Online Geometry Problems

Online Geometry Problem 746: Triangle, Cevian, Parallel, Similarity, Harmonic Mean, Metric Relations. Level: High School, Honors Geometry, College, Mathematics Education

The figure shows a triangle ABC with a cevian BD. AE and CF are parallel to BD (E on CB extended and F on AB extended). Prove that BD is one-half the harmonic mean of AE and CF.
 

Triangle, Cevian, Parallel, Similarity, Harmonic Mean
 

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