c,
$AE\subset (SAC)$
Trong $(ABCD)$, $AC\cap BD=O$
Mà $AC\subset (SAC)$, $BD\subset (SBD)$
$\Rightarrow (SAC)\cap (SBD)=SO$
$SO\cap AE=I$
$\Rightarrow AE\cap (SBD)=I$
Có $AB=\dfrac{3}{2}CD\Leftrightarrow \dfrac{CD}{AB}=\dfrac{2}{3}$
$AB//CD\Rightarrow \dfrac{OC}{OA}=\dfrac{CD}{AB}=\dfrac{2}{3}$ (theo Talet)
Áp dụng Menelaus với $\Delta ACE$, cát tuyến $SIO$:
$\dfrac{SE}{SC}.\dfrac{IA}{IE}.\dfrac{OC}{OA}=1$
$\Rightarrow \dfrac{3}{5}.\dfrac{IA}{IE}.\dfrac{2}{3}=1$
$\Leftrightarrow \dfrac{IA}{IE}=\dfrac{5}{2}$
