Đáp án:
$\begin{array}{l}
a)DK = DF - KF = 15 - 9 = 6\left( {cm} \right)\\
\Rightarrow \frac{{DK}}{{DF}} = \frac{6}{{15}} = \frac{2}{5}\\
Do:\frac{{DI}}{{DE}} = \frac{4}{{10}} = \frac{2}{5}\\
\Rightarrow \frac{{DI}}{{DE}} = \frac{{DK}}{{DF}}\\
\Rightarrow IK//EF\left( {theo\,Talet} \right)\\
\Rightarrow \widehat {DIK} = \widehat {DEF}\left( {so\,le\,trong} \right)\\
b)Do:IK//EF\\
\Rightarrow \frac{{IK}}{{EF}} = \frac{{DI}}{{DE}} = \frac{2}{5}\\
\Rightarrow EF = IK:\frac{2}{5} = 16:\frac{2}{5} = 40\left( {cm} \right)
\end{array}$
