chọn hệ trục Oxy, O trung với D
ta có A(0;a) ,B(a;a) ,C(a;0) ,D(0;0) ,M(a;\(\frac{a}{2}\)), N(x;y)
\(\overrightarrow{AM}\left(a;\frac{a}{2}-a\right)\)
\(\overrightarrow{CN}\left(x-a;y\right),\overrightarrow{ND}\left(-x;-y\right)\)
lai co NC=2ND <=> CN=2ND <=> \(\overrightarrow{CN}=2\overrightarrow{ND}\)
\(\Leftrightarrow\left\{\begin{matrix}x-a=-2x\\-y=-2y\end{matrix}\right.\Leftrightarrow\left\{\begin{matrix}x=\frac{a}{3}\\y=0\end{matrix}\right.\)
=> N(a/3 ; 0)
\(\overrightarrow{AN}\left(\frac{a}{3};-a\right)\)
ta co \(\overrightarrow{AM}\cdot\overrightarrow{AN}=a\cdot\frac{a}{3}+\left(\frac{a}{2}-a\right)\cdot\left(-a\right)\)
=\(\frac{5a^2}{6}\)
