Dear Dr. Paul Yiu, and all Geometer

I proposed a generalization of Simson line theorem as follow:

Let ABC be a triangle, let a line (l) through circumecenter and a point P lie on circumcircle.

Let AP,BP,CP meets (l) at A_P, B_P, C_P.

Denote A0,B0,C0 are projection (mean perpendicular foot) of A_P, B_P, C_P to BC,CA,AB.

Show that: A0,B0,C0 are collinear?

When (l) pass through P, this line is Simson line.



Best regards
Sincerely
Dao Thanh Oai