- Jul 4, 2009[APH]
> Let ABC be a triangle, A'B'C' its medial triangle

It is true and simple, since ABC, A'B'C'

> and P a point.

>

> Let La, Lb, Lc be the reflections of PA', PB', PC'

> in the bisectors AI, BI, CI, resp.

>

> Which is the locus of P such that the triangles

> ABC, Triangle bounded by (La, Lb, Lc) are

> parallelogic ?

>

> It seems the locus is the entire plane.

>

> Parallelogic centers?

are homothetic.

How about if A'B'C' is the orthic triangle?

Which is the locus of P?

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