33-120 Pascal points lie on circumcircle

When I found way ageneralization problem at here Yet Another Seven Circles Theorem, I think may be it is true if P is a line? I check and found problems following. I named problems is 120 Pascal points lie on circumcircle.

Let cyclic hexagon .  meets  at ,  meets  at . meets  at  . Three circle  concurrent at a point lie on circumcircle. Similar we have three circle concurrent at a point  lie on the circle (ABCDEF). With a cyclic hexagon, we have 60 Pascal's line. Then we have 120 Pascal point in configuration