Let's say $AM$ and $AN$ are tangent lines to a circle centered at $O$. $L$ is a point on arc $MN$. Line $ML$ and $NL$ intersect with the line passing $A$ parallel to $MN$, at $P$ and $Q$. If $\angle POQ=45°$, prove that the area of circle $O$ is $2\pi$ times the area of $\triangle OPQ$.
I have discovered that points $ALMQ$ are concyclic, as well as points $ALNP$, but I cannot connect them with the asked area. I believe the problem can be solved using power of a point.