

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