17836Re: A configuration
- Jun 3, 2009[APH]
> > Let ABC be a triangle and A'B'C' the orthic triangle.[JPE]
> > Denote:
> > Lab := The Reflection of BB' in AA'
> > Mab := The Parallel to Lab through C.
> > Lac := The Reflection of CC' in AA'
> > Mac := The Parallel to Lac through B.
> > A* := Mab /\ Mac
> > Similarly B*,C*.
> > 5. Let Na, Nb, Nc be the NPC centers of the triangles
> > A*BC, B*CA, C*AB, resp.
> > The triangles ABC, NaNbNc are perspective.
> > Perspector?
> If U=X(54) is the isogonal conjugate of N andEQUIVALENTLY:
> V=X(140)=midpoint(ON), the perspector is P=-3U+4V
> (this point lies on the line through the Lemoine point and
> the two Corsican Imperial points)
Let ABC be a triangle, A1B1C1 the circumcevian triangle
of H, and M1M2M3 the Medial triangle of ABC.
Let A*,B*,C* be the reflections
of A1,B1,C1 in M1,M2,M3, resp. (symmetric points)
Let Na, Nb, Nc be the NPC centers of the triangles
A*BC, B*CA, C*AB, resp.
The triangles ABC, NaNbNc are perspective.
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