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new(?) property of Thomson and Lucas cubics

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  • rhutson2
    Dear Hyacinthists, Is the following a known result? I did not see it on Bernard s site. The locus of points P such that the reflection in P of the pedal
    Message 1 of 4 , Sep 4, 2012
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      Dear Hyacinthists,

      Is the following a known result? I did not see it on Bernard's site.

      The locus of points P such that the reflection in P of the pedal triangle of P is perspective to ABC is the Thomson cubic. The locus of the perspectors is the Lucas cubic.

      Best regards,
      Randy Hutson
    • rhutson2
      Also, if pedal is replaced with antipedal below, the property holds, except that the locus of the perspectors is the Darboux cubic. Randy
      Message 2 of 4 , Sep 4, 2012
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        Also, if 'pedal' is replaced with 'antipedal' below, the property holds, except that the locus of the perspectors is the Darboux cubic.

        Randy

        --- In Hyacinthos@yahoogroups.com, "rhutson2" <rhutson2@...> wrote:
        >
        > Dear Hyacinthists,
        >
        > Is the following a known result? I did not see it on Bernard's site.
        >
        > The locus of points P such that the reflection in P of the pedal triangle of P is perspective to ABC is the Thomson cubic. The locus of the perspectors is the Lucas cubic.
        >
        > Best regards,
        > Randy Hutson
        >
      • Bernard Gibert
        Dear Randy, ... Isn t it locus property 1 on the Thomson cubic page ? Best regards Bernard [Non-text portions of this message have been removed]
        Message 3 of 4 , Sep 4, 2012
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          Dear Randy,

          > Is the following a known result? I did not see it on Bernard's site.
          >
          > The locus of points P such that the reflection in P of the pedal triangle of P is perspective to ABC is the Thomson cubic. The locus of the perspectors is the Lucas cubic.

          Isn't it locus property 1 on the Thomson cubic page ?

          Best regards

          Bernard

          [Non-text portions of this message have been removed]
        • Randy Hutson
          Dear Bernard, My apologies. I don t know how I missed that. What about the case with antipedal triangles (my following post)? Best regards, Randy ... [Non-text
          Message 4 of 4 , Sep 5, 2012
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            Dear Bernard,

            My apologies. I don't know how I missed that.

            What about the case with antipedal triangles (my following post)?


            Best regards,
            Randy




            >________________________________
            > From: Bernard Gibert <bg42@...>
            >To: Hyacinthos@yahoogroups.com
            >Sent: Wednesday, September 5, 2012 12:12 AM
            >Subject: Re: [EMHL] new(?) property of Thomson and Lucas cubics
            >
            >

            >Dear Randy,
            >
            >> Is the following a known result? I did not see it on Bernard's site.
            >>
            >> The locus of points P such that the reflection in P of the pedal triangle of P is perspective to ABC is the Thomson cubic. The locus of the perspectors is the Lucas cubic.
            >
            >Isn't it locus property 1 on the Thomson cubic page ?
            >
            >Best regards
            >
            >Bernard
            >
            >[Non-text portions of this message have been removed]
            >
            >
            >
            >
            >

            [Non-text portions of this message have been removed]
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