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Math Help - IMO Problem II

  1. #1
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    IMO Problem II

    This problem comes from this year's International Mathematical Olympiad , comparing with another geometry problem on the next day (problem 4) , this seems a little harder . Enjoy !

    Let  I be the incentre of triangle ABC and let  \Gamma be its circumcircle. Let the line  AI intersect  \Gamma again at  D . Let  E be a point on the arc  BDC and  F a point on the side  BC such that

     \angle BAF = \angle CAE < \frac{1}{2} \angle BAC .

    Finally , let  G be the midpoint of the segment  IP . Prove that the lines  DG and  EI intersects on  \Gamma .
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  2. #2
    Senior Member BAdhi's Avatar
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    sir, sorry for the late,late reply. now only i saw this thread

    Quote Originally Posted by simplependulum View Post
    Finally , let  G be the midpoint of the segment  IP .
    could you tell me what is P here?
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  3. #3
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    Quote Originally Posted by BAdhi View Post
    sir, sorry for the late,late reply. now only i saw this thread



    could you tell me what is P here?
    In order that DG and EI intersect on the circumcircle,
    G ought to be the midpoint of IF,
    so I guess that's a typo.
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  4. #4
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    Yes , it is a typo . It should be  IF not  IP .
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