Ta có:$∆$OAB ~$∆$OA’B’

=> $\frac{OA\text{'}}{OA}=\frac{A\text{'}B\text{'}}{AB}$  (1)

Ta lại có:$∆$F’OI ~$∆$F’A’B’

=> $\frac{A\text{'}B\text{'}}{OI}=\frac{F\text{'}A\text{'}}{F\text{'}O}$ 

hay $\frac{A\text{'}B\text{'}}{AB}=\frac{OA\text{'}-OF\text{'}}{OF\text{'}}$ (2)

Từ (1) và (2) suy ra: $\frac{OA\text{'}}{OA}=\frac{OA\text{'}-OF\text{'}}{OF\text{'}}$ (3)

Thay OA’ = 32cm, OF’ = 24cm vào (3) ta được: OA^’ = 96cm.             

Từ (1) suy ra:

$$\begin{gathered} A\text{'}B\text{'}=\frac{OA\text{'}}{OA}\cdot AB \\ A\text{'}B\text{'}=\frac{96}{32}\cdot 2=6cm \end{gathered}$$