Consider the following situation. $BC=24$ $cm$ and $M,N$ are the midpoints of $AC$ and $DE$, respectively. I should find $AD$ and $BM:BN$.
As you see, in the text of the problem, we do not have $\angle BAC=\angle BED$, but it seems like it is given from the drawing. If it is, $\triangle ACB \sim \triangle EDB$. Therefore, $\dfrac{BC}{BD}=\dfrac{AB}{BE}$ and $\dfrac{BM}{BN}=\dfrac{BC}{BD}$. The problem is solved. Can we show that $\angle BAC=\angle BED$ with the given information from the text?