Pinko wrote: Let $ABCD$ be a quadrilateral inscribed in a circle $k$. Let the lines $AC\cap BD=O$, $AD\cap BC=P$, and $AB\cap CD=Q$. Line $QO$ intersects $k$ in points $M$ and $N$. Prove that $PM$ and $PN$ are tangent to $k$. Wait isn't this too well known??? By Brocard we get that $QO$ is the Polar of $P$, So, $PM,PN$ must be tangents to $\odot(ABCD)$.

Pinko wrote: Let $ABCD$ be a quadrilateral inscribed in a circle $k$. Let the lines $AC\cap BD=O$, $AD\cap BC=P$, and $AB\cap CD=Q$. Line $QO$ intersects $k$ in points $M$ and $N$. Prove that $PM$ and $PN$ are tangent to $k$. @above Of course my friend it is well known I do exactly the same thing with @above

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