Đáp án:

OA=d=18cm

A'B'=0,5cm

Giải thích các bước giải:

\(\begin{array}{*{20}{l}}
{b.}\\
{\Delta OA'B'\sim\Delta OAB}\\
{ \Rightarrow \dfrac{{A'B'}}{{AB}} = \dfrac{{OA'}}{{OA}} = \dfrac{{d'}}{d}(1)}\\
{\Delta A'B'F'\sim\Delta OIF'}\\
{{\rm{\;}} \Rightarrow \dfrac{{A'B'}}{{OI}} = \dfrac{{AF'}}{{OF'}} \Rightarrow \dfrac{{A'B'}}{{AB}} = \dfrac{{OA' - OF'}}{{OF'}} = \dfrac{{d' - f}}{f}(2)}\\
{(1),(2) \Rightarrow \dfrac{{d'}}{d} = \dfrac{{d' - f}}{f} \Rightarrow \dfrac{1}{f} = \dfrac{1}{d} + \dfrac{1}{{d'}}}\\
{ \Rightarrow \dfrac{1}{{12}} = \dfrac{1}{{36}} + \dfrac{1}{{d'}} \Rightarrow d' = 18cm}
\end{array}\)

\(\dfrac{{A'B'}}{{AB}} = \dfrac{{d'}}{d} \Rightarrow A'B' = \dfrac{{d'.AB}}{d} = \dfrac{{18.1}}{{36}} = 0,5cm\)