Câu 1: 

Ta có: 

\(\begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} = \dfrac{{15}}{{OA'}}\\
\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF'}}{{OA' + OF'}} = \dfrac{{20}}{{OA' + 20}}\\
 \Rightarrow \dfrac{{15}}{{OA'}} = \dfrac{{20}}{{OA' + 20}} \Rightarrow OA' = 60cm\\
 \Rightarrow \dfrac{{AB}}{{A'B'}} = \dfrac{{15}}{{60}} = \dfrac{1}{4} \Rightarrow A'B' = 20cm
\end{array}\)

Câu 2: 

Ta có: 

\(\begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} = \dfrac{{25}}{{OA'}}\\
\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF'}}{{OA' - OF'}} = \dfrac{{15}}{{OA' - 15}}\\
 \Rightarrow \dfrac{{25}}{{OA'}} = \dfrac{{15}}{{OA' - 15}} \Rightarrow OA' = 37,5cm\\
 \Rightarrow \dfrac{{AB}}{{A'B'}} = \dfrac{2}{3} \Rightarrow A'B' = 7,5cm
\end{array}\)