深度挖掘课本例题,往往可以得到优美的性质或结论,对高考和竞赛的解题有一定的参考价值.本文以人教A版数学选修4—4第4页例1为例,从它的推广到应用进行说明.例题已知△ABC的三边a,b,c满足b~2+c~2=5a~2,BE,CF分别为边AC,AB上的中线,建立适当的平面直角坐标系探究BE与CF的位置关系.课本是通过建立平面直角坐标系,得到BE⊥ Depth digging textbook examples, often can get the beautiful nature or conclusion, the entrance examination and competition problems have a certain reference value.This paper, people teach A version of mathematics elective 4-4 Page 4 Example 1 as an example, from its promotion To the application of the example.Examples of knowledge △ ABC of the three sides a, b, c satisfy b ~ 2 + c ~ 2 = 5a ~ 2, BE, CF, respectively, AC, AB on the median line, the establishment of the appropriate Cartesian coordinates Department to explore the relationship between BE and CF.Textbook is through the establishment of rectangular Cartesian coordinate system, BE ⊥