[tex]\bf BC=2BA\\ BE = 2BD \end{cases} \cfrac{BC}{BE}=\cfrac{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~BA}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~BD}\implies \cfrac{BC}{BE}=\cfrac{BA}{BD}\impliedby \begin{array}{llll} \textit{equal ratio of sides}\\ \textit{similar triangles} \end{array}[/tex]
