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Geometry Proof

  1. Oct 7, 2008 #1
    1. The problem statement, all variables and given/known data
    Let ABC be a triangle, and suppose that AB is the largest side. Prove that the perpendicular from C to the line AB crosses at some point D with A*D*B.

    2. Relevant equations

    3. The attempt at a solution
    I know that since AB is the largest side, that angle ACB is the largest angle. I also know that CD < CB and CD < CA because a perpendicular is the shortest distance from a point to a line.

    I think what I want to say is something like: If we have A*B*D, then we would have CB < CD, which is a contradiction. Is this the right line of thinking, or am I going about this the wrong way?
     
  2. jcsd
  3. Oct 7, 2008 #2

    Dick

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    I think you are thinking along the right general direction. But I don't know if CD is the right segment to focus on. If the order of the points is A*B*D then don't you know AC>AD and AD>AB?
     
  4. Oct 7, 2008 #3
    How do I know that AC > AD from that? If that's true, then I have a contradiction, since AB is supposed to be the longest side, but AC is longer than it.
     
  5. Oct 7, 2008 #4

    Dick

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    AC is the hypotenuse of a right triangle and AD is a leg. AC>AD. Pythagoras told me.
     
  6. Oct 7, 2008 #5
    Duh! :rolleyes: Thanks a lot for your help. :smile:
     
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