a) Gọi $AC\cap MN=G$
Do MN//AB//DC theo định lý Ta-let ta có:
$\dfrac{NB}{NC}=\dfrac{MA}{MD}=\dfrac{1}{3}$
b) Do MG//DC $\Rightarrow \dfrac{AM}{AD}=\dfrac{MG}{DC}=\dfrac{1}{4}$
$MG=\dfrac{DC}{3}=5$
Do $GN//AB\Rightarrow \dfrac{CN}{CB}=\dfrac{GN}{AB}=\dfrac{3}{4}$
suy ra $GN=\dfrac{3AB}{4}=6$
$\Rightarrow MN=GM+GN=11$ cm