## Re: [EMHL] Orthologic?

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• Antreas, A B C , A^B^C^ are not orthologic.  However, A^B^C^ is perspective to ABC at X(262), and to A B C at non-ETC 43.220195027499022, which is also the
Message 1 of 1 , Mar 5, 2013
Antreas,

A'B'C', A^B^C^ are not orthologic.  However, A^B^C^ is perspective to ABC at X(262), and to A"B"C" at non-ETC 43.220195027499022, which is also the center of the circumconic mentioned around post #21466, 1/30/2013.  Also, the centroid of A^B^C^ is the centroid of ABC, and the symmedian point of A^B^C^ = X(381);  X(69) of A^B^C^ = X(376); X(141) of A^B^C^ = X(549); X(193) of A^B^C^ = X(3543); and X(597) of A^B^C^ = X(5).

A^B^C^ can be equivalently defined as:

Let Pa be the parabola with focus A and directrix BC.  Let La be the polar of X(3) wrt Pa.  Define Lb, Lc cyclically.
Let A^ = Lb/\Lc, B^ = Lc/\La, C^ = La/\Lb.

Randy

>________________________________
> From: Antreas Hatzipolakis <anopolis72@...>
>To: Hyacinthos <Hyacinthos@yahoogroups.com>
>Sent: Saturday, March 2, 2013 4:29 PM
>Subject: [EMHL] Orthologic?
>
>

>I am wondering if these triangles are orthologic:
>
>Let A'B'C' be the cevian triangle of I, A"B"C" the medial
>triangle, A*B*C* the circumcevian triangle of G wrt A"B"C",
>and A^B^C^ the triangle bounded by the perpendiculars
>to lines A"A*, B"B*, C"C* at A*,B*,C*, resp.
>
>Are the triangles A'B'C', A^B^C^ orthologic (as my figure shows)?
>
>APH
>
>
>
>

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