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Re: [EMHL] Sharygin lemma?

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  • Nikolaos Dergiades
    Dear Yakub, thank you. But I have not access to this site. Best regards Nikos Dergiades ... ___________________________________________________________
    Message 1 of 5 , Nov 10, 2009
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      Dear Yakub,
      thank you. But I have not access to this site.

      Best regards
      Nikos Dergiades

      >
      > Dear Nikos Dergiades, yes I have a pure geometric proof
      > which is similar to the solution of the problem in the
      > problems section of journal Math. in School (Russian). See
      >
      > Problem 3393, Mathematics in School (in Russian), 6, 1989,
      > 130; Solution: 4, 1990, 70.
      >
      > See also my recent paper for the proof
      >
      > http://f1.grp.yahoofs.com/v1/UPP4Str7mNq-f0xPwnCdMIZZeHHgSFYyUodHyc0qQjXLiGu9hMmVJE-NGz9LMROrkTfs40RJSUgcqugDVGo6rr3_CDv12B4bMw/20092516nev.pdf
      >
      > where the first lemma is about this problem.
      > Yakub.
      >
      >
      >
      > --- In Hyacinthos@yahoogroups.com,
      > Nikolaos Dergiades <ndergiades@...> wrote:
      > >
      > > Dear Yakub,
      > > Do you have a simple proof for this problem?
      > > (I have an algebraic proof not simple,
      > > and no other information)
      > >
      > > Best regards
      > > Nikos Dergiades
      > >
      > > > Dear friends.
      > > > Please inform me. Who can be the author of the
      > following
      > > > interesting geometric problem.
      > > >
      > > > Let ABCD be a convex quadrilateral. Construct a
      > line
      > > > through C intersecting extensions of AB and AD at
      > M and K,
      > > > respectively, such that
      > (1/(Area(BCM)))+(1/(Area(DCK))) is
      > > > minimal.
      > > >
      > > > The answer is MK||BD.
      > > >
      > > > This fact appeared in one russian journal as a
      > problem of
      > > > anonimous author:
      > > >
      > > > Problem 3393, Mathematics in School (in Russian),
      > 6, 1989,
      > > > 130; Solution: 4, 1990, 70.
      > > >
      > > > Is it possible that editor of geometry problems
      > in this
      > > > journal- Sharygin I.F. was author of this
      > problem? But why
      > > > then he didn't indicate his name?
      > > > Do you familiar with this geometric fact? Have
      > you any
      > > > other sources for this problem?
      > > >
      > > > Y.N. Aliyev (Baku)
      > >
      > >
      > >
      > >
      > >       
      > >
      > ___________________________________________________________
      >
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      > >
      >
      >
      >
      >
      > ------------------------------------
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      >
      >
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      >
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      >



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    • yakub.aliyev
      Dear Nikos, use this link: http://www.qafqaz.edu.az/journal/20092516nev.pdf See Lemma 2.1. Best regards, Yakub.
      Message 2 of 5 , Nov 10, 2009
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        Dear Nikos, use this link:
        http://www.qafqaz.edu.az/journal/20092516nev.pdf
        See Lemma 2.1. Best regards, Yakub.

        --- In Hyacinthos@yahoogroups.com, Nikolaos Dergiades <ndergiades@...> wrote:
        >
        > Dear Yakub,
        > thank you. But I have not access to this site.
        >
        > Best regards
        > Nikos Dergiades
        >
        > >
        > > Dear Nikos Dergiades, yes I have a pure geometric proof
        > > which is similar to the solution of the problem in the
        > > problems section of journal Math. in School (Russian). See
        > >
        > > Problem 3393, Mathematics in School (in Russian), 6, 1989,
        > > 130; Solution: 4, 1990, 70.
        > >
        > > See also my recent paper for the proof
        > >
        > > http://f1.grp.yahoofs.com/v1/UPP4Str7mNq-f0xPwnCdMIZZeHHgSFYyUodHyc0qQjXLiGu9hMmVJE-NGz9LMROrkTfs40RJSUgcqugDVGo6rr3_CDv12B4bMw/20092516nev.pdf
        > >
        > > where the first lemma is about this problem.
        > > Yakub.
        > >
        > >
        > >
        > > --- In Hyacinthos@yahoogroups.com,
        > > Nikolaos Dergiades <ndergiades@> wrote:
        > > >
        > > > Dear Yakub,
        > > > Do you have a simple proof for this problem?
        > > > (I have an algebraic proof not simple,
        > > > and no other information)
        > > >
        > > > Best regards
        > > > Nikos Dergiades
        > > >
        > > > > Dear friends.
        > > > > Please inform me. Who can be the author of the
        > > following
        > > > > interesting geometric problem.
        > > > >
        > > > > Let ABCD be a convex quadrilateral. Construct a
        > > line
        > > > > through C intersecting extensions of AB and AD at
        > > M and K,
        > > > > respectively, such that
        > > (1/(Area(BCM)))+(1/(Area(DCK))) is
        > > > > minimal.
        > > > >
        > > > > The answer is MK||BD.
        > > > >
        > > > > This fact appeared in one russian journal as a
        > > problem of
        > > > > anonimous author:
        > > > >
        > > > > Problem 3393, Mathematics in School (in Russian),
        > > 6, 1989,
        > > > > 130; Solution: 4, 1990, 70.
        > > > >
        > > > > Is it possible that editor of geometry problems
        > > in this
        > > > > journal- Sharygin I.F. was author of this
        > > problem? But why
        > > > > then he didn't indicate his name?
        > > > > Do you familiar with this geometric fact? Have
        > > you any
        > > > > other sources for this problem?
        > > > >
        > > > > Y.N. Aliyev (Baku)
        > > >
        > > >
        > > >
        > > >
        > > >       
        > > >
        > > ___________________________________________________________
        > >
        > > > ×ñçóéìïðïéåßôå Yahoo!;
        > > > ÂáñåèÞêáôå ôá åíï÷ëçôéêÜ
        > > ìçíýìáôá (spam); Ã"ï Yahoo! Mail
        > > > äéáèÝôåé ôçí êáëýôåñç äõíáôÞ
        > > ðñïóôáóßá êáôÜ ôùí åíï÷ëçôéêþí
        > > > ìçíõìÜôùí http://login.yahoo.com/config/mail?.intl=gr
        > > >
        > >
        > >
        > >
        > >
        > > ------------------------------------
        > >
        > > Yahoo! Groups Links
        > >
        > >
        > >     Hyacinthos-fullfeatured@yahoogroups.com
        > >
        > >
        > >
        >
        >
        >
        > ___________________________________________________________
        > Χρησιμοποιείτε Yahoo!;
        > Î'αρεθήκατε τα ενοχλητικά μηνύματα (spam); Το Yahoo! Mail
        > διαθέτει την καλύτερη δυνατή προστασία κατά των ενοχλητικών
        > μηνυμάτων http://login.yahoo.com/config/mail?.intl=gr
        >
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