Question 93
Let $O$ be the intersection point of the diagonals of the convex quadrilateral $ABCD$, with $AO = OC$. Points $P$ and $Q$ are marked on the segments $AO$ and $CO$, respectively, such that $PO = OQ$. Let $N$ be the intersection of $AB$ and $DP$, and $K$ be the intersection of $CD$ and $BQ$.
Prove that the points $N$, $O$ and $K$ are collinear.
Prove that the points $N$, $O$ and $K$ are collinear.