Abstract: This paper gives the circle of inversion’s equation for the symmetric point pairsby two points,use it to study the circle of inversion’s some properties,and obtain the unique existence condition of the symmetric point pairs of circle of inversion.On the geometric transformation this paper has solved an inverse problem about the circle of transformation and inversion,which has given the symmetric points pair and radius of base inversion condition.

Key words: symmetric points pair, circie of inversoin, transformation of inversoin, ratio, equation, distribution, property, uniqueness