Let $Q_1,Q_2,Q_3$ be the intersections of $PP_1, PP_2,PP_3$ with the opposing edges of triangle $ABC$. Prove that among the ratios $\frac{PP_1}{PQ_1},\frac{PP_2}{PQ_2},\frac{PP_3}{PQ_3}$ there exists one not larger than 2 and one not smaller than 2.

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