Common tangent circles of two given circles are interesting problems for senior high school's students even for high school's teachers. Now we discuss how to find the cycle for points of tangency. For example, one circle is common tangent to two given circles at two points and two circles are common tangent to two given circles at least three points, and three circles are common tangent to two given circles at least four points. But four circles are common tangent to two given circles at least still four points. So the problem is very charming and we want to know the same problem in three dimensions which had the same property? Fortunately, we can draw down the graphs of the problems in two dimensions or three dimensions by Cabri’s software, and then we can know the interesting property from those graphs.
The author hopes that everyone can learn to draw down the graph of this problem "Four Circles Tangent to Two Circles at Four Points" by Cabri 3D and Cabri II Plus after reading this paper.

[1]Dörrie, H. "Monge's Problem." §31 in 100 Great Problems of Elementary Mathematics: Their History and Solutions.
[2]Jen-Chung Chuan：
http://poncelet.math.nthu.edu.tw/
[3]Math World :
http://mathworld.wolfram.com
[4]高雄市第40屆中小學科學展覽得獎作品專集：http://www.khjh.kh.edu.tw/science40/c1.htm
[5]數學名詞的中英對照：http://www.dcsh.tp.edu.tw/mathj/mathnews/news01/mn0101.htm
[6]維基百科：
http://zh.wikipedia.org/zh-tw/