HYACINTHOS 20737

1. Both Segovia and Picasso points are now in ETC:

X(4549) and X(4550)

2. A proof of perspectivity of the triangles: antipodal triangle of ABC
(=circumcevian of O) and antipodal of orthic (in NPC), by Chandan :

http://www.artofproblemsolving.com/blog/65683
<http://www.artofproblemsolving.com/blog/65683>

3. ABC and The reflection in O of the antipodal triangle of the orthic,
are perspective and the perspector is the Segovia Point of the
circumcevian triangle of O.

Namely:

Let ABC be a triangle and A1B1C1 the orthic triangle.

Let A2B2C2 be the reflection of A1B1C1 in N (this is called 2nd Euler
triangle).

Let A'2B'2C'2 be the reflection of A2B2C2 in O.

The triangles ABC, A'2B'2C'2 are perspective at the Segovia Point of the
circumcevian triangle of O.

I proved it here:

http://anthrakitis.blogspot.com/2012/01/segovia-point-continued.html
<http://anthrakitis.blogspot.com/2012/01/segovia-point-continued.html>

If my computations were correct, the barycentrics of the perspector S'
are:

(cosA * sinA * (1/(1+2cos^2A)) ::)

(if not correct, which the correct are?)

Is this point listed in ETC?


APH


--- In Hyacinthos@yahoogroups.com, Antreas Hatzipolakis <anopolis72@...>
wrote:

>
> A new point I named SEGOVIA point
>
> See:
>
> http://anthrakitis.blogspot.com/2012/01/perspective_14.html

<http://anthrakitis.blogspot.com/2012/01/perspective_14.html>

>
>