Geometry Problem

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

Click the figure below to see the problem 746 details.

## Thursday, May 3, 2012

### Problem 746: Triangle, Cevian, Parallel, Similarity, Harmonic Mean, Metric Relations

Labels:
cevian,
harmonic mean,
metric relations,
parallel,
similarity,
triangle

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Triangle ABE similar to triangle FCB …. ( case AA)

ReplyDeleteSo b/a= BF/AB

Triangle ABD similar to triangle AFC….( Case AA)

So b/x=AF/AB=(AB+BF)/AB=1+BF/AB=1+b/a

And x=ab/(a+b)

x/a + x/b = DC/AC + AD/AC = 1

ReplyDeletex = ab/(a + b)