Question 61
The diagonal $AC$ of a convex quadrilateral $ABCD$ is the bisector of the angle $\angle DCB$. Let $E$ be the intersection of the side $AB$ and the circumcircle of the triangle $ACD$. Let $F$ be the intersection of the side $AD$ and the circumcircle of the triangle $ABC$. Prove that the segments $AC, DE$ and $BF$ intersect in a point.