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Question about Geometry

  1. May 10, 2009 #1
    1. The problem statement, all variables and given/known data

    Let ABC be a right angled triangle such that A=90, AB=AC and let M be the mid point of the side AC. Take the point P on the side BC so that AP is vertical to BM. Let H be the intersection of AP ad BM.

    Find the ratio BP : PC.

    2. Relevant equations

    AB=AC
    AM = MC

    BP : PC = ?

    See the problem here: http://4.bp.blogspot.com/_Qc1Z3hIcYO4/SgbXNoa555I/AAAAAAAABPM/ruupwSz5EoE/s1600-h/bp_pc.JPG.

    3. The attempt at a solution

    I drew parallel lines, and I found some interesting connections. I am very close to the answer, but I still cannot find it.

    Please, see the attachment "parallel_lines.jpg".
     

    Attached Files:

    Last edited: May 10, 2009
  2. jcsd
  3. May 10, 2009 #2

    Attached Files:

    Last edited: May 10, 2009
  4. May 10, 2009 #3
  5. May 10, 2009 #4
    Mass points kill this problem in about 2 seconds. Assign mass 2 to points C and A, so point M has mass 4. Using the fact that BAM ~ BFA ~ AFM, you can find that BF/FM = 4, so point B has mass 1. Thus, BP/CP = [ C ]/[ B ] = 2:1 (where [ ] denotes mass).

    If you don't know what mass points are, you should go learn about them immediately. (They're awesome.)
     
  6. May 13, 2009 #5
    Great thanks for the awesome tip!
     
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