Problem

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

Tags: angle bisector, geometry



Given a convex quadrilateral $ABCD$, such that $OA = \frac{OB \cdot OD}{OC + CD}$ where $O$ is the intersection of the two diagonals. The circumcircle of triangle $ABC$ intersects $BD$ at point $Q$. Prove that $CQ$ bisects $\angle ACD$