Geometry Problem

Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the problem 747 details.

## Thursday, May 3, 2012

### Problem 747: Trapezoid, Diagonals, Parallel, Bases, Midpoint, Similarity, Harmonic Mean

Labels:
base,
diagonal,
harmonic mean,
parallel,
similarity,
trapezoid

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Consider triangle OBA with cevian OE and BC //OE, AD//OE

ReplyDeletePer the result of problem 746 we have OE=a.b/(a+b)

Consider triangle OCD with cevian OF and BC //OF, AD//OF

Per the result of problem 746 we have OF=a.b/(a+b)

So OE=OF and EF= OE+OF= 2a.b/(a+b)