## Re: [EMHL] Sharygin lemma?

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

Best regards

>
> 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.
>
>
> http://f1.grp.yahoofs.com/v1/UPP4Str7mNq-f0xPwnCdMIZZeHHgSFYyUodHyc0qQjXLiGu9hMmVJE-NGz9LMROrkTfs40RJSUgcqugDVGo6rr3_CDv12B4bMw/20092516nev.pdf
>
> Yakub.
>
>
>
> --- In Hyacinthos@yahoogroups.com,
> >
> > Dear Yakub,
> > Do you have a simple proof for this problem?
> > (I have an algebraic proof not simple,
> > and no other information)
> >
> > Best regards
> >
> > > 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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> >
>
>
>
>
> ------------------------------------
>
>
>
>     Hyacinthos-fullfeatured@yahoogroups.com
>
>
>

___________________________________________________________
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• 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
http://www.qafqaz.edu.az/journal/20092516nev.pdf
See Lemma 2.1. Best regards, Yakub.

>
> Dear Yakub,
>
> Best regards
>
> >
> > 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.
> >
> >
> > http://f1.grp.yahoofs.com/v1/UPP4Str7mNq-f0xPwnCdMIZZeHHgSFYyUodHyc0qQjXLiGu9hMmVJE-NGz9LMROrkTfs40RJSUgcqugDVGo6rr3_CDv12B4bMw/20092516nev.pdf
> >
> > Yakub.
> >
> >
> >
> > --- In Hyacinthos@yahoogroups.com,
> > >
> > > Dear Yakub,
> > > Do you have a simple proof for this problem?
> > > (I have an algebraic proof not simple,
> > > and no other information)
> > >
> > > Best regards
> > >
> > > > 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)
> > >
> > >
> > >
> > >
> > >Â  Â  Â Â Â
> > >
> > ___________________________________________________________
> >
> > > ÃÃ¡Ã±Ã¥Ã¨ÃÃªÃ¡Ã´Ã¥ Ã´Ã¡ Ã¥Ã­Ã¯Ã·Ã«Ã§Ã´Ã©ÃªÃ
> > Ã¬Ã§Ã­Ã½Ã¬Ã¡Ã´Ã¡ (spam); Ã"Ã¯ Yahoo! Mail
> > Ã°Ã±Ã¯Ã³Ã´Ã¡Ã³ÃÃ¡ ÃªÃ¡Ã´Ã Ã´Ã¹Ã­ Ã¥Ã­Ã¯Ã·Ã«Ã§Ã´Ã©ÃªÃ¾Ã­
> > >
> >
> >
> >
> >
> > ------------------------------------
> >
> >
> >
> > Â  Â  Hyacinthos-fullfeatured@yahoogroups.com
> >
> >
> >
>
>
>
> ___________________________________________________________
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