[Tran Quang Hung]:
Let ABC be a triangle with incenter I.
Dear Tran Quang Hung.
The isogonal conjugate of I wrt Ka'Kb'Kc is
(r - 4 R) R X(1) + 2 r (2 R - r) X(O) =
(a^2 (a^5-a^4 (b+c)+a^3 (-2 b^2+7 b c-2 c^2)+a (b-c)^2 (b^2-5 b c+c^2)-(b-c)^2 (b^3+c^3)+a^2 (2 b^3-b^2 c-b c^2+2 c^3)) : ...: ...)
on lines {1,3}
With (6-9-13)-search numbers (0.302697058407055, 0.544521460664727, 3.12398175141324)
Angel Montesdeoca
Ka,Kb,Kc are the centers of mixtiliner incircles of ABC at the vertex A,B,C, reps.
Ka',Kb',Kc' are isogonal conjugate points of Ka,Kb,Kc wrt ABC, reps.
Then isogonal conjugate of I wrt Ka'Kb'Kc' lies on OI line of ABC.
Which is this point ?
.
[Angel Montesdeoca]:
Dear Tran Quang Hung.
The isogonal conjugate of I wrt Ka'Kb'Kc is
(r - 4 R) R X(1) + 2 r (2 R - r) X(O) =
(a^2 (a^5-a^4 (b+c)+a^3 (-2 b^2+7 b c-2 c^2)+a (b-c)^2 (b^2-5 b c+c^2)-(b-c)^2 (b^3+c^3)+a^2 (2 b^3-b^2 c-b c^2+2 c^3)) : ...: ...)
on lines {1,3}
With (6-9-13)-search numbers (0.302697058407055, 0.544521460664727, 3.12398175141324)
Angel Montesdeoca
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