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Math Help - Collinear points

  1. #1
    Super Member malaygoel's Avatar
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    Lightbulb Collinear points

    ABC is an acute triangle(all the three angles are acute).
    D,E,F are points on BC,CA,AB respectively such that AD,BE,CF are the altitudes of the triangle.
    FP is perpendicular to BC, P lying on BC
    FQ is perpendicualr to AC, Q lying on AC
    FM is perpendicular to AD, M lying on AD
    FN is perpendicualr to BE, N lying on BE
    Prove that P,Q,M,N are collinear points.

    Keep Smiling
    Malay
    Last edited by malaygoel; December 26th 2006 at 09:47 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by malaygoel View Post
    ABC is an acute triangle(all the three angles are acute).
    D,E,F are points on BC,CA,AB respectively such that AD,BE,CF are the altitudes of the triangle.
    FP iis perpendicular to BC, P lying on BC
    FQ is perpendicualr to AC, Q lying on AC
    PQ interscts AD at M and BE at N.
    Prove that P,Q,M,N are collinear points.

    Keep Smiling
    Malay
    There is nothing to prove:

    "PQ interscts AD at M and BE at N"

    Puts M and N on the segment PQ, so P,Q,M and N are colinear

    A puzzled RonL
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  3. #3
    Super Member malaygoel's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    There is nothing to prove:

    "PQ interscts AD at M and BE at N"

    Puts M and N on the segment PQ, so P,Q,M and N are colinear

    A puzzled RonL
    Sorry
    I will edit the the first post
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