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Olimpiada

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  • Алексей Мякишев
    Dear friends! Happy New Year! Here is a link for geometrical olimpiad in memory of I.F.Sharygin. http://www.geometry.ru/olimp.htm Best regards, Alexei
    Message 1 of 6 , Dec 31, 2008
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      Dear friends!
      Happy New Year!
      Here is a link for geometrical olimpiad in memory of I.F.Sharygin.
      http://www.geometry.ru/olimp.htm
      Best regards,
      Alexei Myakishev


      [Non-text portions of this message have been removed]
    • Luís Lopes
      Dear Hyacinthists, Problem 13 from the link below: TC given (H_a,I,I_a). I would like to have a hint to the TConstruction. Let D be the midpoint of the segment
      Message 2 of 6 , Jan 12, 2009
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        Dear Hyacinthists,

        Problem 13 from the link below: TC given
        (H_a,I,I_a). I would like to have a hint to the TConstruction.
        Let D be the midpoint of the segment (I,I_a).
        I know that D belongs to the circuncircle and B,C
        belong to the circle (D,DI).

        Best regards,
        Luis



        To: Hyacinthos@yahoogroups.comFrom: alex_geom@...: Thu, 1 Jan 2009 10:37:22 +0300Subject: [EMHL] Olimpiada



        Dear friends!Happy New Year!Here is a link for geometrical olimpiad in memory of I.F.Sharygin.http://www.geometry.ru/olimp.htmBest regards,Alexei Myakishev[Non-text portions of this message have been removed]





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        [Non-text portions of this message have been removed]
      • Nikolaos Dergiades
        Dear Luis, If the line II_a meets BC at E then since BI, BI_a are bisectors of
        Message 3 of 6 , Jan 12, 2009
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          Dear Luis,

          If the line II_a meets BC at E then
          since BI, BI_a are bisectors of <ABC the points A, E are
          the harmonic conjugates relative to I, I_a.
          Since AH_a is perpendicular to BC the circumcircle of AH_aE
          is the Apollonius circle of triangle H_aII_a and hence
          H_aE is internal bisector of triangle H_aII_a and
          hence the line BC can be constructed.
          Since we know that DI = DB = DC the points B, C can be
          found as intersections of line BC with the circle (D, DI).
          Finally A can be constructed as intersection of line II_a
          with the perpendicular from H_a to BC.
          Best regards
          Nikos Dergiades

          > Dear Hyacinthists,
          >
          > Problem 13 from the link below: TC given
          > (H_a,I,I_a). I would like to have a hint to the
          > TConstruction.
          > Let D be the midpoint of the segment (I,I_a).
          > I know that D belongs to the circuncircle and B,C
          > belong to the circle (D,DI).
          >
          > Best regards,
          > Luis
          >
          >
          >
          > To: Hyacinthos@yahoogroups.comFrom:
          > alex_geom@...: Thu, 1 Jan 2009 10:37:22
          > +0300Subject: [EMHL] Olimpiada
          >
          >
          >
          > Dear friends!Happy New Year!Here is a link for geometrical
          > olimpiad in memory of
          > I.F.Sharygin.http://www.geometry.ru/olimp.htmBest
          > regards,Alexei Myakishev[Non-text portions of this message
          > have been removed]
          >
          >
          >
          >
          >
          > _________________________________________________________________
          > Cansado de espaço para só 50 fotos? Conheça o Spaces, o
          > site de relacionamentos com até 6,000 fotos!
          > http://www.amigosdomessenger.com.br
          >
          > [Non-text portions of this message have been removed]
          >
          >
          > ------------------------------------
          >
          > Yahoo! Groups Links
          >
          >
          >


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        • Luís Lopes
          Dear Hyacinthists, Nikos Dergiades and Alexei Myakishev, [AM] But don t please publish the solution until April, 1.[AM] Sincerely AlexeyOk. After having sent
          Message 4 of 6 , Jan 13, 2009
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            Dear Hyacinthists, Nikos Dergiades and Alexei Myakishev,

            [AM] But don't please publish the solution until April, 1.[AM] Sincerely AlexeyOk. After having sent the message I wondered
            about a too early posting. Sorry.

            [ND] If the line II_a meets BC at E then [....]
            Thank you very much for your solution, Nikos.

            Best regards
            Luis






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            [Non-text portions of this message have been removed]
          • p28121941
            I think will be useful for the organizers of Contests, Olympiads, and editors of journals with problems that when this type of announcement be made, it
            Message 5 of 6 , Jan 13, 2009
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              I think will be useful for the organizers of Contests, Olympiads, and
              editors of journals with problems that when this type of announcement
              be made, it includes the date until it nobody should send solutions to
              the problems. I am the organizer of the MMC and the past year we had a
              lot of problems due to a too early post of the statements of the
              prproblems in Internet. Really, I honestly think that this is not a
              race to see who is the first one who put the solution available to
              every body...
              Best regards,
              Francisco
              --- In Hyacinthos@yahoogroups.com, Алексей Мякишев
              <alex_geom@...> wrote:
              >
              > Dear friends!
              > Happy New Year!
              > Here is a link for geometrical olimpiad in memory of I.F.Sharygin.
              > http://www.geometry.ru/olimp.htm
              > Best regards,
              > Alexei Myakishev
              >
              >
              > [Non-text portions of this message have been removed]
              >
            • Nikolaos Dergiades
              Dear Francisco, ... You are right. When I answered to the message of Luís Lopes I did n t thought that the ending date of sending solutions had not passed.
              Message 6 of 6 , Jan 13, 2009
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                Dear Francisco,

                > I think will be useful for the organizers of Contests,
                > Olympiads, and
                > editors of journals with problems that when this type of
                > announcement
                > be made, it includes the date until it nobody should send
                > solutions to
                > the problems. I am the organizer of the MMC and the past
                > year we had a
                > lot of problems due to a too early post of the statements
                > of the
                > prproblems in Internet. Really, I honestly think that this
                > is not a
                > race to see who is the first one who put the solution
                > available to
                > every body...
                > Best regards,
                > Francisco

                You are right.
                When I answered to the message of Luís Lopes
                I did n't thought that the ending date of sending solutions
                had not passed. Sorry.
                Best regards
                Nikos Dergiades




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