如图所示,△ABC为等边三角形,BD为AC上的中线,E是BC延长线上一点,且CE=CD,不添加线，请你写出尽可能多的结论，图中有等腰三角形吗？如果有，试证明其中一个等腰三角形（除△ABC外）
图与http://wenwen.soso.com/z/q196535814.htm?w=%C8%E7%CD%BC%CB%F9%CA%BE%2C%A1%F7ABC%CE%AA%B5%C8%B1%DF%C8%FD%BD%C7%D0%CE%2CBD%CE%AAAC%C9%CF%B5%C4%D6%D0%CF%DF%2CE%CA%C7BC%D1%D3%B3%A4%CF%DF%C9%CF%D2%BB%B5%E3%2C%C7%D2CE%3DCD%2C%B2%BB%CC%ED%BC%D3%CF%DF%A3%AC%C7%EB%C4%E3%D0%B4%B3%F6%BE%A1%BF%C9%C4%DC%B6%E0%B5%C4%BD%E1%C2%DB%A3%AC%CD%BC%D6%D0%D3%D0%B5%C8%D1%FC%C8%FD%BD%C7%D0%CE%C2%F0%A3%BF%C8%E7%B9%FB%D3%D0&spi=1&sr=3&w8=%E5%A6%82%E5%9B%BE%E6%89%80%E7%A4%BA%2C%E2%96%B3ABC%E4%B8%BA%E7%AD%89%E8%BE%B9%E4%B8%89%E8%A7%92%E5%BD%A2%2CBD%E4%B8%BAAC%E4%B8%8A%E7%9A%84%E4%B8%AD%E7%BA%BF%2CE%E6%98%AFBC%E5%BB%B6%E9%95%BF%E7%BA%BF%E4%B8%8A%E4%B8%80%E7%82%B9%2C%E4%B8%94CE%3DCD%2C%E4%B8%8D%E6%B7%BB%E5%8A%A0%E7%BA%BF%EF%BC%8C%E8%AF%B7%E4%BD%A0%E5%86%99%E5%87%BA%E5%B0%BD%E5%8F%AF%E8%83%BD%E5%A4%9A%E7%9A%84%E7%BB%93%E8%AE%BA%EF%BC%8C%E5%9B%BE%E4%B8%AD%E6%9C%89%E7%AD%89%E8%85%B0%E4%B8%89%E8%A7%92%E5%BD%A2%E5%90%97%EF%BC%9F%E5%A6%82%E6%9E%9C%E6%9C%89&qf=20&rn=51&qs=4&ch=w.search.3中的一样（把网址复制下来）