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Math Help - 3 angle bisectors

  1. #1
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    3 angle bisectors

    Code:
                   C 
     
     
     
     
     
    B   20    E  15   D    20     F            64             A
    Triangle ABC: a = BC, b = AC, c = AB (c > b > a)
    CD bisects angle ACB, then CE bisects angle BCD and CF bisects angle ACD.
    d = CD, e = CE and f = CF.
    a = 40, b = 96, c = 119, d = 30, e = 30, f = 40.
    The bisectors divide base AB in integer lengths as shown: 20 + 15 + 20 + 64 = 119.
    This is the lowest primitive case of these, lowest being determined by side BC.

    What is the next primitive case?
    HINT: a <> f and d <> e.


    Moderator edit: OK in this subforum.
    Last edited by mr fantastic; April 19th 2011 at 05:48 PM.
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  2. #2
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    Before I "lose" my solution(!) :
    Spoiler:

    Triangle sides are 784-2695-2769
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