[APH]
> Let ABC be a triangle, P = (x:y:z) a point and A'B'C'
> the pedal triangle of P.
>
> Denote:
>
> A* := (The Reflection of BC in BP) /\ (The Reflection of BC in CP)
>
> B* := (The Reflection of CA in CP) /\ (The Reflection of CA in AP)
>
> C* := (The Reflection of AB in AP) /\ (The Reflection of AB in BP)
>
> [The triangles A*BC, B*CA, C*AB share the same incenter P]
>
> Oa := The Circumcenter of A*BC
> Ob := The Circumcenter of B*CA
> Oc := The Circumcenter of C*AB
>
> P* := The Point of Concurrence of the Circumcircles
> of A*BC, B*CA, C*AB
> [We have seen recently this point in Hyacinthos]
>
> La := The Reflection of P*Oa in B'C'
>
> Lb := The Reflection of P*Ob in C'A'
>
> Lc := The Reflection of P*Oc in A'B'.
>
> The Triangles ABC, Triangle bounded by (La,Lb,Lc)
> are parallelogic.
>
> Parallelogic Centers?
> (one center lies on the circumcircle of ABC)

Francisco told me it is not true in general.

However, it seems it is true for P = O

For P = H, it seems that La,Lb,Lc are concurrent.


Antreas