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
