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.