Solution by Francisco Javier García Capitán
FOUR POINTS ON THE EULER LINE
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Παρασκευή 26 Ιουνίου 2026
FOUR POINTS ON THE EULER LINE
Problem by Antreas Hatzipolakis
Solution by Francisco Javier García Capitán
FOUR POINTS ON THE EULER LINE
Solution by Francisco Javier García Capitán
FOUR POINTS ON THE EULER LINE
Δευτέρα 1 Ιουνίου 2026
CYCLOLOGIC
Let ABC be a triangle
Denote
1. Oa, Ob, Oc = the circumcenters of HBC, HCA, HAB, resp.
ABC, OaObOc are cyclologic, since Oa, Ob, Oc are the reflections of O in BC,CA,AB, resp.
Cyclologic center (OaObOc, ABC) = antigonal conjugate of O = X(265)
2. Sa, Sb, Sc = the X(54) of HBC, HCA, HAB, resp.
ABC,SaSbSc are cyclologic
Cyclologic centers?
Denote
1. Oa, Ob, Oc = the circumcenters of HBC, HCA, HAB, resp.
ABC, OaObOc are cyclologic, since Oa, Ob, Oc are the reflections of O in BC,CA,AB, resp.
Cyclologic center (OaObOc, ABC) = antigonal conjugate of O = X(265)
2. Sa, Sb, Sc = the X(54) of HBC, HCA, HAB, resp.
ABC,SaSbSc are cyclologic
Cyclologic centers?
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