Online Geometry Problem 747: Trapezoid, Diagonals, Parallel, Bases, Midpoint, Similarity, Harmonic Mean. Level: High School, Honors Geometry, College, Mathematics Education

The figure shows a trapezoid ABCD with the diagonals AC and BD meeting at O. EF, passing through O, is parallel to the bases AD and BC. Prove that (1) O is the midpoint of EF, (2) EF is the harmonic mean of AD and BC.