Πέμπτη 31 Οκτωβρίου 2019

ADGEOM 4790 * ADGEOM 4791

#4790

Dear Geometers,

Let Ge be Gergonne point of ABC. DEF cevian triangle of Ge. K1,K2,K3 symmedian points of GeEF, GeFD, GeDE respectively. AK1, BK2, CK3 concur. (Not listed in ETC).

Best regards

Abdilkadir Altıntaş, Emirdağ, Türkiye

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#4791

[Abdilkadir Altıntas]:

Let Ge be Gergonne point of ABC. DEF cevian triangle of Ge. K1,K2,K3 symmedian points of GeEF, GeFD, GeDE respectively. AK1, BK2, CK3 concur. (Not listed in ETC).

*** AK1, BK2, CK3 concur  at W = 3s^2 X(1) - 4(r+4R)^2 X(7),

 with first barycentric coordinate:  (a+b-c) (a-b+c) (a^2-5 a (b+c)+4 (b-c)^2).

W lies on lines X(i)X(j) for these {i, j}:  {1,7}, {948,4031}, {1358,18421}, {4495,7195}, {4859,7960}.

 (6 - 9 - 13) - search numbers  of W: (0.577822777754951, 0.636155362937831, 2.93356179475590).

Angel Montesdeoca
 

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