## 22058Fwd: [EGML] Locus problems

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• Mar 18, 2014
Keywords: McCay cubic

---------- Forwarded message ----------
Date: Tue, Mar 18, 2014 at 4:24 AM
Subject: RE: [EGML] Locus problems
To: Anopolis@yahoogroups.com

In general, which is the locus of P such that:

1. The parallels through A",B",C" to AA',BB',CC', resp.
are concurrent at  Q? (also I is on the locus)

M’Cay cubic through excenters and X(1), X(3), X(4),  X(1075), X(1745), X(3362)

For P=I, Q= (b+c)*(a-b+c)*(a+b-c)-a*b*c : : =  (1,3) /\ (4,80)

=  Anticomplement of X(3878) = Reflection of (1/65), (145/3874)

=  ( -0.630855882446927, -0.22633760667943, 4.088524001507182 )

For P=O, Q=H

For P=H, Q=H

2. The triangles ABC and orthic triangle of A"B"C" are perspective at Z?

A circum-sixtic through X(3), X(4)

For P=I, no perspective

For P=O, Z= (94,275) /\ (1144, 4795)  = ( 0.306955496281031, -1.09587885376699, 4.257678074693355 )

For P=H, Z=X(24)

Regards

De: Anopolis@yahoogroups.com [mailto:Anopolis@yahoogroups.com] En nombre de Antreas Hatzipolakis
Enviado el: Lunes, 17 de Marzo de 2014 05:17 p.m.
Para: anopolis@yahoogroups.com
Asunto: [EGML] Locus problems

Let ABC be a triangle and A'B'C' the cevian triangle of P = O.

The circle (O, OA') intersects again BC at A", the circle

(O,OB') the CA at B" and the circle (O,OC') the AB at C".

1. The parallels through A",B",C" to AA', BB', CC' resp.

concur at H.

2. The triangles ABC and orthic triangle of A"B"C" are perspective (??)

In general, which is the locus of P such that:

1. The parallels through A",B",C" to AA',BB',CC', resp.
are concurrent? (also I is on the locus)

2. The triangles ABC and orthic triangle of A"B"C" are perspective?

APH

_