文[1]将《数学教学》的第811号问题进行了拓广,得到了关于三角形内心、外心连线的一个性质.性质在△ABC中,AB>BC>CA,点E、F分别在AB、BC上,满足AE=CF=AC,点O、I分别为△ABC的外心、内心,则OI⊥EF.原文是用解析法来证明的,其计算量偏大.实际上涉及到垂直的证明,我们也可联想到向量的数量积这一基本知识,现给出如下较简证明.首先 In [1], “Mathematics Teaching” No. 811 is extended to get a property about the inner and outer connection of the triangle. The nature is △ ABC, AB> BC> CA, E and F respectively In AB, BC, to meet the AE = CF = AC, the point O, I were △ ABC of the outer, inner, then OI⊥EF. The original is analytic method to prove that its calculation is too large. Actually involved To the vertical proof, we can also think of the basic knowledge of the product of the number of products, and now give the following simplified proof. First