Problem

Source: Turkey TST 1999 - P2

Tags: geometry, geometric transformation, reflection, ratio, circumcircle, cyclic quadrilateral, angle bisector



Let $L$ and $N$ be the mid-points of the diagonals $[AC]$ and $[BD]$ of the cyclic quadrilateral $ABCD$, respectively. If $BD$ is the bisector of the angle $ANC$, then prove that $AC$ is the bisector of the angle $BLD$.