Another orhocenter property

[ins-]

In the acute-angled triangle $ABC$ with orthocenter $H$ and circumcircle $k$ is drawn a line $l$ through $H$ (non-intersecting $AB$). $K$ and $L$ are the intersection points of $k$ and $l$ ($K$ is from the smaller arc $AC$, $L$ is from the smaller arc $BC$). $M$, $N$ and $P$ are the feets of the perpendiculars from the vertices $A$, $B$ and $C$ to $l$, respectively ($M$, $N$, $P$ are internal to $k$). Prove that $PH=|KM-LN|$.

[ins-]

Note that $l$ not intersects the segment AB, but can intersect the line $AB$.

[ins-]

(Оффтоп)

This problem can be solved in at least two different ways. You can see a beautiful solution on the link below:
http://www.artofproblemsolving.com/Foru ... 8&t=506684