Some more facts: *Let I=X(1)-Incenter of ABC. Circle (BIC) intersetcs the AC and AB at Ab, Ac resp. Let GammaA is inversion of line AbAc in the circle (BIC). Oa-center of GammaA. Define Ob,Oc cyclically.
-Oa, Ob, Oc lies on the circle centered at I and passes through O (circumcenter of ABC).
**Let S=X(15)-1st Isodynamic point of ABC. Circle (BSC) intersetcs the AC and AB at Ab, Ac resp. Let GammaA is inversion of line AbAc in the circle (BSC). Oa-center of GammaA. Define Ob,Oc cyclically.
* Oa, Ob, Oc and S lie on the same circle. Orthocenter of OaObOc lies on Euler line of ABC
Some more facts:
ReplyDelete*Let I=X(1)-Incenter of ABC. Circle (BIC) intersetcs the AC and AB at Ab, Ac resp.
Let GammaA is inversion of line AbAc in the circle (BIC). Oa-center of GammaA. Define Ob,Oc cyclically.
-Oa, Ob, Oc lies on the circle centered at I and passes through O (circumcenter of ABC).
**Let S=X(15)-1st Isodynamic point of ABC. Circle (BSC) intersetcs the AC and AB at Ab, Ac resp.
Let GammaA is inversion of line AbAc in the circle (BSC). Oa-center of GammaA. Define Ob,Oc cyclically.
* Oa, Ob, Oc and S lie on the same circle. Orthocenter of OaObOc lies on Euler line of ABC