Eight circles tangent and concurrent at midpoint of NO

Let two triangle ABC and A1B1C1. Such that AB//A1B1,BC//B1C1; AC//A1C1. B1C1 meet AB,AC at Ac,Ab. Define Bc,Ba,Ca,Cb cyclically. Denote O,O1 is center of circumcircle (ABC) and (A1B1C1). Denote Oa is center of circle (AAbAc), Define Ob,Oc cyclically. Oa1 is center of (A1BaCa). Define Ob1,Oc1 cyclically. Prove that: 1-(C1BcAc) tangent with three circle (A1B1C1), (AAcAb), (BBcBa) 2-OaOa1, ObOb1,OcOc1 are concurrent at D and D is midpoints of OO1; when A1B1C1 are median triangle then D is midpoints of center Nine point circle and Circumcircle

 

Đào Thanh Oai

 
Resource Type
Activity
Tags
carnot  ceva  circle  circumcirle  collinear  cyclic  incircle  melelaus  newton  nine  point quadrilateral relative tangential thebault Show More…
Target Group (Age)
19+
Language
English (United Kingdom)
 
 
GeoGebra version
4.4
Views
987
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