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Equilater Triangle

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Equilater Triangle

by umaa » Sun Jul 05, 2009 2:53 pm
[spoiler]OA A. How are we assuming that the smaill triangle is 30-60-90 angle from A? Pls explain[/spoiler]
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by GMATQuantCoach » Sun Jul 05, 2009 6:22 pm
(1) We know triangles DEF, ABF, and CDB are 30-60-90 triangles. We can find the ratio of DF:DE and BD:CD. Since BD = DF, we can calculate the ratio of DF:CD.
We know DF:DE and DF:CD, then we know DF:CE.(We don't really care what the value is.)
Then we know the ratio of DBF's area and ACE's area.
Triangles BCD, ABF, and DEF and all equal.
We can find the ratio of the shaded area to the area of ACE.

(2) This statement doesn't help because you can rotate the inscribed triangle BFD freely.

A is the answer.
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by umaa » Sun Jul 05, 2009 6:41 pm
Got it. Thanks.. Didn't think in that way.
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