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• GENERALIZATION Let ABC be a triangle, Q a point, QaQbQc the pedal triangle of Q, (X) the circumcircle of QaQbQc (=pedal circle of Q), P a point on the OQ line
Message 1 of 22 , Feb 13
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GENERALIZATION

Let ABC be a triangle, Q a point, QaQbQc the pedal triangle of Q,
(X) the circumcircle of QaQbQc (=pedal circle of Q), P a point on
the OQ line and PaPbPc the pedal triangle of P.

Denote:

(X1), (X2), (X3) the reflections of (X) in OPa,OPb,OPc, resp.

A'B'C' = the triangle bounded by the radical axes of ((O),(X1)),((O),(X2)),((O),(X3))

Conjecture:
The triangles A'B'C', X1X2X3 are perspective.

Figure:
http://anthrakitis.blogspot.gr/2013/02/reflecting-pedal-circle.html

Antreas

[APH]
>
> 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???
• Let HaHbHc be the orthic triangle of ABC, (N1),(N2),(N3) the reflections of the NPC (N) in the sidelines HbHc, HcHa, HaHb of HaHbHc resp. and and A B C the
Message 2 of 22 , Feb 14
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Let HaHbHc be the orthic triangle of ABC, (N1),(N2),(N3) the
reflections of the NPC (N) in the sidelines HbHc, HcHa, HaHb of
HaHbHc resp. and and A'B'C' the triangle bounded by the radical
axes of ((O),(N1)), ((O),(N2)), ((O),(N3)), resp.

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

aph

[APH]
> 2. Let HaHbHc be the orthic triangle, (N1),(N2),(N3) the reflections
> of the NPC (N) in the altitudes HHa,HHb,HHc,
> resp. and and A'B'C' the triangle bounded by the radical axes of
> ((O),(N1)), ((O),(N2)), ((O),(N3)), resp.
>
> Are the triangles HaHbHc, A'B'C' perspective ?
• Dear Antreas, The triangles ABC, A B C are perspective. Perspector: (Conway notations) (SA^2-3S^2)(S^2-SB^2)(S^2-SC^2))/SA: ... : ... Best regards. Angel M.
Message 3 of 22 , Feb 14
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Dear Antreas,

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

Perspector: (Conway notations)

(SA^2-3S^2)(S^2-SB^2)(S^2-SC^2))/SA: ... : ...

Best regards.
Angel M.

--- In Hyacinthos@yahoogroups.com, "Antreas" wrote:
>
> Let HaHbHc be the orthic triangle of ABC, (N1),(N2),(N3) the
> reflections of the NPC (N) in the sidelines HbHc, HcHa, HaHb of
> HaHbHc resp. and and A'B'C' the triangle bounded by the radical
> axes of ((O),(N1)), ((O),(N2)), ((O),(N3)), resp.
>
> Are the triangles ABC, A'B'C' perspective ?
>
> aph
• I am not sure If I have already posted this: Let ABC be a triangle, (N1),(N2),(N3) the reflections of (N)[=NPC] in OA,OB,OC, resp. and A B C the triangle
Message 4 of 22 , Feb 20
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I am not sure If I have already posted this:

Let ABC be a triangle, (N1),(N2),(N3) the reflections of
(N)[=NPC] in OA,OB,OC, resp. and A'B'C' the triangle bounded
by the radical axes of ((O),(N1)),((O),(N2)),((O),(N3)).

Are N1N2N3, A'B'C' perspective?

APH
• One more.... HaHbHc = the orthic triangle. (N1) = the circle (Ha, HaN) ie the circle with center Ha and radius HaN =R/2 Similarly (N2),(N3) A B C = the
Message 5 of 22 , Feb 20
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One more....

HaHbHc = the orthic triangle.
(N1) = the circle (Ha, HaN) ie the circle with center Ha and radius HaN =R/2
Similarly (N2),(N3)

A'B'C' = the triangle bounded by the radical axes of
((O),(N1)),((O),(N2)),((O),(N3)).

Are the triangles HaHbHc, N1N2N3 perspective?

aph

On Wed, Feb 20, 2013 at 1:29 PM, Antreas <anopolis72@...> wrote:

> **
>
>
> I am not sure If I have already posted this:
>
> Let ABC be a triangle, (N1),(N2),(N3) the reflections of
> (N)[=NPC] in OA,OB,OC, resp. and A'B'C' the triangle bounded
> by the radical axes of ((O),(N1)),((O),(N2)),((O),(N3)).
>
>
> Are N1N2N3, A'B'C' perspective?
>
> APH
>
> __
>

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