Bài 1:

a) hình vẽ

b) Ta có:

\(\begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} = \dfrac{8}{{OA'}}\\
\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF'}}{{OA' + OF'}} = \dfrac{{12}}{{OA' + 12}}\\
 \Rightarrow \dfrac{8}{{OA'}} = \dfrac{{12}}{{OA' + 12}} \Rightarrow OA' = 24cm\\
 \Rightarrow \dfrac{{AB}}{{A'B'}} = \dfrac{1}{3} \Rightarrow A'B' = 6cm
\end{array}\)

Bài 2:

Ta có:

\(\left\{ \begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} = \dfrac{3}{9} = \dfrac{1}{3}\\
OA' - OA = 10
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
OA' = 15cm\\
OA = 5cm
\end{array} \right.\)

Mà:

\(\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF'}}{{OA' + OF'}} = \dfrac{f}{{15 + 12}} = \dfrac{1}{3} \Rightarrow f = 9cm\)