HYACINTHOS 24956

[Antreas P. Hatzipolakis]:

 

Let ABC be a triangle and A'B'C' the pedal triangle of H.

Denote:

Oha, Oga = the reflections of O in HA, GA, resp.

Ohb, Ogb = the reflections of O in HB, GB, resp.

Ohc, Ogc = the reflections of O in HC, GC, resp

Ma, Mb, Mc = the perepbdicular bisectors of OhaOga, OhbOgb, OhcOgc, resp.

A*B*C* = the triangle bounded by Ma,Mb,Mc

The triangles A'B'C', A*B*C* are parallelogic.

The parallellogic center (A'B'C', A*B*C*) lies on the Euler line.

[Peter Moses]:

Hi Antreas,

 

>The parallellogic center (A'B'C', A*B*C*) lies on the Euler line.

X(427).

The parallellogic center ( A*B*C*, A'B'C'), a^6-b^6+b^4 c^2+b^2 c^4-c^6::,
lies on lines {{2,1495},{3,2918},{4,51},{5, 10984},{6,5064},{25,125},{30, 343},{64,6145},{66,1843},...}

 

Best regards,

Peter Moses.