HYACINTHOS 26078

[Antreas P. Hatzipolakis]:

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

Denote:

 

Ab, Ac = the orthogonal projections of A' on BH, CH, resp.

La = the Euler line of A'AbAc. Similarly Lb, Lc.

A*B*C* = the triangle bounded by La,Lb,Lc.

ABC, A*B*C* are parallelogic.

 

 

[Peter Moses]:

 

Hi Antreas,

 

More complete details ....

 

a^2 (a^8-a^6 b^2-3 a^4 b^4+5 a^2 b^6-2 b^8-a^6 c^2+11 a^4 b^2 c^2-7 a^2 b^4 c^2-3 b^6 c^2-3 a^4 c^4-7 a^2 b^2 c^4+10 b^4 c^4+5 a^2 c^6-3 b^2 c^6-2 c^8):: 

on lines {{3,6030},{20,2888},{22,10606},{26,11468},{30,74},{64,394},{110,2071},{146,1568},{185,1994},{378,5012},{539,12317},{1154,10620},{1204,3146},{1498,11449},{1593,5422},{1597,5640},{1614,11250},{2070,12041},{2777,3153},{2781,11416},{2935,12270},{3060,10605},{3098,11180},{3426,10546},{3448,13399},{3520,10575},{3524,4550},{3529,7689},{3543,11438},{3839,10545},{5189,10990},{5889,12085},{5894,12225},{5897,6080},{6241,12084},{6644,11455},{6800,11410},{9730,12834},{10060,11446},{10298,11204},{11064,12379},{11441,13093}}.

Reflection of X(i) in X(j) for these {i,j}: {{110,2071},{146,1568},{2070, 12041},{3448,13399}}.

5 X[74] - 2 X[3581], X[5189] + 2 X[10990].

Reflection of X(i) in X(j) for these {i,j}: {{110,2071},{146,1568},{2070, 12041},{3448,13399}}.

{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (20,3357,11440),(20,11440, 7691),(22,10606,11454),(64, 11413,12111).

X(775)-anticomplementary conjugate of X(146).

crosssum of X(1562) and X(9409).

Searches: {19. 2144490890056618484880279524, 19. 2306290337569818811704635838,- 18. 5410551979269138216095164336}.

 

Best regards,

Peter Moses.