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Math Help - Bisector

  1. #1
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    Bisector

    The bisector of angle  A of the triangle  ABC meets the opposite side at a point P. If  Q and  R are the respective feet from  B to  AP and from  C to  AP , prove that the points  A,P,Q and  R are harmonic.
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  2. #2
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    Quote Originally Posted by yusukered07 View Post
    The bisector of angle  A of the triangle  ABC meets the opposite side at a point P. If  Q and  R are the respective feet from  B to  AP and from  C to  AP , prove that the points  A,P,Q and  R are harmonic.
    Triangle BPQ and CPR are similar.
    So PQ/PR = BQ/CR.
    Similarly triangle ABQ and ACR are similar.
    So BQ/RC = AQ/AR.
    Combine the two equations and see what you get.
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