## Tangent NPCs / Incircles

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• 1. The NPC(antipedal_of_O) is tangent to Incircle(antipedal_of_O) = = Circumcircle(ABC) = NPC(antipedal_of_H) [Feuerbach point of antipedal_of_O] 2. The
Message 1 of 2 , Mar 19, 2013
1. The NPC(antipedal_of_O) is tangent to Incircle(antipedal_of_O) =
= Circumcircle(ABC) = NPC(antipedal_of_H)
[Feuerbach point of antipedal_of_O]

2. The Incircle(antipedal_of_O) = Circumcircle(ABC) =
= NPC(antipedal_of_H) is tangent to Incircle(antipedal_of_H)
[Feuerbach point of antipedal_of_H]

Generalizations:

Let ABC be a triangle, P,P* two isogonal conjugate points
and A'B'C',A"B"C" the antipedal triangles of P,P*, resp.

Which is the locus of P such that:

1. the NPC(A'B'C') is tangent to NPC(A"B"C")

2. the Incircle(A'B'C') is tangent to Icircle(A"B"C")

McCay cubic + (O) + Linf + ???????????????????????????

APH
• I get K003 (McCay cubic) and K024 for tangents NPCs.
Message 2 of 2 , Mar 19, 2013
I get K003 (McCay cubic) and K024 for tangents NPCs.

--- In Hyacinthos@yahoogroups.com, "Antreas" <anopolis72@...> wrote:
>
> 1. The NPC(antipedal_of_O) is tangent to Incircle(antipedal_of_O) =
> = Circumcircle(ABC) = NPC(antipedal_of_H)
> [Feuerbach point of antipedal_of_O]
>
> 2. The Incircle(antipedal_of_O) = Circumcircle(ABC) =
> = NPC(antipedal_of_H) is tangent to Incircle(antipedal_of_H)
> [Feuerbach point of antipedal_of_H]
>
> Generalizations:
>
> Let ABC be a triangle, P,P* two isogonal conjugate points
> and A'B'C',A"B"C" the antipedal triangles of P,P*, resp.
>
> Which is the locus of P such that:
>
> 1. the NPC(A'B'C') is tangent to NPC(A"B"C")
>
> 2. the Incircle(A'B'C') is tangent to Icircle(A"B"C")
>
> McCay cubic + (O) + Linf + ???????????????????????????
>
> APH
>
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