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Math Help - Geometry

  1. #1
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    Geometry

    Let  P be a point inside the triangle  ABC . The lines  AP , BP and  CP intersect the circumcircle \Gamma of triangle ABC agian at the points K,L and M respectively . The tagent to \Gamma at C intersects the line AB at S . Suppose that SC = SP . Prove that MK=ML .


    If you could answer this problem , you are able to receive the Honourable Mention of this year IMO .


    Moderator edit: Approved Challenge question.
    Last edited by mr fantastic; July 17th 2010 at 09:45 PM. Reason: Approved.
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  2. #2
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    Did you recieve the honourable mention for this year's IMO?
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  3. #3
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by simplependulum View Post
    Let  P be a point inside the triangle  ABC . The lines  AP , BP and  CP intersect the circumcircle \Gamma of triangle ABC agian at the points K,L and M respectively . The tagent to \Gamma at C intersects the line AB at S . Suppose that SC = SP . Prove that MK=ML .


    If you could answer this problem , you are able to receive the Honourable Mention of this year IMO .
    May be a dumb question, but what exactly is  \Gamma in this problem?
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  4. #4
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    Quote Originally Posted by chiph588@ View Post
    May be a dumb question, but what exactly is  \Gamma in this problem?
    \Gamma is the circumcircle = the unique circle passing through all the three vertices of the triangle.

    Tonio
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  5. #5
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by tonio View Post
    \Gamma is the circumcircle = the unique circle passing through all the three vertices of the triangle.

    Tonio
    Wow, I originally read circumference instead of circumcircle!
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  6. #6
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    I don't know , only the contestants getting full mark of at least one problem (of 6 ) would receive the honourable mention in IMO . I am not powerful enough to take a seat in IMO ( hope it's just now but not in the furture ) . My solution looks fine to me but i am not confident to get full mark !
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  7. #7
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    Your question is complete confusion to me...but in case this helps:

    Circle radius 65 is circumcircle of triangle ABC: BC=78, AC=120, AB = 126.
    Point P is inside triangle ABC: PA=104, PB=50, PC=32.
    In other words: a completely integer case.
    This finding of mine not enough for an IMO; can I get just the IM ?
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