We have given square $ABCD$. Line $p$ through point $A$ intersects side $DC$ in point $Q$. Let point $M$ be on side $AB$ and point $N$ on side $BC$, such that line $MN$ is parallel to $p$.
Where should we place point $M$ to maximize the area of quadrilateral $AMNQ$?
I solved given problem analytical, but now I have to solve it geometrically and I have no idea how.
