Difference between revisions of "1961 IMO Problems/Problem 4"
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In the interior of triangle <math>ABC</math> a point ''P'' is given. Let <math>Q_1,Q_2,Q_3</math> be the intersections of <math>PP_1, PP_2,PP_3</math> with the opposing edges of triangle <math>ABC</math>. Prove that among the ratios <math>\frac{PP_1}{PQ_1},\frac{PP_2}{PQ_2},\frac{PP_3}{PQ_3}</math> there exists one not larger than 2 and one not smaller than 2. | In the interior of triangle <math>ABC</math> a point ''P'' is given. Let <math>Q_1,Q_2,Q_3</math> be the intersections of <math>PP_1, PP_2,PP_3</math> with the opposing edges of triangle <math>ABC</math>. Prove that among the ratios <math>\frac{PP_1}{PQ_1},\frac{PP_2}{PQ_2},\frac{PP_3}{PQ_3}</math> there exists one not larger than 2 and one not smaller than 2. | ||
| + | ==Solution== | ||
| + | {{solution}} | ||
Revision as of 10:36, 9 April 2007
Problem
In the interior of triangle 
a point P is given. Let 
be the intersections of 
with the opposing edges of triangle . Prove that among the ratios 
there exists one not larger than 2 and one not smaller than 2.
Solution
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