HYACINTHOS 28076

Antreas P. Hatzipolakis

 

[APH]:

 

Let ABC be a triangle, P a point and A'B'C' the pedal triangle of P.

 

Let Ab, Ac be the orthogonal projections of A on BI, CI, resp.
Let La be the Euler line of AAbAc. Simillarly Lb, Lc.
(La, Lb, Lc concur at Feuerbach point)

Let  L1, L2, L3 be the reflections of La, Lb, Lc, resp. in PA', PB', PC', resp. 

 
For P = I:
1.  L1, L2, L3  are concurrent (on the OI line), 
2. the parallels to L1, L2, L3 through A', B', C', resp. are concurrent (on the OI line)

3. the parallels to L1, L2, L3 through Ia, Ib, Ic (IaIbIc = excentral triangle), resp. are concurrent (on the OI line)

4. Locus of P such that L1, L2, L3 are concurrent?


[Peter Moses]:


Hi Antreas,

1). X(5048).
2). X(1319).
3). X(484).

4) IN line.

Best regards,
Peter Moses