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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.
 
 

Trapezoid, Diagonal, Parallel, Harmonic Mean, Midpoint, Similarity

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Home | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | Art | 741-750 | Trapezoid | Triangles | Parallel lines | Similarity | Harmonic Mean | Email | Solution / comment | by Antonio Gutierrez