$\begin{array}{l}
\left. \begin{array}{l}
{\rm{CK = EA}}\\
\frac{{{\rm B}{\rm{D}}}}{{{\rm{BE}}}} = \frac{{{\rm{EA}}}}{{{\rm{EC}}}}
\end{array} \right\}\mathop {}\nolimits_{}^{} \Rightarrow \mathop {}\nolimits_{}^{} \left\{ \begin{array}{l}
\frac{{{\rm B}{\rm{D}}}}{{{\rm{BE}}}} = \frac{{{\rm{C}}{\rm K}}}{{{\rm{CE}}}}\\
{\rm{tr}}{\rm{.CKD = tr}}{\rm{.AED}}
\end{array} \right.\mathop {}\nolimits_{}^{} \Rightarrow \\
\\
\left\{ \begin{array}{l}
{\rm K}{\rm{D//CB}}\\
{\rm{D}}{\rm K} = {\rm{D}}{\rm E}
\end{array} \right.\mathop {}\nolimits_{}^{} \Rightarrow \mathop {}\nolimits_{}^{} {\rm B}\widehat {\rm{C}}{\rm E} = {\rm B}\widehat {\rm E}{\rm{C}}\mathop {}\nolimits_{}^{} \Rightarrow \mathop {}\nolimits_{}^{} {\rm{BC = BE}}
\end{array}$
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