Inscribed quadrilateral

[ins-]

Quadrilateral $ABCD$ is inscribed in a circle $k$. On $k$ is chosen a point $P$. $K$, $L$, $M$, $N$ are feets of the perpendiculars drawn from $P$ to the lines $AB$, $CD$, $AD$, $BC$ respectively. Prove that $PK.PL=PM.PN$.

(Оффтоп)

It is a very easy problem but it is a beautiful fact.