#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
*** 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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