ANOPOLIS 1466

[APH]

The triangles ABC, A'B'C' are perspective

 

[CL]

 

Another way to build this perspector:

 

Let Q be this perspector.

 

Let A”B”C” be the cevian triangle of O. Tangentes to the incircle through A”, B”, C”  (not the sidelines) touch the incircle at A*, B*, C*, resp.

 

Triangles ABC and A*B*C* are perspective at Q*=Isogonal conjugate of Q.

 

Note: ABC and A*B*C* are perspective for all points P, not only for P=O. If P=u : v : w (trilinears) then the perspector is

    Q* =  a*(b+c-a)*u^2 : b*(a+c-b)*v^2 : c*(a+b-c)*w^2

 

Regards

César Lozada

 

 

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De:  En nombre de Antreas Hatzipolakis
Enviado el: Martes, 06 de Mayo de 2014 05:54 p.m.
Para: anopolis@yahoogroups.com; Hyacinthos
Asunto: [EGML] Perspective?

 

Let ABC be a triangle with excenters Ia,Ib,Ic.

The NPC of  AHIa interscts the excircle (Ia) at A' other than the

Feuerbach point Fa.

The  NPC of  BHIb intersects the excircle (Ib) at B' other than the

Feuerbach point Fb,

The  NPC of  CHIc intersects the excircle (Ic) at C' other than the

Feuerbach point Fc.

Are the triangles ABC, A'B'C' perspective?

In any case, has the triangle A'B'C' any interesting properties?

APH