Đáp án:

a) \(A'B' = 30cm\)

b) \(A'B' = \dfrac{{30}}{7}cm\)

Giải thích các bước giải:

a) Ta có:

\(\begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} = \dfrac{{16}}{{OA'}}\\
\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF'}}{{OA' - OF'}} = \dfrac{{12}}{{OA' - 12}}\\
 \Rightarrow \dfrac{{16}}{{OA'}} = \dfrac{{12}}{{OA' - 12}} \Rightarrow OA' = 48cm\\
 \Rightarrow A'B' = 30cm
\end{array}\)

b) Ta có:

\(\begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} = \dfrac{{16}}{{OA'}}\\
\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF}}{{ - OA' + OF}} = \dfrac{{12}}{{12 - OA'}}\\
 \Rightarrow \dfrac{{16}}{{OA'}} = \dfrac{{12}}{{12 - OA'}} \Rightarrow OA' = \dfrac{{48}}{7}cm\\
 \Rightarrow A'B' = \dfrac{{30}}{7}cm
\end{array}\)