Problem: The Problem of Apollonius
To construct a circle tangent to three given objects -- points, lines, or
circles.
A point if "tangent to" a circle if it is on the circle.
The problem is posed for "general position" -- that is, objects
arranged so that constructions are possible.
Discussion/Solutions? :
There are 10 classes of constructions for this problem.
1. 3 Points (PPP)
2. 2 Points and 1 Line (PPL)
3. 2 Points and 1 Circle (PPC)
4. 1 Point, 1 Line, and 1 Circle (PLC)
5. 1 Point and 2 Lines (PLL)
6. 1 Point and 2 Circles (PCC)
7. 1 Line and 2 Circles (LCC)
8. 2 Lines and 1 Circle (LLC)
9. 3 Lines (LLL)
10. 3 circles (CCC)
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