三角形两边之和大于第三边这一基本性质,看似简单,但它蕴含了平面几何中距离问题的本质即两点之间线段最短,它在解决平面解析几何的最值问题时尤为重要.笔者以近几年的高考试题为例,从三个方面谈谈如何巧用三角形的上述性质探求一类解析几何中的最值问题.一、有关直线和圆的最值问题利用三角形的上述性质可以推导出直线和圆的如下三个结论.结论 1若A、B两点在直线l的两侧,则 It seems simple, but it contains the essence of distance problem in plane geometry. That is, the line segment between two points is the shortest, which is especially important in solving the most value problem of plane analytic geometry. In recent years, the author take the college entrance examination test as an example, from three aspects to talk about how to use the above triangular nature to explore the most value of a class of analytic geometry problems. First, the most value of the straight line and the circle The use of the above properties of the triangle Deduces the following three conclusions of the straight line and the circle: Conclusion 1 If A and B are on two sides of the straight line l, then