对于平面几何问题,借助于有关面积知识以使问题中几何量的关系变得明瞭,甚至使问题得到解决,是常用的证明方法之一。让我们来看下面的例题. 例1 AC、CE是正六边形ABCDEF的两条对角线,点M、N分别内分AC、CE,使AM:AC=CN:CE=r,如果B、M.N三点共线,求r(第23届IMO竞赛题). 解由题设B、M、N三点共线,得等式 For plane geometry problems, it is one of the commonly used methods to prove that the relationship between the geometric quantities in the problem is clear and even the problem is solved. Let’s look at the following example. Example 1 AC and CE are the two diagonals of the regular hexagon ABCDEF. Points M and N are divided into AC and CE, respectively, so that AM:AC=CN:CE=r. If B, MN three points collinear, seeking r (the 23rd IMO competition title). Solution by the question set B, M, N three points collinear, get the equation