Difference between revisions of "2001 IMO Shortlist Problems/G6"
(New page: == Problem == Let <math>ABC</math> be a triangle and <math>P</math> an exterior point in the plane of the triangle. Suppose the lines <math>AP</math>, <math>BP</math>, <math>CP</math> meet...) |
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Revision as of 17:49, 20 August 2008
Problem
Let 
be a triangle and 
an exterior point in the plane of the triangle. Suppose the lines 
, 
, 
meet the sides 
, 
, 
(or extensions thereof) in 
, 
, 
, respectively. Suppose further that the areas of triangles 
, 
, 
are all equal. Prove that each of these areas is equal to the area of triangle itself.
Solution
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