过2点与直线相切的圆的分析与图解

Analytical Proof and Illustrations for Circles Passing Through Two Given Points and Tangent to A Given Line

当已知3圆中的2圆退化成点且另1圆退化成直线时,得到阿波罗尼奥斯问题(Apollonius'Problem)的一种特殊情况。在这个前提下,根据已知2点连线与已知直线的位置关系,过已知2点作与已知直线相切的圆,共有3种情况。当已知2点连线与已知直线斜交时,过已知2点可作2圆与已知直线相切,根据近代欧氏几何中的反演理论,提出了一种作出这2圆的图解方法,并对作图依据进行了分析与论证。

A special condition of Apollonius′Problem is that two of three circles are degenerated into points and another circle is degenerated into line. According to the position relation between the line passing through two given points and the given line, There are three kinds of results when drawing circles passing through two given points and tangent to a given straight line.When the line passing through two given points is oblique to the given line, there are two such circles passing through two given points and tangent to a given line, a graphic method drawing such two circles is provided based on inversive theory of Euclidean geometry.