HYACINTHOS 26131

[Antrewas P. Hatzipolakis]:

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

Denote:

Ab, Ac = the orthogonal projections of A' on AC, AB, resp.

A2 = A'Ab /\ OC'

A3 = A'Ac /\ OB'.

 

Oa = the circumcenter of A'A2A3. Similarly Ob, Oc.

The centroid of OaObOc lies on the Euler line  ??

[Peter Moses]:


Hi Antreas,

 

>The centroid of OaObOc lies on the Euler line. ??

I get:

4 a^4-3 a^2 b^2+b^4-3 a^2 c^2-6 b^2 c^2+c^4:: 

on lines {{2,6},{5,754},{30,5171} ,{140,7751},{157,9909},{523,11 633},{538,549},{543,8703},{547 ,7775},{632,7764},...}.

Complement X[9766].

Midpoint of X(i) and X(j) for these {i,j}: {{2, 8667}, {9740, 11184}}.

Reflection of X(7775) in X(547).

{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,5306,597),(183,230,141),(38 5,3815,3629),(591,1991,69),(53 06,11168,2),(7610,8667,2),(778 8,8860,2).

Searches: {10.0990064313288782 980611128882,2.955887878401193 74296130169171,-3.066799325291 31424111382817092}.

 

Best regards,

Peter Moses.