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Math Help - Geometric puzzle fun

  1. #1
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    Geometric puzzle fun

    Code:
              C
     
     
     
     
    B           D     E                 A
    Triangle ABC has integer sides: perimeter = 96

    CD bisects angle ACB ; CE is a median (thus BE = AE).
    CD and CE both have integer lengths.

    Find the triangle's sides, plus CD and CE.
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  2. #2
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    Hint: CE = 19
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  3. #3
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    can this really be solved without guessing values?
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  4. #4
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    Well, you're given the perimeter=96 :
    so "find" a triangle with integer sides and perimeter = 96 : very few!
    With sides = a>b>c :
    bisector from C = sqrt[ab(1 - k)] where k = c^2 / (a+b)^2

    median from C = sqrt[2(a^2 + b^2) - c^2] / 2

    And I gave median = 19 as clue...so not too difficult to wrap up.
    I'll post/hide the solution (in case I forget!):
    Spoiler:

    triangle: 13-39-44
    bisector = 12
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