Question 84
In triangle $ABC$, altitudes $AD$, $BE$, and $CF$ meet at $H$. Line $EF$ and the perpendicular bisector of $HD$ intersect at point $P$. Point $N$ is the center of the nine-point circle of triangle $ABC$. Point $L$ is on the circumcircle of the triangle such that $\angle PLN = 90^\circ$ and points $A$, $L$ are on opposite sides of line $PN$. Prove that the quadrilateral $ANDL$ is cyclic.