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Math Help - An interesting problem in Geometry

  1. #1
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    An interesting problem in Geometry

    In  \Delta ABC , a line passing through the centroid of the triangle intersects with segments  AB and  AC at  P and  Q respectively .

    Show that :

     \frac{BP}{AP} + \frac{ CQ}{AQ} = 1
    Last edited by simplependulum; June 9th 2010 at 12:41 AM.
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  2. #2
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    Quote Originally Posted by simplependulum View Post
    In  \Delta ABC , a line passing through the centroid of the triangle intersects with segments  AB and  AC at  P and  Q respectively .

    Show that :

     \frac{BP}{AP} + \frac{ CQ}{AQ} = 1
    Dear simplependulum,

    Thanks for submitting this question. I tried it for several days and finally came up with an answer.
    Attached Thumbnails Attached Thumbnails An interesting problem in Geometry-sp1.pdf  
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  3. #3
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    Thanks for the reply , I worried that no one may feel interested in this problem which seems an easy task but actually it needs some time to finish .

    Excellent ! You utilized Menelaus Theorem to solve this problem . I think Menelaus and Ceva is one of the greatest stone in pure geometry , they are applicable and powerful indeed !
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