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I Geometrical problem

  1. Mar 21, 2016 #1
    Hello,

    A friend of mine gave me this puzzle and I'd like to share it with you, math enthusiasts:
    Two ladders intersect in a point O, the first ladder is 3m long and the second one 2m. O is 1m from the ground, that is AC = 2, BD = 3 and OE = 1 (see the image bellow)

    Question: what's the value of DC ?

    Note:
    E is the perpendicular projection of O on [DC] and it does not necessarily divide [DC] in two equal parts.
    problem.png
     
  2. jcsd
  3. Mar 21, 2016 #2

    phyzguy

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    Well, I have an answer. Do you know the answer, or are you asking for help?
     
  4. Mar 21, 2016 #3
    Don't hesitate sharing it, I found the answer in a numerical form, but I'm curious about finding a closed form solution.
     
  5. Mar 21, 2016 #4

    phyzguy

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    Mathematica gave me a closed form solution, but it is very messy.
     
  6. Mar 21, 2016 #5
    How did you approach the problem ?
     
  7. Mar 21, 2016 #6

    phyzguy

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    Maybe not the most elegant way, but I set up 5 unknowns - OD, OC, AD, BC, CD. Using the Pythagorean theorem and similar triangles, you can write 5 equations relating them, then solve them.
     
  8. Mar 21, 2016 #7
    I ended up with a system of two nonlinear equation, I talked about it here https://www.physicsforums.com/threads/a-nonlinear-equation-system.862991/
    I used x =BC and y= AD. Once I found x and y I used Pythagore to find DC. But the x (or y) end up being a solution of a quartic equations ... messy
     
  9. Mar 21, 2016 #8

    phyzguy

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    Yes, I agree that you end up with a quartic.
     
  10. Mar 21, 2016 #9
    The problem is very easy to explain, I wonder if there is a different approach that give an elegant solution.
     
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