The problem of Apollonios is one of the most famous problems of the classical Greek geometry. For three simple geometric objects (points, lines or circles), all circles are to be found which pass through each of the given points and are tangent to the given lines and circles.
There are ten types of the problem which may be labeled with the letters C (circle), L (line) und P (point):
| Type | Given elements |
| CCC problem | three circles |
| CCL problem | two circles and a line |
| CLL problem | one circle and two lines |
| CCP problem | two circles and a point |
| CLP problem | one circle, one line, and a point |
| LLL problem | three lines |
| CPP problem | one circle and two points |
| LLP problem | two lines and a point |
| LPP problem | one line and two points |
| PPP problem | three points |
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| Mathematics Applets |
URL: www.walter-fendt.de/m14e/apolloniosproblem_e.htm
© Walter Fendt, December 27, 2008
Last modification: February 18, 2010