Sunday, December 20, 2009

Fox 216

3 comments:

  1. Triangle PQR is also an ET by symmetry.We assume AB=BC=CA=3 units and this makes CE=√7 by cosine law. Further, CR/RE*EA/AB*BF/FC = 1 (Menelaus) and thus CR/RE * 2/3 *2/1 = 1 or CR/RE = 3/4 or CR/CE=3/7. Likewise,AB/BE * EP/PC * CD/DA =1 and this yields, EP/CE = 1/7 which, in turn, gives PR/CE = 1 - 3/7 - 1/7 = 3/7 or PR = 3/√7
    Finally, A(ABC)/A(PQR)= AB^2/PR^2 = 9/(9/7)= 7 or Option B.
    Ajit

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  2. APR is a 30-60-90 triangle, which can be used as well.

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  3. Yes, indeed! Once you get EP/CE=1/7 we can say that CP/CE=(CE-EP)/CE=6/7 or CP=6*CE/7=6/√7 But AR=CP=6/√7 and so PR=AR/2=3/√7 Hence etc.

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