阿波罗尼斯圆定理、性质及应用探究

Apollonius Circle Theorem, Properties and Applications

圆在高中数学题型中广泛且内容应用灵活,而阿波罗尼斯圆作为一种特殊的圆时常伴随着解三角形、平面向量、立体几何及解析几何等内容出现,将原有常规解复杂的问题进行简化。为避免思维固化、计算繁琐等问题,本文提供了构造阿波罗尼斯圆的两个条件及阿波罗尼斯圆相关性质,提供新型解题思路,使得解题高效化、便捷化、灵巧化。再从不同的应用层次出发,随着层次的递增,学生对性质掌握的要求也就越高,本文设置相关题目逐级加深对性质的理解,便于学生对应不同的层次进行掌握学习。

Circles are widely used in high school mathematics problem types and flexible content, while Apollonian circles, as a special circle, often appear with solving triangles, plane vectors, solid geometry and analytic geometry, simplifying the original conventional solution of complex problems. In order to avoid problems such as solidification of thinking and cumbersome calculation, this paper provides two conditions for constructing Apollonius circles and the related properties of Apollonius circles, and provides new problem-solving ideas, which makes problem solving efficient, convenient and dexterous. Starting from different application levels, with the increase of levels, the higher the requirements of students for mastering nature, this paper sets up related topics to deepen the understanding of nature step by step, so that students can master and learn according to different levels.