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Geometry Problem 1131: Triangle Area, Two Cevians, Equal Product of Areas. Level: High School, SAT Prep, Honors Geometry, College, Math Education

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In a triangle ABC of area S, cevians AD and CE meet at F (figure below). If S1, S2, and S3 are the areas of triangles BDE, DEF, and AFC, respectively, prove that: S.S2 = S1.S3.
 

Infographic Geometry problem 1131 Triangle Area, Two Cevians, Equal Product
 

 

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Last updated: Jul 9, 2015 by Antonio Gutierrez.