Problem of Apollonius

The Problem of Apollonius (Apollonian Problem) is a very famous problem of Greek mathematics. For three geometric objects (circles, straight lines, points) all circles shall be constructed, which are tangent to the given circles or lines and pass through the given points.

There are altogether ten variants of the problem, which are denoted by the symbols C (circle), L (line), and P (point):

Problem variantGiven
CCC Problemthree circles
CCL Problemtwo circles, one line
CLL Problemone circle, two lines
CCP Problemtwo circles, one point
CLP Problemone circle, one line, one point
LLL Problemthree lines
CPP Problemone circle, two points
LLP Problemtwo lines, one point
LPP Problemone line, two points
PPP Problemthree points