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Math Help - Euclidean geometry problems - mostly Menelaus' theorem

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    Euclidean geometry problems - mostly Menelaus' theorem

    3. The incircle of \Delta ABC touches the sides BC, CA, AB at the points  X,Y,Z respectively, and  YZ is produced to meet BC at K
    Show that

    {BX}/{CX} = {BK}/{CK}


    4.A circle meets side BC of \Delta ABC at points L and L', CA at M and M', and AB at N and N'. Show that if AL, BM, CN are concurrent, then AL', BM', CN' are also concurrent.


    6.In \Delta ABC, let E and F be points on the sides AC and AB, respectively, with AE = AF. If
    the median AD intersects the segment EF at the point P, show that
    {PE}/{AB} = {PF}/{AC}

    I'm pretty sure they all just require creative use of Menelaus' theorem, but I can't seem to figure out in which ways
    I don't want the questions solved entirely for me, maybe just some hints (or rot13 the answer so I am encouraged to do it myself before checking)


    Turns out I had to use power of a point as well, done now
    Last edited by jbpellerin; October 20th 2010 at 02:56 PM. Reason: finished!
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