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几何定值问题是平面几何中的一个难点,难之所在,一是题设中某些几何量的任意可变性,给人一种不确定感;二是题断中定值究竞为何,是一个谜。通常的证法是,先由特殊情形探出定值,再证一般情形结论成立,若由题设中某些几何量的可变性,联想到代数中研究变量与常量的函数问题,则可考虑应用函数观点来处理几何定值问题,具体思路是:通过引入适当的几何变量x,利用几何定理、计算公式、三角法等,建立起所要研究的几何量y与变量x间的函数y=F(x),把问题转为研究、考察函数y=F(x)的值,是否与x无关,恒等于某一常数,下面略举数题说明。
Geometry setting problem is a difficult point in plane geometry, and it is difficult to locate it. First, any variability of some geometric quantities in the problem design gives a sense of uncertainty; A mystery. The usual proof method is to first determine the fixed value by special circumstances and then to prove that the general situation is true. If the variability of certain geometric quantities in the problem design is associated with the function of the research variables and constants in algebra, it can be considered. The function point of view is used to deal with the geometrical fixed value problem. The specific idea is: establish a function y=F between the geometric quantity y and the variable x to be studied by introducing an appropriate geometrical variable x, using a geometrical theorem, a calculation formula, a trigonometric method, and the like. (x) Turn the question into a study to see if the value of the function y=F(x) is irrelevant to x and constant equal to a certain constant.