Difference between revisions of "1961 IMO Problems/Problem 4"
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==Problem== | ==Problem== | ||
− | In the interior of [[triangle]] <math> | + | In the interior of [[triangle]] <math>P_1P_2P_3</math> a [[point]] <math>P</math> is given. Let <math>Q_1,Q_2,Q_3</math> be the [[intersection]]s of <math>PP_1, PP_2,PP_3</math> with the opposing [[edge]]s of triangle <math>P_1P_2P_3</math>. Prove that among the [[ratio]]s <math>\frac{PP_1}{PQ_1},\frac{PP_2}{PQ_2},\frac{PP_3}{PQ_3}</math> there exists one not larger than <math>2</math> and one not smaller than <math>2</math>. |
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==Solution== | ==Solution== | ||
{{solution}} | {{solution}} |
Revision as of 01:07, 8 February 2009
Problem
In the interior of triangle a point is given. Let be the intersections of with the opposing edges of triangle . Prove that among the ratios there exists one not larger than and one not smaller than .
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
1961 IMO (Problems) • Resources | ||
Preceded by Problem 3 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 5 |
All IMO Problems and Solutions |