On Mon, Mar 1, 2010 at 12:16 AM, Antreas <

anopolis72@...> wrote:

>

>

> Let ABC be a triangle and HaHbHc its orthic triangle.

> Let IaaIabIac, IbaIbbIbc and IcaIcbIcc be the excentral

> triangles of HBC, HCA, HAB, resp.

>

> I think that the Euler lines of the triangles HaIabIac,

> HbIbcIba, HcIcaIcb (and ABC) are concurrent (at the G of ABC).

>

> Generalization?

>

> Locus ? (if HaHbHc is the pedal triangle of a point P).

>

Locus:

Let ABC be a triangle, P a point and PaPbPc the Cevian (or pedal) Triangle

of P.

Let Iab, Iac be the excenters corresponding to the angles

PBC, PCB of the triangle PBC, resp.

Let La be the Euler Line of the triangle PaIabIac.

Similarly the Euler Lines Lb, Lc of the triangles PbIbcIba, PcIcaIcb, resp.

Which is the locus of P such that La,Lb,Lc are concurrent?

Antreas

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