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Math Help - Help with Geometry Problems?

  1. #1
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    Help with Geometry Problems?

    I'm totally stumped on how to do these:

    1. Let P and Q be the points on the sides AB and BC of a tringle ABC respectively such that BP = 3PA and QC = 2BQ. Let K be the midpoint of the segment PQ. Prove that the area of the triangle AKC is equal to 11S/24, where S is the area of the triangle ABC.

    2. Let ABC be a triangle such that angle ACB = 135. Prove that:

    AB^2=AC^2+BC^2+\sqrt{2}\timesAC\timesBC

    Thanks
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  2. #2
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    Quote Originally Posted by GGGGGGGGGGGGGGGGGG View Post
    1. Let P and Q be the points on the sides AB and BC of a tringle ABC respectively such that BP = 3PA and QC = 2BQ. Let K be the midpoint of the segment PQ. Prove that the area of the triangle AKC is equal to 11S/24, where S is the area of the triangle ABC.
    TRY it using right triangle 3-4-5:
    Code:
     C
    
    (2)
    
     Q
    (1)
     B     (3)      P(1)A
    Place point K on QP as per the problem.
    Area ABC = 6 (easy part!)
    You'll get area AKC = 11/4
    11(6) / 24 = 11/4
    So that worked! I'm too lazy to try "any" triangle
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  3. #3
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    Quote Originally Posted by Wilmer View Post
    Area ABC = 6 (easy part!)
    You'll get area AKC = 11/4
    11(6) / 24 = 11/4
    Sorry stupid question, but how do you get that AKC = 11/4?
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  4. #4
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    Quote Originally Posted by GGGGGGGGGGGGGGGGGG View Post
    how do you get that AKC = 11/4?
    Draw 2 perpendiculars: KD (D on AB) and KE (E on BC).
    You'll now have right triangles KEC and KDA, plus rectangle BDKE to work with.
    If you can't handle that, sorry but you're not ready for "any" triangle.
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  5. #5
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    Thanks very much, anyone have a solution for number 2?
    Last edited by GGGGGGGGGGGGGGGGGG; July 16th 2010 at 03:10 AM.
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