Đáp án:
* TH1: 60cm và 2
* TH2: 20cm và 2
Giải thích các bước giải:
* TH1 : 30cm
Ta có:
\(\begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} = \dfrac{{30}}{{OA'}}\\
\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF'}}{{OA' - OF'}} = \dfrac{{20}}{{OA' - 20}}\\
\Rightarrow \dfrac{{30}}{{OA'}} = \dfrac{{20}}{{OA' - 20}} \Rightarrow OA' = 60cm\\
\Rightarrow \dfrac{{AB}}{{A'B'}} = \dfrac{1}{2}
\end{array}\)
* TH2: 10cm:
Ta có:
\(\begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} = \dfrac{{10}}{{OA'}}\\
\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF'}}{{OA' + OF'}} = \dfrac{{20}}{{OA' + 20}}\\
\Rightarrow \dfrac{{10}}{{OA'}} = \dfrac{{20}}{{OA' + 20}} \Rightarrow OA' = 20cm\\
\Rightarrow \dfrac{{AB}}{{A'B'}} = \dfrac{1}{2}
\end{array}\)