Some problems of seven circle 3

Let six points A,B,C,A', B', C' lie on a circle. B'C' meet AB,AC at Ac,Ab respectively. B'A' meets CA,CB at Cb,Ca reslpectively. A'B' meets BA,BC at Bc,Ba respectively.Construct radical axis of six circles (AAbAc), (B'AbCb), (CCbCa), (A'CaCb), (BBcBa), (C'AcBa) and (O). Intesection of the radical axis are $D,E,F,G,H,I$ and $Q,R,S,T,U,V$ show in the figure. Prove that a- $D,E,F,G,H,I$ lie on a conic; and $Q,R,S,T,U,V$ lie on a conic b- six lie EH,FI,GD,RU,SV,TQ are concurrent

 

Đào Thanh Oai

 
Resource Type
Activity
Tags
circle  collinear  concyclic  cyclic  dao  midpoints  oai  perpendicular  quadrilateral  seven  tangential thanh thebault theorem triangle Show More…
Target Group (Age)
19+
Language
English (United Kingdom)
 
 
GeoGebra version
4.4
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