CAT 2023 Slot 1 Solved Paper

Given $\mathit{A}\mathit{B}\mathit{C}\mathit{D}$ is a cyclic quadrilateral.
Angle ADB = Angle ACB (Angle subtended by chord on the same side of arc)
Angle DAC = Angle DBC (Angle subtended by chord on the same side of arc)
$\Rightarrow$ Triangles $\mathrm{AED}$ and $\mathrm{BEC}$ are similar triangles
Similarly triangles $\mathit{A}\mathit{E}\mathit{B}$ and $\mathit{D}\mathit{E}\mathit{C}$ are also similar using $\mathit{A}\mathit{A}$ similarity property.
Now, given that $\mathit{A}\mathit{B}:\mathit{C}\mathit{D}=2:1$ and $\mathit{B}\mathit{C}:\mathit{A}\mathit{D}=5:4$
$\mathrm{AE}∕\mathrm{BE}=\mathrm{AD}∕\mathrm{BC}=4∕5$ (Similar Triangles $\mathrm{AED}$ and $\mathrm{BEC}$ )
$\mathit{B}\mathit{E}∕\mathit{C}\mathit{E}=\mathit{A}\mathit{B}∕\mathit{C}\mathit{D}=2∕1$ (Similar Triangles AEB and DEC)
Multiplying both, we get $\mathrm{AE}∕\mathrm{CE}=8∕5$.