1992年第九届全国初中联合竞赛试题第二试的第2小题是:题目1如图1,在△ABC中,AB=AC,D是底边BC上一点,E是线段AD上一点,且∠BAC=∠BED=2∠CED,求证:BD=2CD.这是一道较难的平面几何题,究其原因在于所给的条件不是很容易联系在一起,组委会所提供的证明方法借助于△ABC的外接圆.在对这个题目的证法研究中,我们意外地发现BD=2CD等价的结论:BE=2AE. In 1992 the ninth national junior high school joint competition test second test question 2 is: the title 1 as shown in Figure 1, △ ABC, AB = AC, D is the bottom BC point, E is the point AD, And ∠ BAC = ∠ BED = 2 ∠ CED, verify: BD = 2CD. This is a more difficult plane geometry problem, the reason is that given the conditions are not easily linked together, the organizing committee provides proof by means of In the circumcircle of △ ABC, in the proof of concept of this subject, we unexpectedly found the conclusion that BD = 2CD equivalence: BE = 2AE.