N Point Study Composition Problem Geometry Combinations

This paper is going to study point composition of mathematical competitions based on combinatorial geometry. In particular, make a special discussion on the problem of mid-point.At the beginning of the paper we make a brief introduction to some related fundamental knowledge of combinatorial geometry and enumeration methods,then explore the distance between points in the plane and the Angle of the connecting line on the basis of something related to mathematical competition and discuss the structure of convex k-gons and triangle, furthermore, make a special discussion on the problem of mid-point, finally we make some summations and remarks.According to analyzing the references, we discusses in competition mathematics the applications of point composition in combinatorial geometry and the designs of such kinds of questions aiming at grasping the laws of setting questions in mathematical competitions.The innovations of the paper are to show some propositions and corollaries and giving some simple solutions and generalizations to some questions in mathematical competitions independently.