$\left. \begin{matrix}
O\overset{\vartriangle }{\mathop{M}}\,B\Rightarrow NA\left\| MB\xrightarrow[{}]{Thales}\frac{ON}{OM}=\frac{OA}{OB} \right. \\
O\overset{\vartriangle }{\mathop{M}}\,B\Rightarrow NB\left\| MC\xrightarrow[{}]{Thales} \right.\frac{ON}{OM}=\frac{OB}{OC} \\
\end{matrix} \right\}\Rightarrow \frac{OA}{OB}=\frac{OB}{OC}\Rightarrow \frac{2x-8}{x}=\frac{x}{x+3}\Rightarrow {{x}^{2}}-2x-24=0\Rightarrow (x-6)(x+4)=0$
با توجه به شکل $\Rightarrow AB=OB-OA=6-4=2$