Gọi $M$ là trung điểm $BC$
$\Rightarrow ME$ là đường trung bình
$\Rightarrow ME//AB; \, ME= \dfrac{1}{2}AB$
Ta được:
$\dfrac{FM}{FB} = \dfrac{EM}{BD} = \dfrac{\dfrac{1}{2}AB}{\dfrac{3}{4}AB} = \dfrac{2}{3}$ (Theo Thales)
$\Rightarrow \dfrac{FM}{FB} = \dfrac{2}{3}$
$\Rightarrow \dfrac{FM}{MB} = 2$
$\Rightarrow FM = 2BM$
$\Rightarrow FM = 2CM$
$\Rightarrow FC = FM - CM = 2CM - CM = CM$
$\Rightarrow FC = \dfrac{1}{2}BC$
