Online Geometry
Problem 749: Triangle, Rhombus, Parallel, Harmonic
Means,
Metric Relations. Level: High School, Honors Geometry, College,
Mathematics Education

The figure shows a triangle ABC. Points D,
E, F are chosen on AB, BC and AC, respectively, so that ADEF is a
rhombus. Prove that the side of the rhombus is one-half the harmonic mean
of AB and AC.