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把上面的向量法,提炼与改进一下有:(注:即便用向量求E分BM,D分BA等线段的比值,亦有很多方式,楼上仅供参考)
如将公式\eqref{teq03}全部加为红色
\begin{align}
\vv {CE}&=\dfrac 45 \vv {CM}+\dfrac 15 \vv {CB}\\
\vv {CD}&=\dfrac 23 \vv {CA}+\dfrac 13 \vv {CB}\\
\vv {MD}&=-\dfrac 13 \vv {MC}+\dfrac 13 \vv {CB}\label{teq03}\\
\Rightarrow \vv {MD}^2&=\dfrac 59 \vv {MC}^2\\
\vv {MB}&=\vv {MC}+\vv {CB}\tag{4}\label{eq04}\\
\Rightarrow \vv {MB}^2&=5 \vv {MC}^2\\
\therefore MD^2&=\dfrac 19 MB^2\\[2em]
\Rightarrow 3MD&=MB
\end{align} |
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