Geometry Problem. Post your solution in the comments box below.

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

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## Thursday, July 2, 2015

### Geometry Problem 1126: Equilateral Triangle, Circumcircle, Metric Relation, Harmonic Mean

Labels:
circumcircle,
equilateral,
harmonic mean,
metric relations,
similarity,
triangle

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Observe that ∠ADB=∠ADE=60°,

ReplyDeletethus from S(ADB)+S(ADE)=S(BDE),

xe sin60° + xd sin60° = de sin120°

x=de/(d+e)

x/d=BC/EB=AB/EB=1/(EB/AB)=1/(1+d/e)=e/(e+d)

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