Giải thích các bước giải:
Gọi $BC\cap AB=E$
$\to \dfrac{BE}{DC}=\dfrac{EM}{MD}=\dfrac{BM}{MC}=\dfrac{1}{2}$
$\to BE=\dfrac 12 DC, EM=\dfrac 12 MD$
$\to DM=\dfrac{2}{3}DE$
Mà $DN=\dfrac 12MN\to DN=\dfrac 13DM=\dfrac 13.\dfrac 23DE=\dfrac 29DE$
$\to \dfrac{DN}{DE}=\dfrac 29$
$\to \dfrac{DN}{DE-DN}=\dfrac{2}{9-2}$
$\to \dfrac{DN}{NE}=\dfrac{2}{7}$
$\to \dfrac{DK}{AE}=\dfrac{DN}{NE}=\dfrac 27$
$\to \dfrac{DK}{AB+BE}=\dfrac 27$
$\to \dfrac{DK}{CD+\dfrac 12 DC}=\dfrac 27$
$\to \dfrac{DK}{\dfrac 32 DC}=\dfrac 27$
$\to \dfrac{DK}{DC}=\dfrac 37$
$\to \dfrac{DK}{DC-DK}=\dfrac 3{7-3}$
$\to \dfrac{DK}{CK}=\dfrac 3{4}$
