The Exploration Of Geometric Problems In Mathematics Competitions

In recent years,mathematical competition is developing vigorously,and more and more high school students are participating in various mathematical competitions.In various domestic and foreign mathematical competitions,the content is basically stable in four aspects: algebra,geometry,number theory and combination.On the one hand,geometry has a rigorous logical structure.On the other hand,geometry has intuitive and clear images.The solutions to geometric problem are rich and ingenious,so the geometric problem is popular among the students.By observing domestic and foreign mathematical competition topics in recent years,this article mainly studies the content of the circle power and the radical axis,the harmonic point series as well as the inversion transformation and the homothetic transformation in geometric transformation in the same plane.The first section of the first chapter introduces the development and current status of mathematical competition.It has been more than 60 years since the first International Mathematical Olympiads,and various mathematical competitions have attracted people's attention as an important way to discover and train gifted students in mathematics.Although today's mathematical competition is facing some negative voices,it still has vigorous vitality.The second section introduces the status and significance of competition geometry in mathematical competition.Based on the analysis of some examples about the circle power and the radical axis,Chapter 2 gives six new propositions about the circle power and the radical axis.Chapter 3 gives five new propositions about the harmonic point series based on the analysis of some examples about the harmonic point series.Chapter 4 studies the inversion transformation and the homothetic transformation in geometric transformation,focuses more on the study of the inversion transformation,and gives three new propositions about geometric transformation.This article uses the method of literature analysis.The methods of geometry and the methods of algebra,number theory and combination supplement each other.Besides,the problem of geometry has an important position in the mathematical competition.Therefore,the study of geometry is of great significance.