aam@oajrc.org

## 国际应用数学进展

Advances in International Applied Mathematics. 2023; 5: (4) ; 10.12208/j.aam.20231025 .

# The application and promotion of ptolemy's theorem and inequalitiesin maximum-minimum value problems托勒密定理及不等式在最值问题中的应用与推广

*通讯作者： 王洁,单位：扬州大学 江苏扬州；

Published: 2023/10/20 11:28:12

## Abstract

Ptolemy 's theorem and Ptolemy 's inequality are important theorems and corollaries in plane geometry. The use of Ptolemy 's theorem and Ptolemy 's inequality not only plays an important role in solving the problem of plane circle inscribed quadrilateral, but also gives a general solution to a certain kind of maximum-minimum value problems in algebra. This solution expands the problem-solving idea of geometricization of algebraic problems and provides a shortcut for fast problem-solving. In this paper, by analyzing the solution of Ptolemy 's theorem in the maximum value problems of one-variable double-root function, and giving examples to illustrate the solution of Ptolemy 's inequality in the maximum-minimum value problem of plane geometry, the general conclusions of some kinds of maximum value problems of one-variable double-root function in algebra and the maximum-minimum value problems of plane quadrilateral in plane geometry are summarized. On the maximum-minimum value problems such as algebra and plane geometry, a new fast solution method is created for the candidates of high school entrance examination or those who have the ability to participate in mathematics competitions.

Key words： Ptolemy 's theorem; Ptolemaic inequality; Plane and geometry; The Maximum-minimum value problem; Application and promotion

## 参考文献 References

 丁奕涵,张美玲,唐玉华.四点共圆之托勒密定理[J].中学生数学,2022(12):35－36.

 陈武.掌握托勒密定理简证一类几何题[J].中小学数学(初中版),2020(12):29-30.

 闫伟.一道填空压轴题的解法探究及拓展应用[J].数学通讯,2020(09):8-10.

 丁庆彬.对一道托勒密定理模型试题的探究[J].中学数学教学参考,2021(20):26-28.

 刘钢.合纵连横  整体把握——托勒密定理一席谈[J].高中数学教与学,2023(06):11-13.