- As locus problem:

Let ABC be a triangle, P a point and PaPbPc the pedal triangle of P.

Denote:

(N1), (N2), (N3) = the reflections of (N) in PaO, PbO, PcO, resp.

A'B'C' = the triangle bounded by the radical axes of

((O),(N1)), ((O),(N2)),((O),(N3)).

Which is the locus of P such that A'B'C', N1N2N3 are perspective?

Euler Line (?) + ??

APH

GENERALIZATION:

>

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

> Denote:

>

> PaPbPc = the pedal triangle of a point P on the Euler line

>

>

> (N1), (N2), (N3) = the reflections of (N) in PaO, PbO, PcO, resp.

>

> A'B'C' = the triangle bounded by the radical axes of

> ((O),(N1)), ((O),(N2)),((O),(N3)).

>

> A'B'C', N1N2N3 are perspective.

>

> True???

>

>

>

- Are the triangles ABC, A'B'C' perspective?Feuerbach point Fc.The NPC of CHIc intersects the excircle (Ic) at C' other than theFeuerbach point Fb,The NPC of BHIb intersects the excircle (Ib) at B' other than theFeuerbach point Fa.Let ABC be a triangle with excenters Ia,Ib,Ic.

The NPC of AHIa interscts the excircle (Ia) at A' other than theIn any case, has the triangle A'B'C' any interesting properties?APH