ANOPOLIS 301

Antreas P. Hatzipolakis

[APH]

Let ABC be a triangle and A'B'C' the cevian triangle I.

Denote:

Ab,Ac = the reflections of A' in BB', CC', resp.

Bc,Ba = the reflections of B' in CC', AA', resp.

Ca,Cb = the reflections of C' in AA', BB', resp.

L,La,Lb,Lc = the Euler lines of ABC, AAbAc, BBcBa, CCaCb, resp.

Ma, Mb, Mc = the reflections of La, Lb, Lc in AA', BB', CC', resp.

1. L, La, Lb, Lc are concurrent (parallel)

2. Ma, Mb, Mc are concurrent.
Point of concurrence?

 

[Angel Montesdeoca]:

**** The lines Ma, Mb, Mc intersect at:
( a(a^9
- a^8(b+c)
- a^7(b-c)^2
+ a^6(2b^3-b^2c-b*c^2+2c^3)
- a^5(3b^4+b^3c-7b^2c^2+b*c^3+3c^4)
+ 4a^4b*c(b-c)^2(b+c)
+ a^3(b^2-c^2)^2(5b^2-4b*c+5c^2)
- a^2(b-c)^2(2b^5+5b^4c+b^3c^2+b^2c^3+5b*c^4+2c^5)
- a(b^2-c^2)^2(2b^4-3b^3c+5b^2c^2-3b*c^3+2c^4)
+ (b-c)^4(b+c)^3(b^2+c^2)) : ... : ...),

with (6-9-13)-search number: 5.63864638926896001044233914


Figure: http://amontes.webs.ull.es/otrashtm/HechosGeometricos.htm#HG250513

Angel Montesdeoca