- 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 - 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

> - Dear Randy,

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

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

>

> 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

Bernard

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

> 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]

>

>

>

>

>