\(a))\Delta ABC:\)
\(\dfrac{AM}{AB}=\dfrac{AN}{AC}\left(do\dfrac{4}{12}=\dfrac{5}{15}\right).\\ \Rightarrow MN//BC\left(Talet\right).\)
\(b))\Delta ABC:MN//BC\left(cmt\right).\\ \Rightarrow\dfrac{MN}{BC}=\dfrac{AM}{AB}\left(Talet\right).\\ \Rightarrow MN=\dfrac{AM.BC}{AB}=\dfrac{4.21}{12}=7\left(cm\right).\)