Đáp án:

b) \(A'B' = \dfrac{2}{3}cm\)

c) \(OA = 3cm\)

Giải thích các bước giải:

a) Hình vẽ

b) Ta có: 

\(\begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} = \dfrac{6}{{OA'}}\\
\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF}}{{ - OA' + OF}} = \dfrac{3}{{3 - OA'}}\\
 \Rightarrow \dfrac{6}{{OA'}} = \dfrac{3}{{3 - OA'}} \Rightarrow OA' = 2cm\\
 \Rightarrow \dfrac{{AB}}{{A'B'}} = 3 \Rightarrow A'B' = \dfrac{2}{3}cm
\end{array}\)

c) Ta có: 

\(\begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} = 2 \Rightarrow OA = 2.OA'\\
\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF}}{{ - OA' + OF}} = \dfrac{3}{{3 - OA'}}\\
 \Rightarrow 2 = \dfrac{3}{{3 - OA'}} \Rightarrow OA' = 1,5cm\\
 \Rightarrow OA = 3cm
\end{array}\)