Hot issues：
This module collects the frequently encountered and difficult problems for reference only.
This module collects the frequently encountered and difficult problems for reference only.
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在$\triangle ABC$中，$\angle ACB=2\angle B$，$BC=2AC$，求证$\angle A=90°$。
如图：
作$\angle C$的平分线交$AB$与$E$点，则$\triangle BCE$为等腰三角形。
作$BC$的中点$D$，连接$DE$，则： $$ \begin{align} DE ⊥ AB\\ AC=&CD\\ \angle DCE=&\angle ACE\\ CE=&CE\\ =>\triangle ACE≌&\triangle DCE\\ =>\angle CAE=&\angle CDE\\ =>\angle CAE=&90° \end{align} $$ 即$\angle A=90°$得证。