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
