Problem

Source: Indonesia INAMO Shortlist 2009 G7 https://artofproblemsolving.com/community/c1101409_

Tags: angle bisector, geometry



Given a convex quadrilateral ABCD, such that OA=OBODOC+CD where O is the intersection of the two diagonals. The circumcircle of triangle ABC intersects BD at point Q. Prove that CQ bisects ACD