In a regular hexagon $ABCDEF$ with center $O$, points $M$ and $N$ are the midpoints of the sides $CD$ and $DE$, and $L$ the intersection point of $AM$ and $BN$. Prove that: (a) $ABL$ and $DMLN$ have equal areas; (b) $\angle ALD=\angle OLN=60^\circ$; (c) $\angle OLD=90^\circ$.