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Math Help - area proof, maybe menelaus

  1. #1
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    Exclamation area proof, maybe menelaus

    I am completely at a loss as to how to approach this problem
    it's due in about 18 hours, so I'll be working on it only a little bit more, as I also have to sleep sometime tonight
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  2. #2
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    What do you mean by \displaystyle \textrm{[D\,E\,F]} and \displaystyle \textrm{[D\,F\,C]}?
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  3. #3
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    Area of triangle DEF and triangle DFC, respectively
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    And what work have you done yourself so far? It's not in MHF's policy to knowingly complete work that will be graded - only to give a nudge in the right direction...
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  5. #5
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    all I've been able to deduce is that [ABF]=[AFC], [BDF]=[FDC]
    [AFC]=[AED]+[DEF]+[FDC]
    [AFC]=[AED]+1+[BDF]
    [ABE]=[ABF]-1
    and from there it's just substitution of what I already know and no elimination

    and I know we don't provide full solutions, I had some thanks to my name in the past but they seem to be gone since the forum software migration (I spent a long time away)
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  6. #6
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    Mais tabarnak Monsieur Pellerin, c'est quoi cette hostie de torture ?!

    Well, a bit too much for my humble capabilities (plus I hate anything involving Heron's formula!);
    so I set up a program looking at AB=AC in 1/4 increments, similarly with BC, and got this:
    AB=AC=65 and BC=1/4 (yes, 1/4):
    results in areaDEF = .99999815.... (darn close to 1)
    and areaCDF = .06249988... (suspiciously close to 5/8)
    and AD being 65-1 = 64

    So seems you'll get an awfully long skinny isosceles ABC.

    Probably won't help you much...but what the heck: any reply is better than none
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  7. #7
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    using menalaus
    I got AD = 3/2
    then menalaus again BE/ED = 5/3
    then the base*height ratio thing (forget the name)
    I get 5/3 = BE/ED = [BEF]/[DEF] = [BEF]
    and then [DFC]=[BDF]=[DEF]+[BEF] = 1+5/3 = 8/3

    your solution didn't make sense since it would make [BFD] less than 1, but [BFD] contains [DEF]=1

    hurray for sleeping on it then trying again with fresh insight
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  8. #8
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    Quote Originally Posted by jbpellerin View Post
    using menalaus I got AD = 3/2 .....
    your solution didn't make sense since it would make [BFD] less than 1, but [BFD] contains [DEF]=1
    Yep; my bad; at least I got to meet Mr. Menalaus!
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